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href="#Developing_"fractal_geometry"_and_the_Mandelbrot_set"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>Developing "fractal geometry" and the Mandelbrot set</span> </div> </a> <ul id="toc-Developing_"fractal_geometry"_and_the_Mandelbrot_set-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Fractals_and_the_"theory_of_roughness"" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Fractals_and_the_"theory_of_roughness""> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3</span> <span>Fractals and the "theory of roughness"</span> </div> </a> <ul id="toc-Fractals_and_the_"theory_of_roughness"-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Awards_and_honors" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Awards_and_honors"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Awards and honors</span> </div> </a> <ul id="toc-Awards_and_honors-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Death_and_legacy" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Death_and_legacy"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Death and legacy</span> </div> </a> <ul id="toc-Death_and_legacy-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Bibliography" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Bibliography"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Bibliography</span> </div> </a> <button aria-controls="toc-Bibliography-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Bibliography subsection</span> </button> <ul id="toc-Bibliography-sublist" class="vector-toc-list"> <li id="toc-In_English" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#In_English"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.1</span> <span>In English</span> </div> </a> <ul id="toc-In_English-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Notes" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Notes"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Notes</span> </div> </a> <ul id="toc-Notes-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Sources" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Sources"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>Sources</span> </div> </a> <ul id="toc-Sources-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">10</span> <span>External links</span> </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Toggle the table of contents</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Benoit Mandelbrot</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. Available in 66 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-66" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">66 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Beno%C3%AEt_Mandelbrot" title="Benoît Mandelbrot – Afrikaans" lang="af" hreflang="af" data-title="Benoît Mandelbrot" data-language-autonym="Afrikaans" data-language-local-name="Afrikaans" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-als mw-list-item"><a href="https://als.wikipedia.org/wiki/Beno%C3%AEt_Mandelbrot" title="Benoît Mandelbrot – Alemannic" lang="gsw" hreflang="gsw" data-title="Benoît Mandelbrot" data-language-autonym="Alemannisch" data-language-local-name="Alemannic" class="interlanguage-link-target"><span>Alemannisch</span></a></li><li class="interlanguage-link interwiki-am mw-list-item"><a href="https://am.wikipedia.org/wiki/%E1%88%9B%E1%8A%95%E1%8B%B4%E1%88%8D%E1%89%A5%E1%88%AE%E1%89%B5" title="ማንዴልብሮት – Amharic" lang="am" hreflang="am" data-title="ማንዴልብሮት" data-language-autonym="አማርኛ" data-language-local-name="Amharic" class="interlanguage-link-target"><span>አማርኛ</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%A8%D9%8A%D9%86%D9%88%D8%A7_%D9%85%D8%A7%D9%86%D8%AF%D9%84%D8%A8%D8%B1%D9%88%D8%AA" title="بينوا ماندلبروت – Arabic" lang="ar" hreflang="ar" data-title="بينوا ماندلبروت" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-an mw-list-item"><a href="https://an.wikipedia.org/wiki/Beno%C3%AEt_Mandelbrot" title="Benoît Mandelbrot – Aragonese" lang="an" hreflang="an" data-title="Benoît Mandelbrot" data-language-autonym="Aragonés" data-language-local-name="Aragonese" class="interlanguage-link-target"><span>Aragonés</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Beno%C3%AEt_Mandelbrot" title="Benoît Mandelbrot – Asturian" lang="ast" hreflang="ast" data-title="Benoît Mandelbrot" data-language-autonym="Asturianu" data-language-local-name="Asturian" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Benua_Mandelbrot" title="Benua Mandelbrot – Azerbaijani" lang="az" hreflang="az" data-title="Benua Mandelbrot" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbaijani" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-azb mw-list-item"><a href="https://azb.wikipedia.org/wiki/%D8%A8%D9%86%D9%88%D8%A2_%D9%85%D9%86%D8%AF%D9%84%D8%A8%D8%B1%D9%88" title="بنوآ مندلبرو – South Azerbaijani" lang="azb" hreflang="azb" data-title="بنوآ مندلبرو" data-language-autonym="تۆرکجه" data-language-local-name="South Azerbaijani" class="interlanguage-link-target"><span>تۆرکجه</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%AC%E0%A6%A8%E0%A7%8B%E0%A6%AF%E0%A6%BC%E0%A6%BE_%E0%A6%AE%E0%A6%81%E0%A6%A6%E0%A7%87%E0%A6%B2%E0%A6%AC%E0%A7%8D%E0%A6%B0%E0%A7%8B" title="বনোয়া মঁদেলব্রো – Bangla" lang="bn" hreflang="bn" data-title="বনোয়া মঁদেলব্রো" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%91%D0%B5%D0%BD%D0%BE%D0%B0_%D0%9C%D0%B0%D0%BD%D0%B4%D0%B5%D0%BB%D0%B1%D1%80%D0%BE%D1%82" title="Беноа Манделброт – Bulgarian" lang="bg" hreflang="bg" data-title="Беноа Манделброт" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Beno%C3%AEt_Mandelbrot" title="Benoît Mandelbrot – Bosnian" lang="bs" hreflang="bs" data-title="Benoît Mandelbrot" data-language-autonym="Bosanski" data-language-local-name="Bosnian" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Beno%C3%AEt_Mandelbrot" title="Benoît Mandelbrot – Catalan" lang="ca" hreflang="ca" data-title="Benoît Mandelbrot" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Beno%C3%AEt_Mandelbrot" title="Benoît Mandelbrot – Czech" lang="cs" hreflang="cs" data-title="Benoît Mandelbrot" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Beno%C3%AEt_Mandelbrot" title="Benoît Mandelbrot – Danish" lang="da" hreflang="da" data-title="Benoît Mandelbrot" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Beno%C3%AEt_Mandelbrot" title="Benoît Mandelbrot – German" lang="de" hreflang="de" data-title="Benoît Mandelbrot" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Beno%C3%AEt_Mandelbrot" title="Benoît Mandelbrot – Estonian" lang="et" hreflang="et" data-title="Benoît Mandelbrot" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%9C%CF%80%CE%B5%CE%BD%CE%BF%CF%85%CE%AC_%CE%9C%CE%AC%CE%BD%CF%84%CE%B5%CE%BB%CE%BC%CF%80%CF%81%CE%BF%CF%84" title="Μπενουά Μάντελμπροτ – Greek" lang="el" hreflang="el" data-title="Μπενουά Μάντελμπροτ" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Beno%C3%AEt_Mandelbrot" title="Benoît Mandelbrot – Spanish" lang="es" hreflang="es" data-title="Benoît Mandelbrot" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Beno%C3%AEt_Mandelbrot" title="Benoît Mandelbrot – Esperanto" lang="eo" hreflang="eo" data-title="Benoît Mandelbrot" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Beno%C3%AEt_Mandelbrot" title="Benoît Mandelbrot – Basque" lang="eu" hreflang="eu" data-title="Benoît Mandelbrot" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%A8%D9%86%D9%88%D8%A2_%D9%85%D9%86%D8%AF%D9%84%D8%A8%D8%B1%D8%A7%D8%AA" title="بنوآ مندلبرات – Persian" lang="fa" hreflang="fa" data-title="بنوآ مندلبرات" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Beno%C3%AEt_Mandelbrot" title="Benoît Mandelbrot – French" lang="fr" hreflang="fr" data-title="Benoît Mandelbrot" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Beno%C3%AEt_Mandelbrot" title="Benoît Mandelbrot – Irish" lang="ga" hreflang="ga" data-title="Benoît Mandelbrot" data-language-autonym="Gaeilge" data-language-local-name="Irish" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Beno%C3%AEt_Mandelbrot" title="Benoît Mandelbrot – Galician" lang="gl" hreflang="gl" data-title="Benoît Mandelbrot" data-language-autonym="Galego" data-language-local-name="Galician" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EB%B8%8C%EB%88%84%EC%95%84_%EB%A7%9D%EB%8D%B8%EB%B8%8C%EB%A1%9C" title="브누아 망델브로 – Korean" lang="ko" hreflang="ko" data-title="브누아 망델브로" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Beno%C3%AEt_Mandelbrot" title="Benoît Mandelbrot – Croatian" lang="hr" hreflang="hr" data-title="Benoît Mandelbrot" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Benoit_Mandelbrot" title="Benoit Mandelbrot – Ido" lang="io" hreflang="io" data-title="Benoit Mandelbrot" data-language-autonym="Ido" data-language-local-name="Ido" class="interlanguage-link-target"><span>Ido</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Beno%C3%AEt_Mandelbrot" title="Benoît Mandelbrot – Indonesian" lang="id" hreflang="id" data-title="Benoît Mandelbrot" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Beno%C3%AEt_Mandelbrot" title="Benoît Mandelbrot – Icelandic" lang="is" hreflang="is" data-title="Benoît Mandelbrot" data-language-autonym="Íslenska" data-language-local-name="Icelandic" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Beno%C3%AEt_Mandelbrot" title="Benoît Mandelbrot – Italian" lang="it" hreflang="it" data-title="Benoît Mandelbrot" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%91%D7%A0%D7%95%D7%90%D7%94_%D7%9E%D7%A0%D7%93%D7%9C%D7%91%D7%A8%D7%95%D7%98" title="בנואה מנדלברוט – Hebrew" lang="he" hreflang="he" data-title="בנואה מנדלברוט" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%9C%D0%B0%D0%BD%D0%B4%D0%B5%D0%BB%D1%8C%D0%B1%D1%80%D0%BE%D1%82_%D0%91%D0%B5%D0%BD%D1%83%D0%B0" title="Мандельброт Бенуа – Kazakh" lang="kk" hreflang="kk" data-title="Мандельброт Бенуа" data-language-autonym="Қазақша" data-language-local-name="Kazakh" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/Beno%C3%AEt_Mandelbrot" title="Benoît Mandelbrot – Haitian Creole" lang="ht" hreflang="ht" data-title="Benoît Mandelbrot" data-language-autonym="Kreyòl ayisyen" data-language-local-name="Haitian Creole" class="interlanguage-link-target"><span>Kreyòl ayisyen</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Benedictus_Mandelbrot" title="Benedictus Mandelbrot – Latin" lang="la" hreflang="la" data-title="Benedictus Mandelbrot" data-language-autonym="Latina" data-language-local-name="Latin" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Benu%C4%81_Mandelbrots" title="Benuā Mandelbrots – Latvian" lang="lv" hreflang="lv" data-title="Benuā Mandelbrots" data-language-autonym="Latviešu" data-language-local-name="Latvian" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-lb mw-list-item"><a href="https://lb.wikipedia.org/wiki/Beno%C3%AEt_Mandelbrot" title="Benoît Mandelbrot – Luxembourgish" lang="lb" hreflang="lb" data-title="Benoît Mandelbrot" data-language-autonym="Lëtzebuergesch" data-language-local-name="Luxembourgish" class="interlanguage-link-target"><span>Lëtzebuergesch</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Benoit_Mandelbrot" title="Benoit Mandelbrot – Lithuanian" lang="lt" hreflang="lt" data-title="Benoit Mandelbrot" data-language-autonym="Lietuvių" data-language-local-name="Lithuanian" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Beno%C3%AEt_Mandelbrot" title="Benoît Mandelbrot – Hungarian" lang="hu" hreflang="hu" data-title="Benoît Mandelbrot" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-mg mw-list-item"><a href="https://mg.wikipedia.org/wiki/Beno%C3%AEt_Mandelbrot" title="Benoît Mandelbrot – Malagasy" lang="mg" hreflang="mg" data-title="Benoît Mandelbrot" data-language-autonym="Malagasy" data-language-local-name="Malagasy" class="interlanguage-link-target"><span>Malagasy</span></a></li><li class="interlanguage-link interwiki-arz mw-list-item"><a href="https://arz.wikipedia.org/wiki/%D8%A8%D9%8A%D9%86%D9%88%D8%A7_%D9%85%D8%A7%D9%86%D8%AF%D9%84%D8%A8%D8%B1%D9%88%D8%AA" title="بينوا ماندلبروت – Egyptian Arabic" lang="arz" hreflang="arz" data-title="بينوا ماندلبروت" data-language-autonym="مصرى" data-language-local-name="Egyptian Arabic" class="interlanguage-link-target"><span>مصرى</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Beno%C3%AEt_Mandelbrot" title="Benoît Mandelbrot – Dutch" lang="nl" hreflang="nl" data-title="Benoît Mandelbrot" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%83%96%E3%83%8E%E3%83%AF%E3%83%BB%E3%83%9E%E3%83%B3%E3%83%87%E3%83%AB%E3%83%96%E3%83%AD" title="ブノワ・マンデルブロ – Japanese" lang="ja" hreflang="ja" data-title="ブノワ・マンデルブロ" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Beno%C3%AEt_Mandelbrot" title="Benoît Mandelbrot – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Benoît Mandelbrot" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Beno%C3%AEt_Mandelbrot" title="Benoît Mandelbrot – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Benoît Mandelbrot" data-language-autonym="Norsk nynorsk" data-language-local-name="Norwegian Nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-ps mw-list-item"><a href="https://ps.wikipedia.org/wiki/%D8%A8%D9%86%D9%88%D8%A2_%D9%85%D9%86%DA%89%D9%84%D8%A8%D8%B1%D8%A7%D9%BC" title="بنوآ منډلبراټ – Pashto" lang="ps" hreflang="ps" data-title="بنوآ منډلبراټ" data-language-autonym="پښتو" data-language-local-name="Pashto" class="interlanguage-link-target"><span>پښتو</span></a></li><li class="interlanguage-link interwiki-nds mw-list-item"><a href="https://nds.wikipedia.org/wiki/Beno%C3%AEt_Mandelbrot" title="Benoît Mandelbrot – Low German" lang="nds" hreflang="nds" data-title="Benoît Mandelbrot" data-language-autonym="Plattdüütsch" data-language-local-name="Low German" class="interlanguage-link-target"><span>Plattdüütsch</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Beno%C3%AEt_Mandelbrot" title="Benoît Mandelbrot – Polish" lang="pl" hreflang="pl" data-title="Benoît Mandelbrot" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Beno%C3%AEt_Mandelbrot" title="Benoît Mandelbrot – Portuguese" lang="pt" hreflang="pt" data-title="Benoît Mandelbrot" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Beno%C3%AEt_Mandelbrot" title="Benoît Mandelbrot – Romanian" lang="ro" hreflang="ro" data-title="Benoît Mandelbrot" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9C%D0%B0%D0%BD%D0%B4%D0%B5%D0%BB%D1%8C%D0%B1%D1%80%D0%BE%D1%82,_%D0%91%D0%B5%D0%BD%D1%83%D0%B0" title="Мандельброт, Бенуа – Russian" lang="ru" hreflang="ru" data-title="Мандельброт, Бенуа" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Benoit_Mandelbrot" title="Benoit Mandelbrot – Albanian" lang="sq" hreflang="sq" data-title="Benoit Mandelbrot" data-language-autonym="Shqip" data-language-local-name="Albanian" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-scn mw-list-item"><a href="https://scn.wikipedia.org/wiki/Beno%C3%AEt_Mandelbrot" title="Benoît Mandelbrot – Sicilian" lang="scn" hreflang="scn" data-title="Benoît Mandelbrot" data-language-autonym="Sicilianu" data-language-local-name="Sicilian" class="interlanguage-link-target"><span>Sicilianu</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Beno%C3%AEt_Mandelbrot" title="Benoît Mandelbrot – Simple English" lang="en-simple" hreflang="en-simple" data-title="Benoît Mandelbrot" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Beno%C3%AEt_Mandelbrot" title="Benoît Mandelbrot – Slovak" lang="sk" hreflang="sk" data-title="Benoît Mandelbrot" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Beno%C3%AEt_Mandelbrot" title="Benoît Mandelbrot – Slovenian" lang="sl" hreflang="sl" data-title="Benoît Mandelbrot" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%91%D0%B5%D0%BD%D0%BE%D0%B0_%D0%9C%D0%B0%D0%BD%D0%B4%D0%B5%D0%BB%D0%B1%D1%80%D0%BE%D1%82" title="Беноа Манделброт – Serbian" lang="sr" hreflang="sr" data-title="Беноа Манделброт" data-language-autonym="Српски / srpski" data-language-local-name="Serbian" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Beno%C3%AEt_Mandelbrot" title="Benoît Mandelbrot – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Benoît Mandelbrot" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Serbo-Croatian" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Beno%C3%AEt_Mandelbrot" title="Benoît Mandelbrot – Finnish" lang="fi" hreflang="fi" data-title="Benoît Mandelbrot" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Beno%C3%AEt_Mandelbrot" title="Benoît Mandelbrot – Swedish" lang="sv" hreflang="sv" data-title="Benoît Mandelbrot" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B9%80%E0%B8%9A%E0%B8%AD%E0%B8%99%E0%B8%B1%E0%B8%A7_%E0%B8%A1%E0%B9%87%E0%B8%AD%E0%B8%87%E0%B9%81%E0%B8%94%E0%B8%A5%E0%B9%82%E0%B8%9A%E0%B8%A3%E0%B8%95" title="เบอนัว ม็องแดลโบรต – Thai" lang="th" hreflang="th" data-title="เบอนัว ม็องแดลโบรต" data-language-autonym="ไทย" data-language-local-name="Thai" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Benoit_Mandelbrot" title="Benoit Mandelbrot – Turkish" lang="tr" hreflang="tr" data-title="Benoit Mandelbrot" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%91%D0%B5%D0%BD%D1%83%D0%B0_%D0%9C%D0%B0%D0%BD%D0%B4%D0%B5%D0%BB%D1%8C%D0%B1%D1%80%D0%BE%D1%82" title="Бенуа Мандельброт – Ukrainian" lang="uk" hreflang="uk" data-title="Бенуа Мандельброт" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Beno%C3%AEt_Mandelbrot" title="Benoît Mandelbrot – Vietnamese" lang="vi" hreflang="vi" data-title="Benoît Mandelbrot" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnamese" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E6%9C%AC%E5%8D%8E%C2%B7%E6%9B%BC%E5%BE%B7%E5%8D%9A" title="本华·曼德博 – Wu" lang="wuu" hreflang="wuu" data-title="本华·曼德博" data-language-autonym="吴语" data-language-local-name="Wu" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E6%9C%AC%E8%8F%AF%C2%B7%E6%9B%BC%E5%BE%B7%E5%8D%9A" title="本華·曼德博 – Cantonese" lang="yue" hreflang="yue" data-title="本華·曼德博" data-language-autonym="粵語" data-language-local-name="Cantonese" class="interlanguage-link-target"><span>粵語</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E6%9C%AC%E8%8F%AF%C2%B7%E6%9B%BC%E5%BE%B7%E5%8D%9A" title="本華·曼德博 – Chinese" lang="zh" hreflang="zh" data-title="本華·曼德博" data-language-autonym="中文" data-language-local-name="Chinese" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q101740#sitelinks-wikipedia" title="Edit interlanguage links" class="wbc-editpage">Edit links</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Namespaces"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Benoit_Mandelbrot" title="View the content page [c]" accesskey="c"><span>Article</span></a></li><li id="ca-talk" class="vector-tab-noicon mw-list-item"><a href="/wiki/Talk:Benoit_Mandelbrot" 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</div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">From Wikipedia, the free encyclopedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">French-American mathematician (1924–2010)</div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Mandelbrot_set" title="Mandelbrot set">Mandelbrot set</a></div> <p class="mw-empty-elt"> </p> <style data-mw-deduplicate="TemplateStyles:r1257001546">.mw-parser-output .infobox-subbox{padding:0;border:none;margin:-3px;width:auto;min-width:100%;font-size:100%;clear:none;float:none;background-color:transparent}.mw-parser-output .infobox-3cols-child{margin:auto}.mw-parser-output .infobox .navbar{font-size:100%}@media screen{html.skin-theme-clientpref-night .mw-parser-output .infobox-full-data:not(.notheme)>div:not(.notheme)[style]{background:#1f1f23!important;color:#f8f9fa}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .infobox-full-data:not(.notheme) div:not(.notheme){background:#1f1f23!important;color:#f8f9fa}}@media(min-width:640px){body.skin--responsive .mw-parser-output .infobox-table{display:table!important}body.skin--responsive .mw-parser-output .infobox-table>caption{display:table-caption!important}body.skin--responsive .mw-parser-output .infobox-table>tbody{display:table-row-group}body.skin--responsive .mw-parser-output .infobox-table tr{display:table-row!important}body.skin--responsive .mw-parser-output .infobox-table th,body.skin--responsive .mw-parser-output .infobox-table td{padding-left:inherit;padding-right:inherit}}</style><table class="infobox biography vcard"><tbody><tr><th colspan="2" class="infobox-above" style="font-size:125%;"><div class="fn">Benoit Mandelbrot</div></th></tr><tr><td colspan="2" class="infobox-image"><span class="mw-default-size" typeof="mw:File/Frameless"><a href="/wiki/File:Benoit_Mandelbrot,_TED_2010_(3x4_cropped).jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/31/Benoit_Mandelbrot%2C_TED_2010_%283x4_cropped%29.jpg/220px-Benoit_Mandelbrot%2C_TED_2010_%283x4_cropped%29.jpg" decoding="async" width="220" height="293" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/31/Benoit_Mandelbrot%2C_TED_2010_%283x4_cropped%29.jpg/330px-Benoit_Mandelbrot%2C_TED_2010_%283x4_cropped%29.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/31/Benoit_Mandelbrot%2C_TED_2010_%283x4_cropped%29.jpg/440px-Benoit_Mandelbrot%2C_TED_2010_%283x4_cropped%29.jpg 2x" data-file-width="1537" data-file-height="2047" /></a></span><div class="infobox-caption">Mandelbrot at a <a href="/wiki/TED_(conference)" title="TED (conference)">TED conference</a> in 2010</div></td></tr><tr><th scope="row" class="infobox-label">Born</th><td class="infobox-data"><span style="display:none">(<span class="bday">1924-11-20</span>)</span>20 November 1924<br /><div style="display:inline" class="birthplace"><a href="/wiki/Warsaw" title="Warsaw">Warsaw</a>, <a href="/wiki/Second_Polish_Republic" title="Second Polish Republic">Poland</a></div></td></tr><tr><th scope="row" class="infobox-label">Died</th><td class="infobox-data">14 October 2010<span style="display:none">(2010-10-14)</span> (aged 85)<br /><div style="display:inline" class="deathplace"><a href="/wiki/Cambridge,_Massachusetts" title="Cambridge, Massachusetts">Cambridge, Massachusetts</a>, U.S.</div></td></tr><tr><th scope="row" class="infobox-label">Nationality</th><td class="infobox-data category"><style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output .hlist ol ul,.mw-parser-output .hlist ul dl,.mw-parser-output .hlist ul ol,.mw-parser-output .hlist ul ul{display:inline}.mw-parser-output .hlist .mw-empty-li{display:none}.mw-parser-output .hlist dt::after{content:": "}.mw-parser-output .hlist dd::after,.mw-parser-output .hlist li::after{content:" · ";font-weight:bold}.mw-parser-output .hlist dd:last-child::after,.mw-parser-output .hlist dt:last-child::after,.mw-parser-output .hlist li:last-child::after{content:none}.mw-parser-output .hlist dd dd:first-child::before,.mw-parser-output .hlist dd dt:first-child::before,.mw-parser-output .hlist dd li:first-child::before,.mw-parser-output .hlist dt dd:first-child::before,.mw-parser-output .hlist dt dt:first-child::before,.mw-parser-output .hlist dt li:first-child::before,.mw-parser-output .hlist li dd:first-child::before,.mw-parser-output .hlist li dt:first-child::before,.mw-parser-output .hlist li li:first-child::before{content:" (";font-weight:normal}.mw-parser-output .hlist dd dd:last-child::after,.mw-parser-output .hlist dd dt:last-child::after,.mw-parser-output .hlist dd li:last-child::after,.mw-parser-output .hlist dt dd:last-child::after,.mw-parser-output .hlist dt dt:last-child::after,.mw-parser-output .hlist dt li:last-child::after,.mw-parser-output .hlist li dd:last-child::after,.mw-parser-output .hlist li dt:last-child::after,.mw-parser-output .hlist li li:last-child::after{content:")";font-weight:normal}.mw-parser-output .hlist ol{counter-reset:listitem}.mw-parser-output .hlist ol>li{counter-increment:listitem}.mw-parser-output .hlist ol>li::before{content:" "counter(listitem)"\a0 "}.mw-parser-output .hlist dd ol>li:first-child::before,.mw-parser-output .hlist dt ol>li:first-child::before,.mw-parser-output .hlist li ol>li:first-child::before{content:" ("counter(listitem)"\a0 "}</style><div class="hlist"><ul><li>French</li><li>American</li><li>Polish</li></ul></div></td></tr><tr><th scope="row" class="infobox-label">Alma mater</th><td class="infobox-data"><a href="/wiki/%C3%89cole_Polytechnique" class="mw-redirect" title="École Polytechnique">École Polytechnique</a><br /><span class="nowrap"><a href="/wiki/California_Institute_of_Technology" title="California Institute of Technology">California Institute of Technology</a></span><br /><a href="/wiki/University_of_Paris" title="University of Paris">University of Paris</a></td></tr><tr><th scope="row" class="infobox-label">Known for</th><td class="infobox-data"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><div class="hlist nowraplinks"><ul style="line-height:1.25em"><li><a href="/wiki/Mandelbrot_set" title="Mandelbrot set">Mandelbrot set</a></li><li><a href="/wiki/Chaos_theory" title="Chaos theory">Chaos theory</a></li><li><a href="/wiki/Fractal" title="Fractal">Fractals</a></li><li><a href="/wiki/Zipf%E2%80%93Mandelbrot_law" title="Zipf–Mandelbrot law">Zipf–Mandelbrot law</a></li></ul></div></td></tr><tr><th scope="row" class="infobox-label">Spouse(s)</th><td class="infobox-data"><div style="display: inline-block; line-height: 1.2em; padding: .1em 0;">Aliette Kagan (1932–2023)<br /><span style="font-size:85%;">(m. 1955–2010; his death)</span></div></td></tr><tr><th scope="row" class="infobox-label">Awards</th><td class="infobox-data"><div style="display: inline-block; line-height: 1.2em; padding: .1em 0; line-height:1.15em;white-space:nowrap"><i><a href="/wiki/L%C3%A9gion_d%27honneur" class="mw-redirect" title="Légion d'honneur">Légion d'honneur</a></i><br /><span style="font-size:85%;">(<i>Chevalier</i> 1990 <b>·</b> <i>Officier</i> 2006)</span></div> <br /> 2003  <a href="/wiki/Japan_Prize" title="Japan Prize">Japan Prize</a><br />1993  <a href="/wiki/Wolf_Prize" title="Wolf Prize">Wolf Prize</a><br />1989  <a href="/wiki/Harvey_Prize" title="Harvey Prize">Harvey Prize</a><br />1986  <a href="/wiki/Franklin_Medal" title="Franklin Medal">Franklin Medal</a><br />1985  <a href="/wiki/Barnard_Medal_for_Meritorious_Service_to_Science" title="Barnard Medal for Meritorious Service to Science">Barnard Medal</a></td></tr><tr><td colspan="2" class="infobox-full-data"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1257001546"><b>Scientific career</b></td></tr><tr><th scope="row" class="infobox-label">Fields</th><td class="infobox-data category"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><div class="hlist"><ul><li><a href="/wiki/Mathematics" title="Mathematics">Mathematics</a></li><li><a href="/wiki/Aerodynamics" title="Aerodynamics">Aerodynamics</a></li></ul></div></td></tr><tr><th scope="row" class="infobox-label">Institutions</th><td class="infobox-data"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><div class="hlist"><ul><li><a href="/wiki/Yale_University" title="Yale University">Yale University</a></li><li><a href="/wiki/IBM" title="IBM">IBM</a></li></ul></div> <div style="display: inline-block; line-height: 1.2em; padding: .1em 0;"><a href="/wiki/Pacific_Northwest_National_Laboratory" title="Pacific Northwest National Laboratory">Pacific Northwest National Laboratory</a></div></td></tr><tr><th scope="row" class="infobox-label"><a href="/wiki/Doctoral_advisor" title="Doctoral advisor">Doctoral advisor</a></th><td class="infobox-data"><a href="/wiki/Paul_L%C3%A9vy_(mathematician)" title="Paul Lévy (mathematician)">Paul Lévy</a></td></tr><tr><th scope="row" class="infobox-label">Doctoral students</th><td class="infobox-data"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><div class="hlist nowraplinks"><ul style="line-height:1.25em"><li><a href="/wiki/Laurent-Emmanuel_Calvet" title="Laurent-Emmanuel Calvet">L. E. Calvet</a></li><li><a href="/wiki/Eugene_Fama" title="Eugene Fama">Eugene Fama</a></li><li><a href="/wiki/Ken_Musgrave" title="Ken Musgrave">Ken Musgrave</a></li><li><a href="/wiki/Murad_Taqqu" title="Murad Taqqu">Murad Taqqu</a></li></ul></div></td></tr><tr style="display:none"><td colspan="2"> </td></tr></tbody></table> <p><b>Benoit B. Mandelbrot</b><sup id="cite_ref-Mandelbrot's_name_3-0" class="reference"><a href="#cite_note-Mandelbrot's_name-3"><span class="cite-bracket">[</span>a<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>b<span class="cite-bracket">]</span></a></sup> (20 November 1924 – 14 October 2010) was a Polish-born French-American <a href="/wiki/Mathematician" title="Mathematician">mathematician</a> and <a href="/wiki/Polymath" title="Polymath">polymath</a> with broad interests in the practical sciences, especially regarding what he labeled as "the art of <a href="#Fractals_and_the_"theory_of_roughness"">roughness</a>" of physical phenomena and "the uncontrolled element in life".<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> He referred to himself as a "fractalist"<sup id="cite_ref-maverick_11-0" class="reference"><a href="#cite_note-maverick-11"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> and is recognized for his contribution to the field of <a href="/wiki/Fractal_geometry" class="mw-redirect" title="Fractal geometry">fractal geometry</a>, which included coining the word "fractal", as well as developing a theory of "roughness and <a href="/wiki/Self-similarity" title="Self-similarity">self-similarity</a>" in nature.<sup id="cite_ref-nature_12-0" class="reference"><a href="#cite_note-nature-12"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> </p><p>In 1936, at the age of 11, Mandelbrot and his family emigrated from <a href="/wiki/Warsaw" title="Warsaw">Warsaw</a>, Poland, to France. After <a href="/wiki/World_War_II" title="World War II">World War II</a> ended, Mandelbrot studied mathematics, graduating from universities in Paris and in the United States and receiving a master's degree in <a href="/wiki/Aeronautics" title="Aeronautics">aeronautics</a> from the <a href="/wiki/California_Institute_of_Technology" title="California Institute of Technology">California Institute of Technology</a>. He spent most of his career in both the United States and France, having <a href="/wiki/Multiple_citizenship" title="Multiple citizenship">dual</a> <a href="/wiki/French_nationality_law" title="French nationality law">French</a> and <a href="/wiki/United_States_nationality_law#Dual_citizenship" title="United States nationality law">American</a> citizenship. In 1958, he began a 35-year career at <a href="/wiki/IBM" title="IBM">IBM</a>, where he became an <a href="/wiki/IBM_Fellow" title="IBM Fellow">IBM Fellow</a>, and periodically took leaves of absence to teach at <a href="/wiki/Harvard_University" title="Harvard University">Harvard University</a>. At Harvard, following the publication of his study of U.S. commodity markets in relation to cotton futures, he taught economics and applied sciences. </p><p>Because of his access to IBM's computers, Mandelbrot was one of the first to use computer graphics to create and display fractal geometric images, leading to his discovery of the <a href="/wiki/Mandelbrot_set" title="Mandelbrot set">Mandelbrot set</a> in 1980. He showed how visual complexity can be created from simple rules. He said that things typically considered to be "rough", a "mess", or "chaotic", such as clouds or shorelines, actually had a "degree of order".<sup id="cite_ref-Wolfram_13-0" class="reference"><a href="#cite_note-Wolfram-13"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> His math- and geometry-centered research included contributions to such fields as <a href="/wiki/Statistical_physics" class="mw-redirect" title="Statistical physics">statistical physics</a>, <a href="/wiki/Meteorology" title="Meteorology">meteorology</a>, <a href="/wiki/Hydrology" title="Hydrology">hydrology</a>, <a href="/wiki/Geomorphology" title="Geomorphology">geomorphology</a>, <a href="/wiki/Anatomy" title="Anatomy">anatomy</a>, <a href="/wiki/Taxonomy_(biology)" title="Taxonomy (biology)">taxonomy</a>, <a href="/wiki/Neurology" title="Neurology">neurology</a>, <a href="/wiki/Linguistics" title="Linguistics">linguistics</a>, <a href="/wiki/Information_technology" title="Information technology">information technology</a>, <a href="/wiki/Computer_graphics" title="Computer graphics">computer graphics</a>, <a href="/wiki/Economics" title="Economics">economics</a>, <a href="/wiki/Geology" title="Geology">geology</a>, <a href="/wiki/Medicine" title="Medicine">medicine</a>, <a href="/wiki/Physical_cosmology" title="Physical cosmology">physical cosmology</a>, <a href="/wiki/Engineering" title="Engineering">engineering</a>, <a href="/wiki/Chaos_theory" title="Chaos theory">chaos theory</a>, <a href="/wiki/Econophysics" title="Econophysics">econophysics</a>, <a href="/wiki/Metallurgy" title="Metallurgy">metallurgy</a>, and the <a href="/wiki/Social_science" title="Social science">social sciences</a>.<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> </p><p>Toward the end of his career, he was <a href="/wiki/Sterling_Professor" title="Sterling Professor">Sterling Professor</a> of Mathematical Sciences at <a href="/wiki/Yale_University" title="Yale University">Yale University</a>, where he was the oldest professor in Yale's history to receive tenure.<sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> Mandelbrot also held positions at the <a href="/wiki/Pacific_Northwest_National_Laboratory" title="Pacific Northwest National Laboratory">Pacific Northwest National Laboratory</a>, <a href="/wiki/Universit%C3%A9_Lille_Nord_de_France" class="mw-redirect" title="Université Lille Nord de France">Université Lille Nord de France</a>, <a href="/wiki/Institute_for_Advanced_Study" title="Institute for Advanced Study">Institute for Advanced Study</a> and <a href="/wiki/Centre_National_de_la_Recherche_Scientifique" class="mw-redirect" title="Centre National de la Recherche Scientifique">Centre National de la Recherche Scientifique</a>. During his career, he received over 15 honorary doctorates and served on many science journals, along with winning numerous awards. His autobiography, <i>The Fractalist: Memoir of a Scientific Maverick</i>, was published posthumously in 2012. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Early_years">Early years</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Benoit_Mandelbrot&action=edit&section=1" title="Edit section: Early years"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1257001546"><table class="infobox" style="width: 210px; clear: right; float:right;margin:0 0 1.5em 1.5em"><tbody><tr><th colspan="2" class="infobox-above" style="font-size:115%">External videos</th></tr><tr><td colspan="2" class="infobox-image"><span typeof="mw:File"><a href="/wiki/File:Mandelbrot_p1130861.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/7b/Mandelbrot_p1130861.jpg/210px-Mandelbrot_p1130861.jpg" decoding="async" width="210" height="158" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/7b/Mandelbrot_p1130861.jpg/315px-Mandelbrot_p1130861.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/7b/Mandelbrot_p1130861.jpg/420px-Mandelbrot_p1130861.jpg 2x" data-file-width="2560" data-file-height="1920" /></a></span></td></tr><tr><td colspan="2" class="infobox-full-data" style="text-align: left"><span typeof="mw:File"><span><img alt="video icon" src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Nuvola_apps_kaboodle.svg/16px-Nuvola_apps_kaboodle.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Nuvola_apps_kaboodle.svg/24px-Nuvola_apps_kaboodle.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1b/Nuvola_apps_kaboodle.svg/32px-Nuvola_apps_kaboodle.svg.png 2x" data-file-width="128" data-file-height="128" /></span></span> <a rel="nofollow" class="external text" href="http://www.webofstories.com/play/benoit.mandelbrot/1;jsessionid=E8EB8E149375B3987E49D5E4F02FCB57">Family background and early education</a>, (4:11) Benoit Mandelbrot interview, Part 1 of 144, <a href="/wiki/Web_of_Stories" title="Web of Stories">Web of Stories</a><sup id="cite_ref-wos1_16-0" class="reference"><a href="#cite_note-wos1-16"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup></td></tr></tbody></table> <p>Benedykt Mandelbrot<sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> was born in a <a href="/wiki/Lithuanian_Jews" class="mw-redirect" title="Lithuanian Jews">Lithuanian Jewish</a> family, in <a href="/wiki/Warsaw" title="Warsaw">Warsaw</a> during the <a href="/wiki/Second_Polish_Republic" title="Second Polish Republic">Second Polish Republic</a>.<sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> His father made his living trading clothing; his mother was a dental surgeon. During his first two school years, he was tutored privately by an uncle who despised <a href="/wiki/Rote_learning" title="Rote learning">rote learning</a>: "Most of my time was spent playing chess, reading maps and learning how to open my eyes to everything around me."<sup id="cite_ref-wolf_19-0" class="reference"><a href="#cite_note-wolf-19"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> </p><p>In 1936, when he was 11, the family emigrated from Poland to France. The move, <a href="/wiki/World_War_II" title="World War II">World War II</a>, and the influence of his father's brother, the mathematician <a href="/wiki/Szolem_Mandelbrojt" title="Szolem Mandelbrojt">Szolem Mandelbrojt</a> (who had moved to Paris around 1920), further prevented a standard education. "The fact that my parents, as economic and political refugees, joined Szolem in France saved our lives," he writes.<sup id="cite_ref-maverick_11-1" class="reference"><a href="#cite_note-maverick-11"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 17">: 17 </span></sup><sup id="cite_ref-bbc_obit_20-0" class="reference"><a href="#cite_note-bbc_obit-20"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> </p><p>Mandelbrot attended the Lycée Rollin (now the <a href="/wiki/Coll%C3%A8ge-lyc%C3%A9e_Jacques-Decour" title="Collège-lycée Jacques-Decour">Collège-lycée Jacques-Decour</a>) in Paris until the start of <a href="/wiki/World_War_II" title="World War II">World War II</a>, when his family moved to <a href="/wiki/Tulle" title="Tulle">Tulle</a>, France. He was helped by <a href="/wiki/Rabbi" title="Rabbi">Rabbi</a> <a href="/wiki/David_Feuerwerker" title="David Feuerwerker">David Feuerwerker</a>, the Rabbi of <a href="/wiki/Brive-la-Gaillarde" title="Brive-la-Gaillarde">Brive-la-Gaillarde</a>, to continue his studies.<sup id="cite_ref-maverick_11-2" class="reference"><a href="#cite_note-maverick-11"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 62–63">: 62–63 </span></sup><sup id="cite_ref-21" class="reference"><a href="#cite_note-21"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> Much of France was occupied by the Nazis at the time, and Mandelbrot recalls this period: </p> <style data-mw-deduplicate="TemplateStyles:r1244412712">.mw-parser-output .templatequote{overflow:hidden;margin:1em 0;padding:0 32px}.mw-parser-output .templatequotecite{line-height:1.5em;text-align:left;margin-top:0}@media(min-width:500px){.mw-parser-output .templatequotecite{padding-left:1.6em}}</style><blockquote class="templatequote"><p>Our constant fear was that a sufficiently determined foe might report us to an authority and we would be sent to our deaths. This happened to a close friend from Paris, <a href="/wiki/Zina_Morhange" title="Zina Morhange">Zina Morhange</a>, a physician in a nearby county seat. Simply to eliminate the competition, another physician denounced her ... We escaped this fate. Who knows why?<sup id="cite_ref-maverick_11-3" class="reference"><a href="#cite_note-maverick-11"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 49">: 49 </span></sup></p></blockquote> <p>In 1944, Mandelbrot returned to Paris, studied at the <a href="/wiki/Lyc%C3%A9e_du_Parc" title="Lycée du Parc">Lycée du Parc</a> in <a href="/wiki/Lyon" title="Lyon">Lyon</a>, and in 1945 to 1947 attended the <a href="/wiki/%C3%89cole_Polytechnique" class="mw-redirect" title="École Polytechnique">École Polytechnique</a>, where he studied under <a href="/wiki/Gaston_Julia" title="Gaston Julia">Gaston Julia</a> and <a href="/wiki/Paul_L%C3%A9vy_(mathematician)" title="Paul Lévy (mathematician)">Paul Lévy</a>. From 1947 to 1949 he studied at California Institute of Technology, where he earned a master's degree in aeronautics.<sup id="cite_ref-guardian_obit_2-1" class="reference"><a href="#cite_note-guardian_obit-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> Returning to France, he obtained his <a href="/wiki/Doctor_of_Philosophy" title="Doctor of Philosophy">PhD degree</a> in Mathematical Sciences at the <a href="/wiki/University_of_Paris" title="University of Paris">University of Paris</a> in 1952.<sup id="cite_ref-wolf_19-1" class="reference"><a href="#cite_note-wolf-19"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Research_career">Research career</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Benoit_Mandelbrot&action=edit&section=2" title="Edit section: Research career"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>From 1949 to 1958, Mandelbrot was a staff member at the <a href="/wiki/Centre_National_de_la_Recherche_Scientifique" class="mw-redirect" title="Centre National de la Recherche Scientifique">Centre National de la Recherche Scientifique</a>. During this time he spent a year at the <a href="/wiki/Institute_for_Advanced_Study" title="Institute for Advanced Study">Institute for Advanced Study</a> in <a href="/wiki/Princeton,_New_Jersey" title="Princeton, New Jersey">Princeton, New Jersey</a>, where he was sponsored by <a href="/wiki/John_von_Neumann" title="John von Neumann">John von Neumann</a>. In 1955 he married Aliette Kagan and moved to <a href="/wiki/Geneva,_Switzerland" class="mw-redirect" title="Geneva, Switzerland">Geneva, Switzerland</a> (to collaborate with <a href="/wiki/Jean_Piaget" title="Jean Piaget">Jean Piaget</a> at the International Centre for Genetic Epistemology) and later to the <a href="/wiki/Universit%C3%A9_Lille_Nord_de_France" class="mw-redirect" title="Université Lille Nord de France">Université Lille Nord de France</a>.<sup id="cite_ref-people_22-0" class="reference"><a href="#cite_note-people-22"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> In 1958 the couple moved to the United States where Mandelbrot joined the research staff at the <a href="/wiki/IBM" title="IBM">IBM</a> <a href="/wiki/Thomas_J._Watson_Research_Center" title="Thomas J. Watson Research Center">Thomas J. Watson Research Center</a> in <a href="/wiki/Yorktown_Heights,_New_York" title="Yorktown Heights, New York">Yorktown Heights, New York</a>.<sup id="cite_ref-people_22-1" class="reference"><a href="#cite_note-people-22"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> He remained at IBM for 35 years, becoming an IBM Fellow, and later Fellow <a href="/wiki/Emeritus" title="Emeritus">Emeritus</a>.<sup id="cite_ref-wolf_19-2" class="reference"><a href="#cite_note-wolf-19"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> </p><p>From 1951 onward, Mandelbrot worked on problems and published papers not only in mathematics but in applied fields such as <a href="/wiki/Information_theory" title="Information theory">information theory</a>, economics, and <a href="/wiki/Fluid_dynamics" title="Fluid dynamics">fluid dynamics</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Randomness_and_fractals_in_financial_markets">Randomness and fractals in financial markets</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Benoit_Mandelbrot&action=edit&section=3" title="Edit section: Randomness and fractals in financial markets"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Mandelbrot saw <a href="/wiki/Financial_market" title="Financial market">financial markets</a> as an example of "wild randomness", characterized by concentration and long-range dependence. He developed several original approaches for modelling financial fluctuations.<sup id="cite_ref-23" class="reference"><a href="#cite_note-23"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> In his early work, he found that the price changes in <a href="/wiki/Financial_market" title="Financial market">financial markets</a> did not follow a <a href="/wiki/Gaussian_distribution" class="mw-redirect" title="Gaussian distribution">Gaussian distribution</a>, but rather <a href="/wiki/Paul_L%C3%A9vy_(mathematician)" title="Paul Lévy (mathematician)">Lévy</a> <a href="/wiki/Stable_distributions" class="mw-redirect" title="Stable distributions">stable distributions</a> having infinite <a href="/wiki/Variance" title="Variance">variance</a>. He found, for example, that cotton prices followed a Lévy stable distribution with parameter <i>α</i> equal to 1.7 rather than 2 as in a Gaussian distribution. "Stable" distributions have the property that the sum of many instances of a random variable follows the same distribution but with a larger <a href="/wiki/Scale_parameter" title="Scale parameter">scale parameter</a>.<sup id="cite_ref-24" class="reference"><a href="#cite_note-24"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> The latter work from the early 60s was done with daily data of cotton prices from 1900, long before he introduced the word 'fractal'. In later years, after the concept of fractals had matured, the study of financial markets in the context of fractals became possible only after the availability of high frequency data in finance. </p><p>In the late 1980s, Mandelbrot used intra-daily tick data supplied by Olsen & Associates in Zurich<sup id="cite_ref-25" class="reference"><a href="#cite_note-25"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-26" class="reference"><a href="#cite_note-26"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> to apply fractal theory to market microstructure. This cooperation led to the publication of the first comprehensive papers on scaling law in finance.<sup id="cite_ref-27" class="reference"><a href="#cite_note-27"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-28" class="reference"><a href="#cite_note-28"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup> This law shows similar properties at different time scales, confirming Mandelbrot's insight of the fractal nature of market microstructure. Mandelbrot's own research in this area is presented in his books <i>Fractals and Scaling in Finance</i><sup id="cite_ref-29" class="reference"><a href="#cite_note-29"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup> and <i>The (Mis)behavior of Markets</i>.<sup id="cite_ref-30" class="reference"><a href="#cite_note-30"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Developing_"fractal_geometry"_and_the_Mandelbrot_set"><span id="Developing_.22fractal_geometry.22_and_the_Mandelbrot_set"></span>Developing "fractal geometry" and the Mandelbrot set</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Benoit_Mandelbrot&action=edit&section=4" title="Edit section: Developing "fractal geometry" and the Mandelbrot set"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>As a visiting professor at <a href="/wiki/Harvard_University" title="Harvard University">Harvard University</a>, Mandelbrot began to study mathematical objects called <a href="/wiki/Julia_set" title="Julia set">Julia sets</a> that were <a href="/wiki/Invariant_(mathematics)" title="Invariant (mathematics)">invariant</a> under certain transformations of the <a href="/wiki/Complex_plane" title="Complex plane">complex plane</a>. Building on previous work by <a href="/wiki/Gaston_Julia" title="Gaston Julia">Gaston Julia</a> and <a href="/wiki/Pierre_Fatou" title="Pierre Fatou">Pierre Fatou</a>, Mandelbrot used a computer to plot images of the Julia sets. While investigating the topology of these Julia sets, he studied the <a href="/wiki/Mandelbrot_set" title="Mandelbrot set">Mandelbrot set</a> which was introduced by him in 1979. </p> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Mandelbrot_p1130876.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1a/Mandelbrot_p1130876.jpg/220px-Mandelbrot_p1130876.jpg" decoding="async" width="220" height="165" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1a/Mandelbrot_p1130876.jpg/330px-Mandelbrot_p1130876.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1a/Mandelbrot_p1130876.jpg/440px-Mandelbrot_p1130876.jpg 2x" data-file-width="2560" data-file-height="1920" /></a><figcaption>Mandelbrot speaking about the <a href="/wiki/Mandelbrot_set" title="Mandelbrot set">Mandelbrot set</a>, during his acceptance speech for the <a href="/wiki/L%C3%A9gion_d%27honneur" class="mw-redirect" title="Légion d'honneur">Légion d'honneur</a> in 2006</figcaption></figure> <p>In 1975, Mandelbrot coined the term <i><a href="/wiki/Fractal" title="Fractal">fractal</a></i> to describe these structures and first published his ideas in the French book <i>Les Objets Fractals: Forme, Hasard et Dimension</i>, later translated in 1977 as <i>Fractals: Form, Chance and Dimension</i>.<sup id="cite_ref-31" class="reference"><a href="#cite_note-31"><span class="cite-bracket">[</span>29<span class="cite-bracket">]</span></a></sup> According to computer scientist and physicist <a href="/wiki/Stephen_Wolfram" title="Stephen Wolfram">Stephen Wolfram</a>, the book was a "breakthrough" for Mandelbrot, who until then would typically "apply fairly straightforward mathematics ... to areas that had barely seen the light of serious mathematics before".<sup id="cite_ref-Wolfram_13-1" class="reference"><a href="#cite_note-Wolfram-13"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> Wolfram adds that as a result of this new research, he was no longer a "wandering scientist", and later called him "the father of fractals": </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1244412712"><blockquote class="templatequote"><p>Mandelbrot ended up doing a great piece of science and identifying a much stronger and more fundamental idea—put simply, that there are some geometric shapes, which he called "fractals", that are equally "rough" at all scales. No matter how close you look, they never get simpler, much as the section of a rocky coastline you can see at your feet looks just as jagged as the stretch you can see from space.<sup id="cite_ref-Wolfram_13-2" class="reference"><a href="#cite_note-Wolfram-13"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup></p></blockquote> <p>Wolfram briefly describes fractals as a form of geometric repetition, "in which smaller and smaller copies of a pattern are successively nested inside each other, so that the same intricate shapes appear no matter how much you zoom in to the whole. <a href="/wiki/Fern" title="Fern">Fern leaves</a> and <a href="/wiki/Romanesco_broccoli" title="Romanesco broccoli">Romanesque broccoli</a> are two examples from nature."<sup id="cite_ref-Wolfram_13-3" class="reference"><a href="#cite_note-Wolfram-13"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> He points out an unexpected conclusion: </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1244412712"><blockquote class="templatequote"><p>One might have thought that such a simple and fundamental form of regularity would have been studied for hundreds, if not thousands, of years. But it was not. In fact, it rose to prominence only over the past 30 or so years—almost entirely through the efforts of one man, the mathematician Benoit Mandelbrot.<sup id="cite_ref-Wolfram_13-4" class="reference"><a href="#cite_note-Wolfram-13"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup></p></blockquote> <p>Mandelbrot used the term "fractal" as it derived from the Latin word "fractus", defined as broken or shattered glass. Using the newly developed IBM computers at his disposal, Mandelbrot was able to create fractal images using graphics computer code, images that an interviewer described as looking like "the delirious exuberance of the 1960s <a href="/wiki/Psychedelic_art" title="Psychedelic art">psychedelic art</a> with forms hauntingly reminiscent of nature and the human body". He also saw himself as a "would-be Kepler", after the 17th-century scientist <a href="/wiki/Johannes_Kepler" title="Johannes Kepler">Johannes Kepler</a>, who calculated and described the orbits of the planets.<sup id="cite_ref-32" class="reference"><a href="#cite_note-32"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup> </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Newton-lplane-Mandelbrot.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Newton-lplane-Mandelbrot.jpg/220px-Newton-lplane-Mandelbrot.jpg" decoding="async" width="220" height="176" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Newton-lplane-Mandelbrot.jpg/330px-Newton-lplane-Mandelbrot.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Newton-lplane-Mandelbrot.jpg/440px-Newton-lplane-Mandelbrot.jpg 2x" data-file-width="6000" data-file-height="4800" /></a><figcaption>A Mandelbrot set</figcaption></figure> <p>Mandelbrot, however, never felt he was inventing a new idea. He described his feelings in a documentary with science writer Arthur C. Clarke: </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1244412712"><blockquote class="templatequote"><p>Exploring this set I certainly never had the feeling of invention. I never had the feeling that my imagination was rich enough to invent all those extraordinary things on discovering them. They were there, even though nobody had seen them before. It's marvelous, a very simple formula explains all these very complicated things. So the goal of science is starting with a mess, and explaining it with a simple formula, a kind of dream of science.<sup id="cite_ref-Clarke_33-0" class="reference"><a href="#cite_note-Clarke-33"><span class="cite-bracket">[</span>31<span class="cite-bracket">]</span></a></sup></p></blockquote> <p>According to Clarke, "the <a href="/wiki/Mandelbrot_set" title="Mandelbrot set">Mandelbrot set</a> is indeed one of the most astonishing discoveries in the entire history of mathematics. Who could have dreamed that such an incredibly simple equation could have generated images of literally <i>infinite</i> complexity?" Clarke also notes an "odd coincidence": </p> <blockquote><p>the name Mandelbrot, and the word "<a href="/wiki/Mandala" title="Mandala">mandala</a>"—for a religious symbol—which I'm sure is a pure coincidence, but indeed the Mandelbrot set does seem to contain an enormous number of mandalas.<sup id="cite_ref-Clarke_33-1" class="reference"><a href="#cite_note-Clarke-33"><span class="cite-bracket">[</span>31<span class="cite-bracket">]</span></a></sup></p></blockquote> <p>In 1982, Mandelbrot expanded and updated his ideas in <i><a href="/wiki/The_Fractal_Geometry_of_Nature" title="The Fractal Geometry of Nature">The Fractal Geometry of Nature</a></i>.<sup id="cite_ref-34" class="reference"><a href="#cite_note-34"><span class="cite-bracket">[</span>32<span class="cite-bracket">]</span></a></sup> This influential work brought fractals into the mainstream of professional and popular mathematics, as well as silencing critics, who had dismissed fractals as "<a href="/wiki/Artifact_(observational)" class="mw-redirect" title="Artifact (observational)">program artifacts</a>". </p><p>Mandelbrot left IBM in 1987, after 35 years and 12 days, when IBM decided to end pure research in his division.<sup id="cite_ref-wos44_35-0" class="reference"><a href="#cite_note-wos44-35"><span class="cite-bracket">[</span>33<span class="cite-bracket">]</span></a></sup> He joined the Department of Mathematics at <a href="/wiki/Yale" class="mw-redirect" title="Yale">Yale</a>, and obtained his first <a href="/wiki/Tenure" class="mw-redirect" title="Tenure">tenured</a> post in 1999, at the age of 75.<sup id="cite_ref-Tenner_36-0" class="reference"><a href="#cite_note-Tenner-36"><span class="cite-bracket">[</span>34<span class="cite-bracket">]</span></a></sup> At the time of his retirement in 2005, he was Sterling Professor of Mathematical Sciences. </p> <div class="mw-heading mw-heading3"><h3 id="Fractals_and_the_"theory_of_roughness""><span id="Fractals_and_the_.22theory_of_roughness.22"></span>Fractals and the "theory of roughness"</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Benoit_Mandelbrot&action=edit&section=5" title="Edit section: Fractals and the "theory of roughness""><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Mandelbrot created the first-ever "theory of roughness", and he saw "roughness" in the shapes of mountains, <a href="/wiki/Coastline" class="mw-redirect" title="Coastline">coastlines</a> and <a href="/wiki/River_basin" class="mw-redirect" title="River basin">river basins</a>; the structures of plants, <a href="/wiki/Blood_vessel" title="Blood vessel">blood vessels</a> and <a href="/wiki/Lung" title="Lung">lungs</a>; the clustering of <a href="/wiki/Galaxy" title="Galaxy">galaxies</a>. His personal quest was to create some mathematical formula to measure the overall "roughness" of such objects in nature.<sup id="cite_ref-maverick_11-4" class="reference"><a href="#cite_note-maverick-11"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: xi">: xi </span></sup> He began by asking himself various kinds of questions related to nature: </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1244412712"><blockquote class="templatequote"><p>Can <a href="/wiki/Geometry" title="Geometry">geometry</a> deliver what the Greek root of its name [geo-] seemed to promise—truthful measurement, not only of cultivated fields along the Nile River but also of untamed Earth?<sup id="cite_ref-maverick_11-5" class="reference"><a href="#cite_note-maverick-11"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: xii">: xii </span></sup></p></blockquote> <p>In his paper "<a href="/wiki/How_Long_Is_the_Coast_of_Britain%3F_Statistical_Self-Similarity_and_Fractional_Dimension" class="mw-redirect" title="How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension">How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension</a>", published in <a href="/wiki/Science_(journal)" title="Science (journal)"><i>Science</i></a> in 1967, Mandelbrot discusses <a href="/wiki/Self-similarity" title="Self-similarity">self-similar</a> curves that have <a href="/wiki/Hausdorff_dimension" title="Hausdorff dimension">Hausdorff dimension</a> that are examples of <i>fractals</i>, although Mandelbrot does not use this term in the paper, as he did not coin it until 1975. The paper is one of Mandelbrot's first publications on the topic of fractals.<sup id="cite_ref-37" class="reference"><a href="#cite_note-37"><span class="cite-bracket">[</span>35<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Mandelbrot_Science_1967_38-0" class="reference"><a href="#cite_note-Mandelbrot_Science_1967-38"><span class="cite-bracket">[</span>36<span class="cite-bracket">]</span></a></sup> </p><p>Mandelbrot emphasized the use of fractals as realistic and useful models for describing many "rough" phenomena in the real world. He concluded that "real roughness is often fractal and can be measured."<sup id="cite_ref-maverick_11-6" class="reference"><a href="#cite_note-maverick-11"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 296">: 296 </span></sup> Although Mandelbrot coined the term "fractal", some of the mathematical objects he presented in <i><a href="/wiki/The_Fractal_Geometry_of_Nature" title="The Fractal Geometry of Nature">The Fractal Geometry of Nature</a></i> had been previously described by other mathematicians. Before Mandelbrot, however, they were regarded as isolated curiosities with unnatural and non-intuitive properties. Mandelbrot brought these objects together for the first time and turned them into essential tools for the long-stalled effort to extend the scope of science to explaining non-smooth, "rough" objects in the real world. His methods of research were both old and new: </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1244412712"><blockquote class="templatequote"><p>The form of geometry I increasingly favored is the oldest, most concrete, and most inclusive, specifically empowered by the eye and helped by the hand and, today, also by the computer ... bringing an element of unity to the worlds of knowing and feeling ... and, unwittingly, as a bonus, for the purpose of creating beauty.<sup id="cite_ref-maverick_11-7" class="reference"><a href="#cite_note-maverick-11"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 292">: 292 </span></sup></p></blockquote><p> Fractals are also found in human pursuits, such as music, painting, architecture, and in the financial field. Mandelbrot believed that fractals, far from being unnatural, were in many ways more intuitive and natural than the artificially smooth objects of traditional <a href="/wiki/Euclidean_geometry" title="Euclidean geometry">Euclidean geometry</a>: </p><blockquote><p>Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.<br />  —Mandelbrot, in his introduction to <i>The Fractal Geometry of Nature</i></p></blockquote> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Mandel_zoom_08_satellite_antenna.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/fc/Mandel_zoom_08_satellite_antenna.jpg/220px-Mandel_zoom_08_satellite_antenna.jpg" decoding="async" width="220" height="165" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/fc/Mandel_zoom_08_satellite_antenna.jpg/330px-Mandel_zoom_08_satellite_antenna.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/fc/Mandel_zoom_08_satellite_antenna.jpg/440px-Mandel_zoom_08_satellite_antenna.jpg 2x" data-file-width="2560" data-file-height="1920" /></a><figcaption>Section of a Mandelbrot set</figcaption></figure> <p>Mandelbrot has been called an artist, and a visionary<sup id="cite_ref-RLD_39-0" class="reference"><a href="#cite_note-RLD-39"><span class="cite-bracket">[</span>37<span class="cite-bracket">]</span></a></sup> and a maverick.<sup id="cite_ref-40" class="reference"><a href="#cite_note-40"><span class="cite-bracket">[</span>38<span class="cite-bracket">]</span></a></sup> His informal and passionate style of writing and his emphasis on visual and geometric intuition (supported by the inclusion of numerous illustrations) made <i>The Fractal Geometry of Nature</i> accessible to non-specialists. The book sparked widespread popular interest in fractals and contributed to chaos theory and other fields of science and mathematics. </p><p>Mandelbrot also put his ideas to work in cosmology. He offered in 1974 a new explanation of <a href="/wiki/Olbers%27_paradox" class="mw-redirect" title="Olbers' paradox">Olbers' paradox</a> (the "dark night sky" riddle), demonstrating the consequences of fractal theory as a <a href="/wiki/Necessity_and_sufficiency" title="Necessity and sufficiency">sufficient, but not necessary</a>, resolution of the paradox. He postulated that if the <a href="/wiki/Star" title="Star">stars</a> in the universe were fractally distributed (for example, like <a href="/wiki/Cantor_dust" class="mw-redirect" title="Cantor dust">Cantor dust</a>), it would not be necessary to rely on the <a href="/wiki/Big_Bang" title="Big Bang">Big Bang</a> theory to explain the paradox. His model would not rule out a Big Bang, but would allow for a dark sky even if the Big Bang had not occurred.<sup id="cite_ref-41" class="reference"><a href="#cite_note-41"><span class="cite-bracket">[</span>39<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Awards_and_honors">Awards and honors</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Benoit_Mandelbrot&action=edit&section=6" title="Edit section: Awards and honors"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Mandelbrot's awards include the <a href="/wiki/Wolf_Prize" title="Wolf Prize">Wolf Prize</a> for Physics in 1993, the <a href="/wiki/Lewis_Fry_Richardson" title="Lewis Fry Richardson">Lewis Fry Richardson</a> Prize of the <a href="/wiki/European_Geophysical_Society" class="mw-redirect" title="European Geophysical Society">European Geophysical Society</a> in 2000, the <a href="/wiki/Japan_Prize" title="Japan Prize">Japan Prize</a> in 2003,<sup id="cite_ref-jp_42-0" class="reference"><a href="#cite_note-jp-42"><span class="cite-bracket">[</span>40<span class="cite-bracket">]</span></a></sup> and the Einstein Lectureship of the <a href="/wiki/American_Mathematical_Society" title="American Mathematical Society">American Mathematical Society</a> in 2006. </p><p>The small asteroid <a href="/wiki/27500_Mandelbrot" class="mw-redirect" title="27500 Mandelbrot">27500 Mandelbrot</a> was named in his honor. In November 1990, he was made a Chevalier in France's <a href="/wiki/Legion_of_Honour" title="Legion of Honour">Legion of Honour</a>. In December 2005, Mandelbrot was appointed to the position of Battelle Fellow at the <a href="/wiki/Pacific_Northwest_National_Laboratory" title="Pacific Northwest National Laboratory">Pacific Northwest National Laboratory</a>.<sup id="cite_ref-43" class="reference"><a href="#cite_note-43"><span class="cite-bracket">[</span>41<span class="cite-bracket">]</span></a></sup> Mandelbrot was promoted to an Officer of the Legion of Honour in January 2006.<sup id="cite_ref-44" class="reference"><a href="#cite_note-44"><span class="cite-bracket">[</span>42<span class="cite-bracket">]</span></a></sup> An honorary degree from <a href="/wiki/Johns_Hopkins_University" title="Johns Hopkins University">Johns Hopkins University</a> was bestowed on Mandelbrot in the May 2010 commencement exercises.<sup id="cite_ref-45" class="reference"><a href="#cite_note-45"><span class="cite-bracket">[</span>43<span class="cite-bracket">]</span></a></sup> </p><p>A partial list of awards received by Mandelbrot:<sup id="cite_ref-Vita_46-0" class="reference"><a href="#cite_note-Vita-46"><span class="cite-bracket">[</span>44<span class="cite-bracket">]</span></a></sup> </p> <style data-mw-deduplicate="TemplateStyles:r1184024115">.mw-parser-output .div-col{margin-top:0.3em;column-width:30em}.mw-parser-output .div-col-small{font-size:90%}.mw-parser-output .div-col-rules{column-rule:1px solid #aaa}.mw-parser-output .div-col dl,.mw-parser-output .div-col ol,.mw-parser-output .div-col ul{margin-top:0}.mw-parser-output .div-col li,.mw-parser-output .div-col dd{page-break-inside:avoid;break-inside:avoid-column}</style><div class="div-col" style="column-width: 25em;"> <ul><li>2004 Best Business Book of the Year Award</li> <li>AMS Einstein Lectureship</li> <li>Barnard Medal</li> <li>Caltech Service</li> <li><a href="/wiki/Casimir_Funk" title="Casimir Funk">Casimir Funk</a> Natural Sciences Award</li> <li><a href="/wiki/Charles_Proteus_Steinmetz" title="Charles Proteus Steinmetz">Charles Proteus Steinmetz</a> Medal</li> <li>High School Spelling Bee (1940)</li> <li>Fellow, American Geophysical Union</li> <li><a href="/wiki/Fellow_of_the_American_Statistical_Association" class="mw-redirect" title="Fellow of the American Statistical Association">Fellow of the American Statistical Association</a><sup id="cite_ref-47" class="reference"><a href="#cite_note-47"><span class="cite-bracket">[</span>45<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/Fellow_of_the_American_Physical_Society" class="mw-redirect" title="Fellow of the American Physical Society">Fellow of the American Physical Society</a> (1987) <sup id="cite_ref-48" class="reference"><a href="#cite_note-48"><span class="cite-bracket">[</span>46<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/The_Franklin_Institute_Awards" class="mw-redirect" title="The Franklin Institute Awards">Franklin Medal</a></li> <li><a href="/wiki/Harvey_Prize" title="Harvey Prize">Harvey Prize</a> (1989)</li> <li>Honda Prize</li> <li><a href="/wiki/Humboldt_Prize" class="mw-redirect" title="Humboldt Prize">Humboldtpreis</a></li> <li>IBM Fellowship</li> <li>Japan Prize (2003)</li> <li><a href="/wiki/John_Scott_Award" class="mw-redirect" title="John Scott Award">John Scott Award</a></li> <li>Légion d'honneur (<a href="/wiki/Legion_of_Honour" title="Legion of Honour">Legion of Honour</a>)</li> <li>Lewis Fry Richardson Medal</li> <li>Medaglia della Presidenza della Repubblica Italiana</li> <li>Médaille de Vermeil de la Ville de Paris</li> <li>Nevada Prize</li> <li>Member of the <a href="/wiki/Norwegian_Academy_of_Science_and_Letters" title="Norwegian Academy of Science and Letters">Norwegian Academy of Science and Letters</a>.<sup id="cite_ref-49" class="reference"><a href="#cite_note-49"><span class="cite-bracket">[</span>47<span class="cite-bracket">]</span></a></sup></li> <li>Member of the <a href="/wiki/American_Philosophical_Society" title="American Philosophical Society">American Philosophical Society</a> (2004) <sup id="cite_ref-50" class="reference"><a href="#cite_note-50"><span class="cite-bracket">[</span>48<span class="cite-bracket">]</span></a></sup></li> <li>Science for Art</li> <li>Sven Berggren-Priset</li> <li>Wacław Sierpiński medal of the Polish Mathematical Society (2005) <sup id="cite_ref-51" class="reference"><a href="#cite_note-51"><span class="cite-bracket">[</span>49<span class="cite-bracket">]</span></a></sup></li> <li>Władysław Orlicz Prize</li> <li><a href="/wiki/Wolf_Foundation_Prize" class="mw-redirect" title="Wolf Foundation Prize">Wolf Foundation Prize</a> for Physics (1993)</li></ul> </div> <div class="mw-heading mw-heading2"><h2 id="Death_and_legacy">Death and legacy</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Benoit_Mandelbrot&action=edit&section=7" title="Edit section: Death and legacy"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Mandelbrot died from <a href="/wiki/Pancreatic_cancer" title="Pancreatic cancer">pancreatic cancer</a> at the age of 85 in a <a href="/wiki/Hospice" title="Hospice">hospice</a> in <a href="/wiki/Cambridge,_Massachusetts" title="Cambridge, Massachusetts">Cambridge, Massachusetts</a>, on 14 October 2010.<sup id="cite_ref-nyt_obit_1-1" class="reference"><a href="#cite_note-nyt_obit-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-52" class="reference"><a href="#cite_note-52"><span class="cite-bracket">[</span>50<span class="cite-bracket">]</span></a></sup> Reacting to news of his death, mathematician <a href="/wiki/Heinz-Otto_Peitgen" title="Heinz-Otto Peitgen">Heinz-Otto Peitgen</a> said: "[I]f we talk about impact inside mathematics, and applications in the sciences, he is one of the most important figures of the last fifty years."<sup id="cite_ref-nyt_obit_1-2" class="reference"><a href="#cite_note-nyt_obit-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p><p><a href="/wiki/Chris_Anderson_(entrepreneur)" title="Chris Anderson (entrepreneur)">Chris Anderson</a>, <a href="/wiki/TED_(conference)" title="TED (conference)">TED conference</a> curator, described Mandelbrot as "an icon who changed how we see the world".<sup id="cite_ref-53" class="reference"><a href="#cite_note-53"><span class="cite-bracket">[</span>51<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Nicolas_Sarkozy" title="Nicolas Sarkozy">Nicolas Sarkozy</a>, <a href="/wiki/President_of_France" title="President of France">President of France</a> at the time of Mandelbrot's death, said Mandelbrot had "a powerful, original mind that never shied away from innovating and shattering preconceived notions [... h]is work, developed entirely outside mainstream research, led to modern information theory."<sup id="cite_ref-54" class="reference"><a href="#cite_note-54"><span class="cite-bracket">[</span>52<span class="cite-bracket">]</span></a></sup> Mandelbrot's obituary in <i>The Economist</i> points out his fame as "celebrity beyond the academy" and lauds him as the "father of fractal geometry".<sup id="cite_ref-55" class="reference"><a href="#cite_note-55"><span class="cite-bracket">[</span>53<span class="cite-bracket">]</span></a></sup> </p><p>Best-selling essayist-author <a href="/wiki/Nassim_Nicholas_Taleb" title="Nassim Nicholas Taleb">Nassim Nicholas Taleb</a> has remarked that Mandelbrot's book <i>The (Mis)Behavior of Markets</i> is in his opinion "The deepest and most realistic finance book ever published".<sup id="cite_ref-nature_12-1" class="reference"><a href="#cite_note-nature-12"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Bibliography">Bibliography</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Benoit_Mandelbrot&action=edit&section=8" title="Edit section: Bibliography"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="In_English">In English</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Benoit_Mandelbrot&action=edit&section=9" title="Edit section: In English"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><i>Fractals: Form, Chance and Dimension</i>, 1977, 2020</li> <li><i><a href="/wiki/The_Fractal_Geometry_of_Nature" title="The Fractal Geometry of Nature">The Fractal Geometry of Nature</a></i>, 1982</li> <li><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFMandelbrot1983" class="citation book cs1">Mandelbrot, Benoît B. (1983). <a href="/wiki/The_Fractal_Geometry_of_Nature" title="The Fractal Geometry of Nature"><i>The Fractal Geometry of Nature</i></a>. San Francisco: W.H. Freeman. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-7167-1186-5" title="Special:BookSources/978-0-7167-1186-5"><bdi>978-0-7167-1186-5</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Fractal+Geometry+of+Nature&rft.place=San+Francisco&rft.pub=W.H.+Freeman&rft.date=1983&rft.isbn=978-0-7167-1186-5&rft.aulast=Mandelbrot&rft.aufirst=Beno%C3%AEt+B.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABenoit+Mandelbrot" class="Z3988"></span></li> <li>Mandelbrot, B. (1959) Variables et processus stochastiques de Pareto-Levy, et la repartition des revenus. Comptes rendus de l'Académie des Sciences de Paris, 249, 613–615.</li> <li>Mandelbrot, B. (1960) The Pareto-Levy law and the distribution of income. International Economic Review, 1, 79–106.</li> <li>Mandelbrot, B. (1961) Stable Paretian random functions and the multiplicative variation of income. Econometrica, 29, 517–543.</li> <li>Mandelbrot, B. (1964) Random walks, fire damage amount and other Paretian risk phenomena. Operations Research, 12, 582–585.</li> <li><i>Fractals and Scaling in Finance: Discontinuity, Concentration, Risk. Selecta Volume E</i>, 1997 by Benoit B. Mandelbrot and R.E. Gomory</li> <li>Mandelbrot, Benoit B. (1997) <i>Fractals and Scaling in Finance: Discontinuity, Concentration, Risk</i>, Springer.</li> <li><i>Fractales, hasard et finance</i>, 1959–1997, 1 November 1998</li> <li><i>Multifractals and 1/ƒ Noise: Wild Self-Affinity in Physics (1963–1976)</i> (Selecta; V.N) 18 January 1999 by J.M. Berger and Benoit B. Mandelbrot</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMandelbrot1999" class="citation journal cs1">Mandelbrot, Benoît (February 1999). "A Multifractal Walk down Wall Street". <i><a href="/wiki/Scientific_American" title="Scientific American">Scientific American</a></i>. <b>280</b> (2): 70. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1999SciAm.280b..70M">1999SciAm.280b..70M</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1038%2Fscientificamerican0299-70">10.1038/scientificamerican0299-70</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Scientific+American&rft.atitle=A+Multifractal+Walk+down+Wall+Street&rft.volume=280&rft.issue=2&rft.pages=70&rft.date=1999-02&rft_id=info%3Adoi%2F10.1038%2Fscientificamerican0299-70&rft_id=info%3Abibcode%2F1999SciAm.280b..70M&rft.aulast=Mandelbrot&rft.aufirst=Beno%C3%AEt&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABenoit+Mandelbrot" class="Z3988"></span></li> <li><i>Gaussian Self-Affinity and Fractals: Globality, The Earth, 1/f Noise, and R/S (Selected Works of Benoit B. Mandelbrot)</i> 14 December 2001 by Benoit Mandelbrot and F.J. Damerau</li> <li>Mandelbrot, Benoit B., <i>Gaussian Self-Affinity and Fractals</i>, Springer: 2002.</li> <li><i>Fractals and Chaos: The Mandelbrot Set and Beyond</i>, 9 January 2004</li> <li>Mandelbrot, Benoit B. (2010). <a rel="nofollow" class="external text" href="https://www.amazon.com/Fractalist-Memoir-Scientific-Maverick/dp/030738991X"><i>The Fractalist, Memoir of a Scientific Maverick.</i></a> New York: <a rel="nofollow" class="external text" href="http://www.randomhouse.com/highschool/catalog/display.pperl?isbn=9780307389916&view=email_prep">Vintage Books</a>, Division of Random House. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-307-38991-6" title="Special:BookSources/978-0-307-38991-6">978-0-307-38991-6</a></li> <li><i>The Fractalist: Memoir of a Scientific Maverick</i>, 2014</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="Hudson" class="citation book cs1">Hudson, Richard L.; Mandelbrot, Benoît B. (2004). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/misbehaviorofmar00beno"><i>The (Mis)Behavior of Markets: A Fractal View of Risk, Ruin, and Reward</i></a></span>. New York: Basic Books. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-465-04355-2" title="Special:BookSources/978-0-465-04355-2"><bdi>978-0-465-04355-2</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+%28Mis%29Behavior+of+Markets%3A+A+Fractal+View+of+Risk%2C+Ruin%2C+and+Reward&rft.place=New+York&rft.pub=Basic+Books&rft.date=2004&rft.isbn=978-0-465-04355-2&rft.aulast=Hudson&rft.aufirst=Richard+L.&rft.au=Mandelbrot%2C+Beno%C3%AEt+B.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fmisbehaviorofmar00beno&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABenoit+Mandelbrot" class="Z3988"></span>; (2006 <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0465043576" title="Special:BookSources/978-0465043576">978-0465043576</a>)</li> <li><a href="/wiki/Heinz-Otto_Peitgen" title="Heinz-Otto Peitgen">Heinz-Otto Peitgen</a>, <a href="/wiki/Hartmut_J%C3%BCrgens" title="Hartmut Jürgens">Hartmut Jürgens</a>, <a href="/wiki/Dietmar_Saupe" title="Dietmar Saupe">Dietmar Saupe</a> and Cornelia Zahlten: <i>Fractals: An Animated Discussion</i> (63 min video film, interviews with Benoît Mandelbrot and Edward Lorenz, computer animations), W.H. Freeman and Company, 1990. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-7167-2213-5" title="Special:BookSources/0-7167-2213-5">0-7167-2213-5</a> (re-published by Films for the Humanities & Sciences, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-7365-0520-8" title="Special:BookSources/978-0-7365-0520-8">978-0-7365-0520-8</a>)</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMandelbrotTaleb2006" class="citation news cs1">Mandelbrot, Benoît; Taleb, Nassim (23 March 2006). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20101023201028/http://www.ft.com/cms/s/2/5372968a-ba82-11da-980d-0000779e2340,dwp_uuid=77a9a0e8-b442-11da-bd61-0000779e2340.html">"A focus on the exceptions that prove the rule"</a>. <i><a href="/wiki/Financial_Times" title="Financial Times">Financial Times</a></i>. Archived from <a rel="nofollow" class="external text" href="https://www.ft.com/cms/s/2/5372968a-ba82-11da-980d-0000779e2340,dwp_uuid=77a9a0e8-b442-11da-bd61-0000779e2340.html">the original</a> on 23 October 2010<span class="reference-accessdate">. Retrieved <span class="nowrap">17 October</span> 2010</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Financial+Times&rft.atitle=A+focus+on+the+exceptions+that+prove+the+rule&rft.date=2006-03-23&rft.aulast=Mandelbrot&rft.aufirst=Beno%C3%AEt&rft.au=Taleb%2C+Nassim&rft_id=http%3A%2F%2Fwww.ft.com%2Fcms%2Fs%2F2%2F5372968a-ba82-11da-980d-0000779e2340%2Cdwp_uuid%3D77a9a0e8-b442-11da-bd61-0000779e2340.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABenoit+Mandelbrot" class="Z3988"></span></li> <li><a rel="nofollow" class="external text" href="https://www.pbs.org/wgbh/nova/fractals/">"Hunting the Hidden Dimension: mysteriously beautiful fractals are shaking up the world of mathematics and deepening our understanding of nature"</a>, <i><a href="/wiki/Nova_(American_TV_series)" class="mw-redirect" title="Nova (American TV series)">NOVA</a></i>, WGBH Educational Foundation, Boston for PBS, first aired 28 October 2008.</li></ul> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Benoit_Mandelbrot&action=edit&section=10" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1184024115"><div class="div-col" style="column-width: 35em;"> <ul><li><a href="/wiki/Pink_noise" title="Pink noise">1/f noise</a> – Signal with equal energy per octave</li> <li><a href="/wiki/Fractal_dimension" title="Fractal dimension">Fractal dimension</a> – Ratio providing a statistical index of complexity variation with scale</li> <li><a href="/wiki/Fractional_Brownian_motion" title="Fractional Brownian motion">Fractional Brownian motion</a> – Probability theory concept</li> <li><a href="/wiki/How_Long_Is_the_Coast_of_Britain%3F_Statistical_Self-Similarity_and_Fractional_Dimension" class="mw-redirect" title="How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension">How Long is the Coast of Britain?</a> – Counterintuitive observation that the coastline of a landmass does not have a well-defined length<span style="display:none" class="category-annotation-with-redirected-description">Pages displaying short descriptions of redirect targets</span></li> <li><a href="/wiki/Hurst_exponent" title="Hurst exponent">Hurst exponent</a> – A measure of the long-range dependence of a time series</li> <li><a href="/wiki/Kurtosis_risk" title="Kurtosis risk">Kurtosis risk</a> – Term in decision theory</li> <li><a href="/wiki/Lacunarity" title="Lacunarity">Lacunarity</a> – Term in geometry and fractal analysis</li> <li><a href="/wiki/List_of_Poles#Mathematics" class="mw-redirect" title="List of Poles">List of Poles</a></li> <li><a href="/wiki/Louis_Bachelier" title="Louis Bachelier">Louis Bachelier</a> – French pioneer in mathematical economics (1870-1946)</li> <li><a href="/wiki/Mandelbrot_Competition" title="Mandelbrot Competition">Mandelbrot Competition</a> – High school mathematics competition</li> <li><a href="/wiki/Multifractal_system" title="Multifractal system">Multifractal system</a> – System with multiple fractal dimensions</li> <li><a href="/wiki/Self-similarity" title="Self-similarity">Self-similarity</a> – Whole of an object being mathematically similar to part of itself</li> <li><a href="/wiki/Seven_states_of_randomness" title="Seven states of randomness">Seven states of randomness</a> – Extensions of the concept of randomness</li> <li><a href="/wiki/Skewness_risk" title="Skewness risk">Skewness risk</a> – Financial modeling term</li> <li><a href="/wiki/Zipf%E2%80%93Mandelbrot_law" title="Zipf–Mandelbrot law">Zipf–Mandelbrot law</a> – Discrete probability distribution</li></ul></div> <div class="mw-heading mw-heading2"><h2 id="Notes">Notes</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Benoit_Mandelbrot&action=edit&section=11" title="Edit section: Notes"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist reflist-lower-alpha"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-Mandelbrot's_name-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-Mandelbrot's_name_3-0">^</a></b></span> <span class="reference-text">In his autobiography, Mandelbrot did not add a <a href="/wiki/Circumflex" title="Circumflex">circumflex</a> to the "i" (i.e. "î") in his first name, as is usual for <a href="/wiki/Beno%C3%AEt" title="Benoît">the French given name</a>. He included "B" as a <a href="/wiki/Middle_initial" class="mw-redirect" title="Middle initial">middle initial</a>. His <i>New York Times</i> obituary stated that "he added the middle initial himself, though it does not stand for a middle name",<sup id="cite_ref-nyt_obit_1-0" class="reference"><a href="#cite_note-nyt_obit-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> an assertion that is supported by his obituary in <i>The Guardian</i>.<sup id="cite_ref-guardian_obit_2-0" class="reference"><a href="#cite_note-guardian_obit-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup></span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text">Pronounced <span class="rt-commentedText nowrap"><span class="IPA nopopups noexcerpt" lang="en-fonipa"><a href="/wiki/Help:IPA/English" title="Help:IPA/English">/<span style="border-bottom:1px dotted"><span title="/ˈ/: primary stress follows">ˈ</span><span title="'m' in 'my'">m</span><span title="/æ/: 'a' in 'bad'">æ</span><span title="'n' in 'nigh'">n</span><span title="'d' in 'dye'">d</span><span title="/əl/: 'le' in 'bottle'">əl</span><span title="'b' in 'buy'">b</span><span title="'r' in 'rye'">r</span><span title="/ɒ/: 'o' in 'body'">ɒ</span><span title="'t' in 'tie'">t</span></span>/</a></span></span> <a href="/wiki/Help:Pronunciation_respelling_key" title="Help:Pronunciation respelling key"><i title="English pronunciation respelling"><span style="font-size:90%">MAN</span>-dəl-brot</i></a> or <span class="rt-commentedText nowrap"><span class="IPA nopopups noexcerpt" lang="en-fonipa"><a href="/wiki/Help:IPA/English" title="Help:IPA/English">/<span style="border-bottom:1px dotted"><span title="/ˈ/: primary stress follows">ˈ</span><span title="'m' in 'my'">m</span><span title="/æ/: 'a' in 'bad'">æ</span><span title="'n' in 'nigh'">n</span><span title="'d' in 'dye'">d</span><span title="/əl/: 'le' in 'bottle'">əl</span><span title="'b' in 'buy'">b</span><span title="'r' in 'rye'">r</span><span title="/oʊ/: 'o' in 'code'">oʊ</span><span title="'t' in 'tie'">t</span></span>/</a></span></span> <a href="/wiki/Help:Pronunciation_respelling_key" title="Help:Pronunciation respelling key"><i title="English pronunciation respelling"><span style="font-size:90%">MAN</span>-dəl-broht</i></a> in English.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> When speaking in French, Mandelbrot pronounced his name <span class="IPA nowrap" lang="fr-Latn-fonipa"><a href="/wiki/Help:IPA/French" title="Help:IPA/French">[bənwa<span class="wrap"> </span>mɑ̃dɛlbʁot]</a></span>.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Benoit_Mandelbrot&action=edit&section=12" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239543626"><div class="reflist"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-nyt_obit-1"><span class="mw-cite-backlink">^ <a href="#cite_ref-nyt_obit_1-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-nyt_obit_1-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-nyt_obit_1-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHoffman2010" class="citation news cs1">Hoffman, Jascha (16 October 2010). <a rel="nofollow" class="external text" href="https://www.nytimes.com/2010/10/17/us/17mandelbrot.html">"Benoît Mandelbrot, Mathematician, Dies at 85"</a>. <i>The New York Times</i>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20101018200532/http://www.nytimes.com/2010/10/17/us/17mandelbrot.html">Archived</a> from the original on 18 October 2010<span class="reference-accessdate">. Retrieved <span class="nowrap">16 October</span> 2010</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=The+New+York+Times&rft.atitle=Beno%C3%AEt+Mandelbrot%2C+Mathematician%2C+Dies+at+85&rft.date=2010-10-16&rft.aulast=Hoffman&rft.aufirst=Jascha&rft_id=https%3A%2F%2Fwww.nytimes.com%2F2010%2F10%2F17%2Fus%2F17mandelbrot.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABenoit+Mandelbrot" class="Z3988"></span></span> </li> <li id="cite_note-guardian_obit-2"><span class="mw-cite-backlink">^ <a href="#cite_ref-guardian_obit_2-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-guardian_obit_2-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLesmoir-Gordon2010" class="citation news cs1">Lesmoir-Gordon, Nigel (17 October 2010). <a rel="nofollow" class="external text" href="https://www.theguardian.com/science/2010/oct/17/benoit-mandelbrot-obituary">"Benoît Mandelbrot obituary"</a>. <i><a href="/wiki/The_Guardian" title="The Guardian">The Guardian</a></i>. London. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20130917122909/http://www.theguardian.com/science/2010/oct/17/benoit-mandelbrot-obituary">Archived</a> from the original on 17 September 2013<span class="reference-accessdate">. Retrieved <span class="nowrap">17 October</span> 2010</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=The+Guardian&rft.atitle=Beno%C3%AEt+Mandelbrot+obituary&rft.date=2010-10-17&rft.aulast=Lesmoir-Gordon&rft.aufirst=Nigel&rft_id=https%3A%2F%2Fwww.theguardian.com%2Fscience%2F2010%2Foct%2F17%2Fbenoit-mandelbrot-obituary&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABenoit+Mandelbrot" class="Z3988"></span></span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFReference-OED-Mandelbrot" class="citation encyclopaedia cs1"><span class="id-lock-subscription" title="Paid subscription required"><a rel="nofollow" class="external text" href="https://www.oed.com/search/dictionary/?q=Mandelbrot">"Mandelbrot"</a></span>. <i><a href="/wiki/Oxford_English_Dictionary" title="Oxford English Dictionary">Oxford English Dictionary</a></i> (Online ed.). <a href="/wiki/Oxford_University_Press" title="Oxford University Press">Oxford University Press</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Mandelbrot&rft.btitle=Oxford+English+Dictionary&rft.edition=Online&rft.pub=Oxford+University+Press&rft_id=https%3A%2F%2Fwww.oed.com%2Fsearch%2Fdictionary%2F%3Fq%3DMandelbrot&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABenoit+Mandelbrot" class="Z3988"></span> <span style="font-size:0.95em; font-size:95%; color: var( --color-subtle, #555 )">(Subscription or <a rel="nofollow" class="external text" href="https://www.oed.com/public/login/loggingin#withyourlibrary">participating institution membership</a> required.)</span></span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWells2008" class="citation book cs1"><a href="/wiki/John_C._Wells" title="John C. Wells">Wells, John C.</a> (2008). <i>Longman Pronunciation Dictionary</i> (3rd ed.). Longman. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-4058-8118-0" title="Special:BookSources/978-1-4058-8118-0"><bdi>978-1-4058-8118-0</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Longman+Pronunciation+Dictionary&rft.edition=3rd&rft.pub=Longman&rft.date=2008&rft.isbn=978-1-4058-8118-0&rft.aulast=Wells&rft.aufirst=John+C.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABenoit+Mandelbrot" class="Z3988"></span></span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text">Recording of the ceremony on 11 September 2006 at which Mandelbrot received the insignia for an Officer of the <a href="/wiki/Legion_of_Honour" title="Legion of Honour"><i>Légion d'honneur</i></a>.</span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.insidescience.org/news/remembering-father-fractals">"Remembering the Father of Fractals"</a>. 22 October 2010. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20180108174954/https://www.insidescience.org/news/remembering-father-fractals">Archived</a> from the original on 8 January 2018<span class="reference-accessdate">. Retrieved <span class="nowrap">8 January</span> 2018</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Remembering+the+Father+of+Fractals&rft.date=2010-10-22&rft_id=https%3A%2F%2Fwww.insidescience.org%2Fnews%2Fremembering-father-fractals&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABenoit+Mandelbrot" class="Z3988"></span></span> </li> <li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMandelbrot2010" class="citation cs2">Mandelbrot, Benoit (February 2010), <a rel="nofollow" class="external text" href="https://web.archive.org/web/20160414183649/https://www.ted.com/talks/benoit_mandelbrot_fractals_the_art_of_roughness?language=en">"Fractals and the art of roughness"</a>, <i>TED.com</i>, archived from <a rel="nofollow" class="external text" href="https://www.ted.com/talks/benoit_mandelbrot_fractals_the_art_of_roughness?language=en">the original</a> on 14 April 2016</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=TED.com&rft.atitle=Fractals+and+the+art+of+roughness&rft.date=2010-02&rft.aulast=Mandelbrot&rft.aufirst=Benoit&rft_id=https%3A%2F%2Fwww.ted.com%2Ftalks%2Fbenoit_mandelbrot_fractals_the_art_of_roughness%3Flanguage%3Den&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABenoit+Mandelbrot" class="Z3988"></span></span> </li> <li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text"><a href="#Hudson">Hudson & Mandelbrot</a>, Prelude, page xviii</span> </li> <li id="cite_note-maverick-11"><span class="mw-cite-backlink">^ <a href="#cite_ref-maverick_11-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-maverick_11-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-maverick_11-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-maverick_11-3"><sup><i><b>d</b></i></sup></a> <a href="#cite_ref-maverick_11-4"><sup><i><b>e</b></i></sup></a> <a href="#cite_ref-maverick_11-5"><sup><i><b>f</b></i></sup></a> <a href="#cite_ref-maverick_11-6"><sup><i><b>g</b></i></sup></a> <a href="#cite_ref-maverick_11-7"><sup><i><b>h</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMandelbrot2012" class="citation book cs1">Mandelbrot, Benoit (2012). <i>The Fractalist: Memoir of a Scientific Maverick</i>. Pantheon Books. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-307-38991-6" title="Special:BookSources/978-0-307-38991-6"><bdi>978-0-307-38991-6</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Fractalist%3A+Memoir+of+a+Scientific+Maverick&rft.pub=Pantheon+Books&rft.date=2012&rft.isbn=978-0-307-38991-6&rft.aulast=Mandelbrot&rft.aufirst=Benoit&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABenoit+Mandelbrot" class="Z3988"></span></span> </li> <li id="cite_note-nature-12"><span class="mw-cite-backlink">^ <a href="#cite_ref-nature_12-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-nature_12-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGomory2010" class="citation journal cs1"><a href="/wiki/Ralph_E._Gomory" title="Ralph E. Gomory">Gomory, R.</a> (2010). <a rel="nofollow" class="external text" href="https://doi.org/10.1038%2F468378a">"Benoît Mandelbrot (1924–2010)"</a>. <i>Nature</i>. <b>468</b> (7322): 378. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2010Natur.468..378G">2010Natur.468..378G</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1038%2F468378a">10.1038/468378a</a></span>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/21085164">21085164</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:4393964">4393964</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Nature&rft.atitle=Beno%C3%AEt+Mandelbrot+%281924%E2%80%932010%29&rft.volume=468&rft.issue=7322&rft.pages=378&rft.date=2010&rft_id=info%3Adoi%2F10.1038%2F468378a&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A4393964%23id-name%3DS2CID&rft_id=info%3Apmid%2F21085164&rft_id=info%3Abibcode%2F2010Natur.468..378G&rft.aulast=Gomory&rft.aufirst=R.&rft_id=https%3A%2F%2Fdoi.org%2F10.1038%252F468378a&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABenoit+Mandelbrot" class="Z3988"></span></span> </li> <li id="cite_note-Wolfram-13"><span class="mw-cite-backlink">^ <a href="#cite_ref-Wolfram_13-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Wolfram_13-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-Wolfram_13-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-Wolfram_13-3"><sup><i><b>d</b></i></sup></a> <a href="#cite_ref-Wolfram_13-4"><sup><i><b>e</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWolfram2012" class="citation news cs1">Wolfram, Stephen (22 November 2012). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20170825102714/https://www.wsj.com/articles/SB10001424127887324439804578107271772910506">"The Father of Fractals"</a>. <i><a href="/wiki/The_Wall_Street_Journal" title="The Wall Street Journal">The Wall Street Journal</a></i>. Archived from <a rel="nofollow" class="external text" href="https://www.wsj.com/articles/SB10001424127887324439804578107271772910506">the original</a> on 25 August 2017.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=The+Wall+Street+Journal&rft.atitle=The+Father+of+Fractals&rft.date=2012-11-22&rft.aulast=Wolfram&rft.aufirst=Stephen&rft_id=https%3A%2F%2Fwww.wsj.com%2Farticles%2FSB10001424127887324439804578107271772910506&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABenoit+Mandelbrot" class="Z3988"></span></span> </li> <li id="cite_note-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-14">^</a></b></span> <span class="reference-text">list includes specific sciences mentioned in <a href="#Hudson">Hudson & Mandelbrot</a>, the Prelude, p. xvi, and p. 26</span> </li> <li id="cite_note-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-15">^</a></b></span> <span class="reference-text"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFOlson2004" class="citation web cs1"><a href="/wiki/Steve_Olson_(writer)" class="mw-redirect" title="Steve Olson (writer)">Olson, Steve</a> (November–December 2004). <a rel="nofollow" class="external text" href="http://archives.yalealumnimagazine.com/issues/2004_11/mandelbrot.html">"The Genius of the Unpredictable"</a>. <i>Yale Alumni Magazine</i>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20141022092605/http://archives.yalealumnimagazine.com/issues/2004_11/mandelbrot.html">Archived</a> from the original on 22 October 2014<span class="reference-accessdate">. Retrieved <span class="nowrap">22 July</span> 2014</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Yale+Alumni+Magazine&rft.atitle=The+Genius+of+the+Unpredictable&rft.date=2004-11%2F2004-12&rft.aulast=Olson&rft.aufirst=Steve&rft_id=http%3A%2F%2Farchives.yalealumnimagazine.com%2Fissues%2F2004_11%2Fmandelbrot.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABenoit+Mandelbrot" class="Z3988"></span></span> </li> <li id="cite_note-wos1-16"><span class="mw-cite-backlink"><b><a href="#cite_ref-wos1_16-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMandelbrotBernard_SapovalDaniel_Zajdenweber1998" class="citation web cs1">Mandelbrot, Benoît; Bernard Sapoval; Daniel Zajdenweber (May 1998). <a rel="nofollow" class="external text" href="http://www.webofstories.com/play/9596">"Web of Stories – Benoît Mandelbrot – Family background and early education"</a>. <a href="/wiki/Web_of_Stories" title="Web of Stories">Web of Stories</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20110911162528/http://www.webofstories.com/play/9596">Archived</a> from the original on 11 September 2011<span class="reference-accessdate">. Retrieved <span class="nowrap">19 October</span> 2010</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Web+of+Stories+%E2%80%93+Beno%C3%AEt+Mandelbrot+%E2%80%93+Family+background+and+early+education&rft.pub=Web+of+Stories&rft.date=1998-05&rft.aulast=Mandelbrot&rft.aufirst=Beno%C3%AEt&rft.au=Bernard+Sapoval&rft.au=Daniel+Zajdenweber&rft_id=http%3A%2F%2Fwww.webofstories.com%2Fplay%2F9596&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABenoit+Mandelbrot" class="Z3988"></span></span> </li> <li id="cite_note-17"><span class="mw-cite-backlink"><b><a href="#cite_ref-17">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGołąb-Meyer2011" class="citation journal cs1">Gołąb-Meyer, Zofia (Spring 2011). <a rel="nofollow" class="external text" href="http://www.foton.if.uj.edu.pl/documents/12579485/8a780912-d415-4ece-8f8c-59b8134ca4a1">"Benoit Mandelbrot (1924–2010) – ojciec geometrii fraktalnej"</a>. <i>Foton</i>. <b>112</b>. 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Retrieved <span class="nowrap">25 December</span> 2021</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Foton&rft.atitle=Benoit+Mandelbrot+%281924%E2%80%932010%29+%E2%80%93+ojciec+geometrii+fraktalnej&rft.ssn=spring&rft.volume=112&rft.pages=50&rft.date=2011&rft.aulast=Go%C5%82%C4%85b-Meyer&rft.aufirst=Zofia&rft_id=http%3A%2F%2Fwww.foton.if.uj.edu.pl%2Fdocuments%2F12579485%2F8a780912-d415-4ece-8f8c-59b8134ca4a1&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABenoit+Mandelbrot" class="Z3988"></span></span> </li> <li id="cite_note-18"><span class="mw-cite-backlink"><b><a href="#cite_ref-18">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHoffman2010" class="citation news cs1">Hoffman, Jascha (16 October 2010). <a rel="nofollow" class="external text" href="https://www.nytimes.com/2010/10/17/us/17mandelbrot.html">"Benoît Mandelbrot, Novel Mathematician, Dies at 85 (Published 2010)"</a>. <i>The New York Times</i>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0362-4331">0362-4331</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20170121082521/http://www.nytimes.com/2010/10/17/us/17mandelbrot.html">Archived</a> from the original on 21 January 2017<span class="reference-accessdate">. Retrieved <span class="nowrap">20 November</span> 2020</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=The+New+York+Times&rft.atitle=Beno%C3%AEt+Mandelbrot%2C+Novel+Mathematician%2C+Dies+at+85+%28Published+2010%29&rft.date=2010-10-16&rft.issn=0362-4331&rft.aulast=Hoffman&rft.aufirst=Jascha&rft_id=https%3A%2F%2Fwww.nytimes.com%2F2010%2F10%2F17%2Fus%2F17mandelbrot.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABenoit+Mandelbrot" class="Z3988"></span></span> </li> <li id="cite_note-wolf-19"><span class="mw-cite-backlink">^ <a href="#cite_ref-wolf_19-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-wolf_19-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-wolf_19-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMandelbrot2002" class="citation web cs1">Mandelbrot, Benoît (2002). <a rel="nofollow" class="external text" href="http://users.math.yale.edu/~bbm3/web_pdfs/mavericksApprenticeship.pdf">"The Wolf Prizes for Physics, <i>A Maverick's Apprenticeship</i>"</a> <span class="cs1-format">(PDF)</span>. Imperial College Press. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20131203024639/http://users.math.yale.edu/~bbm3/web_pdfs/mavericksApprenticeship.pdf">Archived</a> <span class="cs1-format">(PDF)</span> from the original on 3 December 2013<span class="reference-accessdate">. Retrieved <span class="nowrap">23 April</span> 2012</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=The+Wolf+Prizes+for+Physics%2C+A+Maverick%27s+Apprenticeship&rft.pub=Imperial+College+Press&rft.date=2002&rft.aulast=Mandelbrot&rft.aufirst=Beno%C3%AEt&rft_id=http%3A%2F%2Fusers.math.yale.edu%2F~bbm3%2Fweb_pdfs%2FmavericksApprenticeship.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABenoit+Mandelbrot" class="Z3988"></span></span> </li> <li id="cite_note-bbc_obit-20"><span class="mw-cite-backlink"><b><a href="#cite_ref-bbc_obit_20-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation news cs1"><a rel="nofollow" class="external text" href="https://www.bbc.co.uk/news/world-europe-11560101">"<span class="cs1-kern-left"></span>'Fractal' mathematician Benoît Mandelbrot dies aged 85"</a>. <i><a href="/wiki/BBC_Online" title="BBC Online">BBC Online</a></i>. 17 October 2010. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20101018045143/http://www.bbc.co.uk/news/world-europe-11560101">Archived</a> from the original on 18 October 2010<span class="reference-accessdate">. Retrieved <span class="nowrap">17 October</span> 2010</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=BBC+Online&rft.atitle=%27Fractal%27+mathematician+Beno%C3%AEt+Mandelbrot+dies+aged+85&rft.date=2010-10-17&rft_id=https%3A%2F%2Fwww.bbc.co.uk%2Fnews%2Fworld-europe-11560101&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABenoit+Mandelbrot" class="Z3988"></span></span> </li> <li id="cite_note-21"><span class="mw-cite-backlink"><b><a href="#cite_ref-21">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHemenway2005" class="citation book cs1">Hemenway, P. (2005). <i>Divine proportion: Phi in art, nature and science</i>. 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(1984). <a rel="nofollow" class="external text" href="http://users.math.yale.edu/~bbm3/web_pdfs/inHisOwnWords.pdf">"Mathematical People, <i>Interview of B. B. Mandelbrot</i>"</a> <span class="cs1-format">(PDF)</span>. Interviewed by Anthony Barcellos. Birkhaüser. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20150427164851/http://users.math.yale.edu/~bbm3/web_pdfs/inHisOwnWords.pdf">Archived</a> <span class="cs1-format">(PDF)</span> from the original on 27 April 2015<span class="reference-accessdate">. Retrieved <span class="nowrap">25 June</span> 2013</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Mathematical+People%2C+Interview+of+B.+B.+Mandelbrot&rft.pub=Birkha%C3%BCser&rft.date=1984&rft.aulast=Mandelbrot&rft.aufirst=B.+B.&rft_id=http%3A%2F%2Fusers.math.yale.edu%2F~bbm3%2Fweb_pdfs%2FinHisOwnWords.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABenoit+Mandelbrot" class="Z3988"></span></span> </li> <li id="cite_note-23"><span class="mw-cite-backlink"><b><a href="#cite_ref-23">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCont2010" class="citation encyclopaedia cs1">Cont, Rama (15 May 2010). "Mandelbrot, Benoit". <i>Encyclopedia of Quantitative Finance</i>. pp. eqf01006. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1002%2F9780470061602.eqf01006">10.1002/9780470061602.eqf01006</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780470057568" title="Special:BookSources/9780470057568"><bdi>9780470057568</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Mandelbrot%2C+Benoit&rft.btitle=Encyclopedia+of+Quantitative+Finance&rft.pages=eqf01006&rft.date=2010-05-15&rft_id=info%3Adoi%2F10.1002%2F9780470061602.eqf01006&rft.isbn=9780470057568&rft.aulast=Cont&rft.aufirst=Rama&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABenoit+Mandelbrot" class="Z3988"></span></span> </li> <li id="cite_note-24"><span class="mw-cite-backlink"><b><a href="#cite_ref-24">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.newscientist.com/article/mg15420784.700-flight-over-wall-st.html">"New Scientist<i>, 19 April 1997"</i></a><i>. Newscientist.com. 19 April 1997. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20100421101729/http://www.newscientist.com/article/mg15420784.700-flight-over-wall-st.html">Archived</a> from the original on 21 April 2010<span class="reference-accessdate">. Retrieved <span class="nowrap">17 October</span> 2010</span>.</i></cite><i><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=New+Scientist%2C+19+April+1997&rft.pub=Newscientist.com&rft.date=1997-04-19&rft_id=https%3A%2F%2Fwww.newscientist.com%2Farticle%2Fmg15420784.700-flight-over-wall-st.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABenoit+Mandelbrot" class="Z3988"></span></i></span> </li> <li id="cite_note-25"><span class="mw-cite-backlink"><b><a href="#cite_ref-25">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDavidson1997" class="citation journal cs1">Davidson, Clive (15 December 1997). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20210711170709/https://www.joc.com/wildly-random-market-moves_19971215.html">"Wildly Random Market Moves"</a>. <i>Journal of Commerce</i>. Archived from <a rel="nofollow" class="external text" href="https://www.joc.com/wildly-random-market-moves_19971215.html">the original</a> on 11 July 2021 – via JOC.com.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Commerce&rft.atitle=Wildly+Random+Market+Moves&rft.date=1997-12-15&rft.aulast=Davidson&rft.aufirst=Clive&rft_id=https%3A%2F%2Fwww.joc.com%2Fwildly-random-market-moves_19971215.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABenoit+Mandelbrot" class="Z3988"></span></span> </li> <li id="cite_note-26"><span class="mw-cite-backlink"><b><a href="#cite_ref-26">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMuldoon2019" class="citation web cs1">Muldoon, Oliver (14 October 2019). <a rel="nofollow" class="external text" href="https://medium.com/swlh/the-wandering-scientist-turned-father-of-fractals-4dcdc867d4dd">"The Wandering Scientist Turned Father of Fractals"</a>. <i>Medium.com</i><span class="reference-accessdate">. Retrieved <span class="nowrap">19 March</span> 2021</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Medium.com&rft.atitle=The+Wandering+Scientist+Turned+Father+of+Fractals&rft.date=2019-10-14&rft.aulast=Muldoon&rft.aufirst=Oliver&rft_id=https%3A%2F%2Fmedium.com%2Fswlh%2Fthe-wandering-scientist-turned-father-of-fractals-4dcdc867d4dd&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABenoit+Mandelbrot" class="Z3988"></span></span> </li> <li id="cite_note-27"><span class="mw-cite-backlink"><b><a href="#cite_ref-27">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMüllerDacorognaOlsenPictet1990" class="citation journal cs1">Müller, Ulrich A.; Dacorogna, Michel M.; Olsen, Richard B.; Pictet, Oliver V.; Schwarz, Matthias; Morgenegg, Claude (December 1990). <a rel="nofollow" class="external text" href="https://doi.org/10.1016/0378-4266(90)90009-Q">"Statistical study of foreign exchange rates, empirical evidence of a price change scaling law, and intraday analysis"</a>. <i>Journal of Banking and Finance</i>. <b>14</b> (6): 1189–1208. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2F0378-4266%2890%2990009-Q">10.1016/0378-4266(90)90009-Q</a> – via Elsevier Science Direct.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Banking+and+Finance&rft.atitle=Statistical+study+of+foreign+exchange+rates%2C+empirical+evidence+of+a+price+change+scaling+law%2C+and+intraday+analysis&rft.volume=14&rft.issue=6&rft.pages=1189-1208&rft.date=1990-12&rft_id=info%3Adoi%2F10.1016%2F0378-4266%2890%2990009-Q&rft.aulast=M%C3%BCller&rft.aufirst=Ulrich+A.&rft.au=Dacorogna%2C+Michel+M.&rft.au=Olsen%2C+Richard+B.&rft.au=Pictet%2C+Oliver+V.&rft.au=Schwarz%2C+Matthias&rft.au=Morgenegg%2C+Claude&rft_id=https%3A%2F%2Fdoi.org%2F10.1016%2F0378-4266%2890%2990009-Q&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABenoit+Mandelbrot" class="Z3988"></span></span> </li> <li id="cite_note-28"><span class="mw-cite-backlink"><b><a href="#cite_ref-28">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMüllerDacorognaDavéPictet1995" class="citation journal cs1">Müller, U. A.; Dacorogna, M. M.; Davé, R. D.; Pictet, O. V.; Olsen, R. B.; Ward, J. R. (28 June 1995). "FRACTALS AND INTRINSIC TIME – A CHALLENGE TO ECONOMETRICIANS". <i>Opening Lecture of the XXXIXth International Conference of the Applied Econometrics Association (AEA)</i>. <a href="/wiki/CiteSeerX_(identifier)" class="mw-redirect" title="CiteSeerX (identifier)">CiteSeerX</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.197.2969">10.1.1.197.2969</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Opening+Lecture+of+the+XXXIXth+International+Conference+of+the+Applied+Econometrics+Association+%28AEA%29&rft.atitle=FRACTALS+AND+INTRINSIC+TIME+%E2%80%93+A+CHALLENGE+TO+ECONOMETRICIANS&rft.date=1995-06-28&rft_id=https%3A%2F%2Fciteseerx.ist.psu.edu%2Fviewdoc%2Fsummary%3Fdoi%3D10.1.1.197.2969%23id-name%3DCiteSeerX&rft.aulast=M%C3%BCller&rft.aufirst=U.+A.&rft.au=Dacorogna%2C+M.+M.&rft.au=Dav%C3%A9%2C+R.+D.&rft.au=Pictet%2C+O.+V.&rft.au=Olsen%2C+R.+B.&rft.au=Ward%2C+J.+R.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABenoit+Mandelbrot" class="Z3988"></span></span> </li> <li id="cite_note-29"><span class="mw-cite-backlink"><b><a href="#cite_ref-29">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMandelbrot1997" class="citation book cs1">Mandelbrot, Benoit (1997). <i>Fractals and Scaling in Finance</i>. Springer. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-4757-2763-0" title="Special:BookSources/978-1-4757-2763-0"><bdi>978-1-4757-2763-0</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Fractals+and+Scaling+in+Finance&rft.pub=Springer&rft.date=1997&rft.isbn=978-1-4757-2763-0&rft.aulast=Mandelbrot&rft.aufirst=Benoit&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABenoit+Mandelbrot" class="Z3988"></span></span> </li> <li id="cite_note-30"><span class="mw-cite-backlink"><b><a href="#cite_ref-30">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMandelbrot2004" class="citation book cs1">Mandelbrot, Benoit (2004). <i>The (Mis)behavior of Markets</i>. Profile Books. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9781861977656" title="Special:BookSources/9781861977656"><bdi>9781861977656</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+%28Mis%29behavior+of+Markets&rft.pub=Profile+Books&rft.date=2004&rft.isbn=9781861977656&rft.aulast=Mandelbrot&rft.aufirst=Benoit&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABenoit+Mandelbrot" class="Z3988"></span></span> </li> <li id="cite_note-31"><span class="mw-cite-backlink"><b><a href="#cite_ref-31">^</a></b></span> <span class="reference-text"><i>Fractals: Form, Chance and Dimension</i>, by Benoît Mandelbrot; W H Freeman and Co, 1977; <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-7167-0473-0" title="Special:BookSources/0-7167-0473-0">0-7167-0473-0</a></span> </li> <li id="cite_note-32"><span class="mw-cite-backlink"><b><a href="#cite_ref-32">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFIvry2012" class="citation web cs1">Ivry, Benjamin (17 November 2012). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20130602171300/http://forward.com/articles/166094/benoit-mandelbrot-influenced-art-and-mathematics/?p=all">"Benoit Mandelbrot Influenced Art and Mathematics"</a>. <i><a href="/wiki/The_Jewish_Daily_Forward" class="mw-redirect" title="The Jewish Daily Forward">The Jewish Daily Forward</a></i>. Archived from <a rel="nofollow" class="external text" href="http://forward.com/articles/166094/benoit-mandelbrot-influenced-art-and-mathematics/?p=all">the original</a> on 2 June 2013.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=The+Jewish+Daily+Forward&rft.atitle=Benoit+Mandelbrot+Influenced+Art+and+Mathematics&rft.date=2012-11-17&rft.aulast=Ivry&rft.aufirst=Benjamin&rft_id=http%3A%2F%2Fforward.com%2Farticles%2F166094%2Fbenoit-mandelbrot-influenced-art-and-mathematics%2F%3Fp%3Dall&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABenoit+Mandelbrot" class="Z3988"></span></span> </li> <li id="cite_note-Clarke-33"><span class="mw-cite-backlink">^ <a href="#cite_ref-Clarke_33-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Clarke_33-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation cs2"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20170531193057/https://www.youtube.com/watch?v=Lk6QU94xAb8"><i>Arthur C Clarke – Fractals – The Colors Of Infinity</i></a>, 25 December 2010, archived from <a rel="nofollow" class="external text" href="https://www.youtube.com/watch?v=Lk6QU94xAb8">the original</a> on 31 May 2017 – via YouTube</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Arthur+C+Clarke+%E2%80%93+Fractals+%E2%80%93+The+Colors+Of+Infinity&rft.date=2010-12-25&rft_id=https%3A%2F%2Fwww.youtube.com%2Fwatch%3Fv%3DLk6QU94xAb8&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABenoit+Mandelbrot" class="Z3988"></span></span> </li> <li id="cite_note-34"><span class="mw-cite-backlink"><b><a href="#cite_ref-34">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMandelbrot1982" class="citation book cs1">Mandelbrot, Benoît (1982). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20151130231048/https://books.google.com/books?id=xJ4qiEBNP4gC&printsec=frontcover"><i>The Fractal Geometry of Nature</i></a>. W H Freeman & Co. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-7167-1186-9" title="Special:BookSources/0-7167-1186-9"><bdi>0-7167-1186-9</bdi></a>. Archived from <a rel="nofollow" class="external text" href="https://books.google.com/books?id=xJ4qiEBNP4gC">the original</a> on 30 November 2015.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Fractal+Geometry+of+Nature&rft.pub=W+H+Freeman+%26+Co&rft.date=1982&rft.isbn=0-7167-1186-9&rft.aulast=Mandelbrot&rft.aufirst=Beno%C3%AEt&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DxJ4qiEBNP4gC&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABenoit+Mandelbrot" class="Z3988"></span></span> </li> <li id="cite_note-wos44-35"><span class="mw-cite-backlink"><b><a href="#cite_ref-wos44_35-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMandelbrotBernard_SapovalDaniel_Zajdenweber1998" class="citation web cs1">Mandelbrot, Benoît; Bernard Sapoval; Daniel Zajdenweber (May 1998). <a rel="nofollow" class="external text" href="http://www.webofstories.com/play/10483">"Benoît Mandelbrot • IBM: background and policies"</a>. <a href="/wiki/Web_of_Stories" title="Web of Stories">Web of Stories</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20110908162215/http://www.webofstories.com/play/10483">Archived</a> from the original on 8 September 2011<span class="reference-accessdate">. Retrieved <span class="nowrap">17 October</span> 2010</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Beno%C3%AEt+Mandelbrot+%E2%80%A2+IBM%3A+background+and+policies&rft.pub=Web+of+Stories&rft.date=1998-05&rft.aulast=Mandelbrot&rft.aufirst=Beno%C3%AEt&rft.au=Bernard+Sapoval&rft.au=Daniel+Zajdenweber&rft_id=http%3A%2F%2Fwww.webofstories.com%2Fplay%2F10483&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABenoit+Mandelbrot" class="Z3988"></span></span> </li> <li id="cite_note-Tenner-36"><span class="mw-cite-backlink"><b><a href="#cite_ref-Tenner_36-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFTenner2010" class="citation news cs1">Tenner, Edward (16 October 2010). <a rel="nofollow" class="external text" href="https://www.theatlantic.com/technology/archive/2010/10/benoit-mandelbrot-the-maverick-1924-2010/64684/">"Benoît Mandelbrot the Maverick, 1924–2010"</a>. <i><a href="/wiki/The_Atlantic" title="The Atlantic">The Atlantic</a></i>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20101018132145/http://www.theatlantic.com/technology/archive/2010/10/benoit-mandelbrot-the-maverick-1924-2010/64684/">Archived</a> from the original on 18 October 2010<span class="reference-accessdate">. Retrieved <span class="nowrap">16 October</span> 2010</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=The+Atlantic&rft.atitle=Beno%C3%AEt+Mandelbrot+the+Maverick%2C+1924%E2%80%932010&rft.date=2010-10-16&rft.aulast=Tenner&rft.aufirst=Edward&rft_id=https%3A%2F%2Fwww.theatlantic.com%2Ftechnology%2Farchive%2F2010%2F10%2Fbenoit-mandelbrot-the-maverick-1924-2010%2F64684%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABenoit+Mandelbrot" class="Z3988"></span></span> </li> <li id="cite_note-37"><span class="mw-cite-backlink"><b><a href="#cite_ref-37">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation news cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20181231150228/https://www.nytimes.com/2010/10/17/us/17mandelbrot.html?adxnnl=1&adxnnlx=1332064840-%2FvD0Sjafcl9t9BNghRf8Qw">"Benoît Mandelbrot, Novel Mathematician, Dies at 85"</a>. <i>The New York Times</i>. 17 October 2010. Archived from <a rel="nofollow" class="external text" href="https://www.nytimes.com/2010/10/17/us/17mandelbrot.html?adxnnl=1&adxnnlx=1332064840-/vD0Sjafcl9t9BNghRf8Qw">the original</a> on 31 December 2018. <q>Dr. Mandelbrot traced his work on fractals to a question he first encountered as a young researcher: how long is the coast of Britain?"<span class="cs1-kern-right"></span></q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=The+New+York+Times&rft.atitle=Beno%C3%AEt+Mandelbrot%2C+Novel+Mathematician%2C+Dies+at+85&rft.date=2010-10-17&rft_id=https%3A%2F%2Fwww.nytimes.com%2F2010%2F10%2F17%2Fus%2F17mandelbrot.html%3Fadxnnl%3D1%26adxnnlx%3D1332064840-%2FvD0Sjafcl9t9BNghRf8Qw&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABenoit+Mandelbrot" class="Z3988"></span></span> </li> <li id="cite_note-Mandelbrot_Science_1967-38"><span class="mw-cite-backlink"><b><a href="#cite_ref-Mandelbrot_Science_1967_38-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMandelbrot1967" class="citation journal cs1">Mandelbrot, Benoit B. (5 May 1967). <a rel="nofollow" class="external text" href="http://users.math.yale.edu/~bbm3/web_pdfs/howLongIsTheCoastOfBritain.pdf">"How long is the coast of Britain? Statistical self-similarity and fractional dimension"</a> <span class="cs1-format">(PDF)</span>. <i>Science</i>. <b>156</b> (3775): 636–638. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1967Sci...156..636M">1967Sci...156..636M</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1126%2Fscience.156.3775.636">10.1126/science.156.3775.636</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/17837158">17837158</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:15662830">15662830</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20150713023120/http://www.sciencemag.org/content/156/3775/636">Archived</a> from the original on 13 July 2015<span class="reference-accessdate">. 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Retrieved <span class="nowrap">17 October</span> 2010</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=United+Press+International&rft.atitle=Beno%C3%AEt+Mandelbrot%2C+fractals+pioneer%2C+dies&rft.date=2010-10-16&rft_id=http%3A%2F%2Fwww.upi.com%2FScience_News%2F2010%2F10%2F16%2FBenoit-Mandelbrot-fractals-pioneer-dies%2FUPI-11551287266964%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABenoit+Mandelbrot" class="Z3988"></span></span> </li> <li id="cite_note-53"><span class="mw-cite-backlink"><b><a href="#cite_ref-53">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation news cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20101019233754/http://www.montrealgazette.com/technology/Mandelbrot%2Bfather%2Bfractal%2Bgeometry%2Bdies/3682961/story.html">"Mandelbrot, father of fractal geometry, dies"</a>. <i><a href="/wiki/The_Gazette_(Montreal)" title="The Gazette (Montreal)">The Gazette</a></i>. Archived from <a rel="nofollow" class="external text" href="https://montrealgazette.com/technology/Mandelbrot+father+fractal+geometry+dies/3682961/story.html">the original</a> on 19 October 2010<span class="reference-accessdate">. Retrieved <span class="nowrap">16 October</span> 2010</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=The+Gazette&rft.atitle=Mandelbrot%2C+father+of+fractal+geometry%2C+dies&rft_id=https%3A%2F%2Fmontrealgazette.com%2Ftechnology%2FMandelbrot%2Bfather%2Bfractal%2Bgeometry%2Bdies%2F3682961%2Fstory.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABenoit+Mandelbrot" class="Z3988"></span></span> </li> <li id="cite_note-54"><span class="mw-cite-backlink"><b><a href="#cite_ref-54">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation news cs1 cs1-prop-foreign-lang-source"><a rel="nofollow" class="external text" href="http://www.lefigaro.fr/flash-actu/2010/10/16/97001-20101016FILWWW00611-sarkozy-rend-hommage-a-mandelbrot.php">"Sarkozy rend hommage à Mandelbrot"</a> [Sarkozy pays homage to Mandelbrot]. <i><a href="/wiki/Le_Figaro" title="Le Figaro">Le Figaro</a></i> (in French). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20130728181450/http://www.lefigaro.fr/flash-actu/2010/10/16/97001-20101016FILWWW00611-sarkozy-rend-hommage-a-mandelbrot.php">Archived</a> from the original on 28 July 2013<span class="reference-accessdate">. Retrieved <span class="nowrap">17 October</span> 2010</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Le+Figaro&rft.atitle=Sarkozy+rend+hommage+%C3%A0+Mandelbrot&rft_id=http%3A%2F%2Fwww.lefigaro.fr%2Fflash-actu%2F2010%2F10%2F16%2F97001-20101016FILWWW00611-sarkozy-rend-hommage-a-mandelbrot.php&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABenoit+Mandelbrot" class="Z3988"></span></span> </li> <li id="cite_note-55"><span class="mw-cite-backlink"><b><a href="#cite_ref-55">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://www.economist.com/node/17305197">Benoît Mandelbrot's obituary</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20101024200744/http://www.economist.com/node/17305197">Archived</a> 24 October 2010 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>. <i>The Economist</i> (21 October 2010)</span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="Sources">Sources</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Benoit_Mandelbrot&action=edit&section=13" title="Edit section: Sources"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFrameCohen2015" class="citation book cs1">Frame, Michael; Cohen, Nathan (2015). <i>Benoit Mandelbrot: A Life in Many Dimensions</i>. Singapore: World Scientific Publishing Company. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-981-4366-06-9" title="Special:BookSources/978-981-4366-06-9"><bdi>978-981-4366-06-9</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Benoit+Mandelbrot%3A+A+Life+in+Many+Dimensions&rft.place=Singapore&rft.pub=World+Scientific+Publishing+Company&rft.date=2015&rft.isbn=978-981-4366-06-9&rft.aulast=Frame&rft.aufirst=Michael&rft.au=Cohen%2C+Nathan&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABenoit+Mandelbrot" class="Z3988"></span></li></ul> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Benoit_Mandelbrot&action=edit&section=14" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1235681985">.mw-parser-output .side-box{margin:4px 0;box-sizing:border-box;border:1px solid #aaa;font-size:88%;line-height:1.25em;background-color:var(--background-color-interactive-subtle,#f8f9fa);display:flow-root}.mw-parser-output .side-box-abovebelow,.mw-parser-output .side-box-text{padding:0.25em 0.9em}.mw-parser-output .side-box-image{padding:2px 0 2px 0.9em;text-align:center}.mw-parser-output .side-box-imageright{padding:2px 0.9em 2px 0;text-align:center}@media(min-width:500px){.mw-parser-output .side-box-flex{display:flex;align-items:center}.mw-parser-output .side-box-text{flex:1;min-width:0}}@media(min-width:720px){.mw-parser-output .side-box{width:238px}.mw-parser-output .side-box-right{clear:right;float:right;margin-left:1em}.mw-parser-output .side-box-left{margin-right:1em}}</style><style data-mw-deduplicate="TemplateStyles:r1237033735">@media print{body.ns-0 .mw-parser-output .sistersitebox{display:none!important}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}</style><div class="side-box side-box-right plainlinks sistersitebox"><style data-mw-deduplicate="TemplateStyles:r1126788409">.mw-parser-output .plainlist ol,.mw-parser-output .plainlist ul{line-height:inherit;list-style:none;margin:0;padding:0}.mw-parser-output .plainlist ol li,.mw-parser-output .plainlist ul li{margin-bottom:0}</style> <div class="side-box-flex"> <div class="side-box-image"><span class="noviewer" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/30px-Commons-logo.svg.png" decoding="async" width="30" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/45px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/59px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></span></span></div> <div class="side-box-text plainlist">Wikimedia Commons has media related to <a href="https://commons.wikimedia.org/wiki/Beno%C3%AEt_Mandelbrot" class="extiw" title="commons:Benoît Mandelbrot"><span style="font-style:italic; font-weight:bold;">Benoît Mandelbrot</span></a>.</div></div> </div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1235681985"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1237033735"><div class="side-box side-box-right plainlinks sistersitebox"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409"> <div class="side-box-flex"> <div class="side-box-image"><span class="noviewer" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikiquote-logo.svg/34px-Wikiquote-logo.svg.png" decoding="async" width="34" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikiquote-logo.svg/51px-Wikiquote-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikiquote-logo.svg/68px-Wikiquote-logo.svg.png 2x" data-file-width="300" data-file-height="355" /></span></span></div> <div class="side-box-text plainlist">Wikiquote has quotations related to <i><b><a href="https://en.wikiquote.org/wiki/Special:Search/Benoit_Mandelbrot" class="extiw" title="q:Special:Search/Benoit Mandelbrot">Benoit Mandelbrot</a></b></i>.</div></div> </div> <ul><li><a rel="nofollow" class="external text" href="https://mathgenealogy.org/id.php?id=60791">Benoit Mandelbrot</a> at the <a href="/wiki/Mathematics_Genealogy_Project" title="Mathematics Genealogy Project">Mathematics Genealogy Project</a></li> <li><a rel="nofollow" class="external text" href="http://users.math.yale.edu/mandelbrot/">Mandelbrot's page at Yale</a></li> <li><a rel="nofollow" class="external text" href="http://www.ted.com/talks/benoit_mandelbrot_fractals_the_art_of_roughness.html">"Benoît Mandelbrot: Fractals and the art of roughness"</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20140217132541/http://www.ted.com/talks/benoit_mandelbrot_fractals_the_art_of_roughness.html">Archived</a> 17 February 2014 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a> (TED address).</li> <li><a rel="nofollow" class="external text" href="http://video.mit.edu/watch/fractals-in-science-engineering-and-finance-roughness-and-beauty-9893/">Fractals in Science, Engineering and Finance</a> (lecture).</li> <li><a rel="nofollow" class="external text" href="http://video.ft.com/v/63078298001/Why-efficient-markets-collapse-Mandelbrot">FT.com interview</a> on the subject of the financial markets which includes his critique of the "efficient market" hypothesis.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFTaylor2011" class="citation journal cs1">Taylor, Richard (2011). <a rel="nofollow" class="external text" href="https://doi.org/10.1063%2F1.3603925">"Obituaries: Benoit Mandelbrot"</a>. <i><a href="/wiki/Physics_Today" title="Physics Today">Physics Today</a></i>. <b>64</b> (6): 63. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2011PhT....64f..63T">2011PhT....64f..63T</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1063%2F1.3603925">10.1063/1.3603925</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physics+Today&rft.atitle=Obituaries%3A+Benoit+Mandelbrot&rft.volume=64&rft.issue=6&rft.pages=63&rft.date=2011&rft_id=info%3Adoi%2F10.1063%2F1.3603925&rft_id=info%3Abibcode%2F2011PhT....64f..63T&rft.aulast=Taylor&rft.aufirst=Richard&rft_id=https%3A%2F%2Fdoi.org%2F10.1063%252F1.3603925&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABenoit+Mandelbrot" class="Z3988"></span></li> <li><a rel="nofollow" class="external text" href="http://www.webofstories.com/people/benoit.mandelbrot/1">Mandelbrot relates his life story</a> (<a href="/wiki/Web_of_Stories" title="Web of Stories">Web of Stories</a>).</li> <li><a rel="nofollow" class="external text" href="http://dynkincollection.library.cornell.edu/biographies/882">Interview (1 January 1981, Ithaca, NY)</a> held by the <a href="/wiki/Eugene_Dynkin" title="Eugene Dynkin">Eugene Dynkin</a> Collection of Mathematics Interviews, <a href="/wiki/Cornell_University_Library" title="Cornell University Library">Cornell University Library</a>.</li> <li><a rel="nofollow" class="external text" href="https://www.youtube.com/watch?v=1o5FMTHkLQg">Video animation of Mandelbrot set</a>, zoom factor 10<sup>342</sup>.</li> <li><a rel="nofollow" class="external text" href="https://www.youtube.com/watch?v=82xDvdgrzx0"><span class="plainlinks">Video animation of Mandelbulb</span></a> on <a href="/wiki/YouTube_video_(identifier)" class="mw-redirect" title="YouTube video (identifier)">YouTube</a>, a three-dimensional Mandelbrot-set projection.</li> <li><a rel="nofollow" class="external text" href="https://www.youtube.com/watch?v=VB-XUoDqYfs"><span class="plainlinks">Video fly-through an animated Mandelbulb world</span></a> on <a href="/wiki/YouTube_video_(identifier)" class="mw-redirect" title="YouTube video (identifier)">YouTube</a></li> <li><a rel="nofollow" class="external text" href="https://www.imdb.com/name/nm0541707/">Benoit Mandelbrot</a> at <a href="/wiki/IMDb_(identifier)" class="mw-redirect" title="IMDb (identifier)">IMDb</a></li> <li><a rel="nofollow" class="external text" href="https://www.ted.com/speakers/benoit_mandelbrot">Benoit Mandelbrot</a> at <a href="/wiki/TED_(conference)" title="TED (conference)">TED</a> <span class="mw-valign-text-top noprint" typeof="mw:File/Frameless"><a href="https://www.wikidata.org/wiki/Q101740#P2611" title="Edit this at Wikidata"><img alt="Edit this at Wikidata" src="//upload.wikimedia.org/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/10px-OOjs_UI_icon_edit-ltr-progressive.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/15px-OOjs_UI_icon_edit-ltr-progressive.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/20px-OOjs_UI_icon_edit-ltr-progressive.svg.png 2x" data-file-width="20" data-file-height="20" /></a></span></li> <li><a rel="nofollow" class="external text" href="http://www.nasonline.org/publications/biographical-memoirs/memoir-pdfs/mandelbrot-benoit.pdf">Michael Frame, "Benoit B. Mandelbrot", Biographical Memoirs of the National Academy of Sciences (2014)</a></li></ul> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1236075235">.mw-parser-output .navbox{box-sizing:border-box;border:1px solid #a2a9b1;width:100%;clear:both;font-size:88%;text-align:center;padding:1px;margin:1em auto 0}.mw-parser-output .navbox .navbox{margin-top:0}.mw-parser-output .navbox+.navbox,.mw-parser-output .navbox+.navbox-styles+.navbox{margin-top:-1px}.mw-parser-output .navbox-inner,.mw-parser-output .navbox-subgroup{width:100%}.mw-parser-output .navbox-group,.mw-parser-output .navbox-title,.mw-parser-output .navbox-abovebelow{padding:0.25em 1em;line-height:1.5em;text-align:center}.mw-parser-output .navbox-group{white-space:nowrap;text-align:right}.mw-parser-output .navbox,.mw-parser-output .navbox-subgroup{background-color:#fdfdfd}.mw-parser-output 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.navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}html.skin-theme-clientpref-night .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Wolf_Prize_in_Physics" title="Template:Wolf Prize in Physics"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Wolf_Prize_in_Physics" title="Template talk:Wolf Prize in Physics"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Wolf_Prize_in_Physics" title="Special:EditPage/Template:Wolf Prize in Physics"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Laureates_of_the_Wolf_Prize_in_Physics" style="font-size:114%;margin:0 4em">Laureates of the <a href="/wiki/Wolf_Prize_in_Physics" title="Wolf Prize in Physics">Wolf Prize in Physics</a></div></th></tr><tr><th scope="row" class="navbox-group" style="background:#d3d3d3;;width:1%">1970s</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Chien-Shiung_Wu" title="Chien-Shiung Wu">Chien-Shiung Wu</a> (1978)</li> <li><a href="/wiki/George_Uhlenbeck" title="George Uhlenbeck">George Uhlenbeck</a> / <a href="/wiki/Giuseppe_Occhialini" title="Giuseppe Occhialini">Giuseppe Occhialini</a> (1979)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="background:#d3d3d3;;width:1%">1980s</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Michael_Fisher" title="Michael Fisher">Michael Fisher</a> / <a href="/wiki/Leo_Kadanoff" title="Leo Kadanoff">Leo Kadanoff</a> / <a href="/wiki/Kenneth_G._Wilson" title="Kenneth G. Wilson">Kenneth G. Wilson</a> (1980)</li> <li><a href="/wiki/Freeman_Dyson" title="Freeman Dyson">Freeman Dyson</a> / <a href="/wiki/Gerard_%27t_Hooft" title="Gerard 't Hooft">Gerardus 't Hooft</a> / <a href="/wiki/Victor_Weisskopf" title="Victor Weisskopf">Victor Weisskopf</a> (1981)</li> <li><a href="/wiki/Leon_M._Lederman" title="Leon M. Lederman">Leon M. Lederman</a> / <a href="/wiki/Martin_Lewis_Perl" title="Martin Lewis Perl">Martin Lewis Perl</a> (1982)</li> <li><a href="/wiki/Erwin_Hahn" title="Erwin Hahn">Erwin Hahn</a> / <a href="/wiki/Peter_Hirsch" title="Peter Hirsch">Peter Hirsch</a> / <a href="/wiki/Theodore_Maiman" title="Theodore Maiman">Theodore Maiman</a> (1983–84)</li> <li><a href="/wiki/Conyers_Herring" title="Conyers Herring">Conyers Herring</a> / <a href="/wiki/Philippe_Nozi%C3%A8res" title="Philippe Nozières">Philippe Nozières</a> (1984–85)</li> <li><a href="/wiki/Mitchell_Feigenbaum" title="Mitchell Feigenbaum">Mitchell Feigenbaum</a> / <a href="/wiki/Albert_J._Libchaber" title="Albert J. Libchaber">Albert J. Libchaber</a> (1986)</li> <li><a href="/wiki/Herbert_Friedman" title="Herbert Friedman">Herbert Friedman</a> / <a href="/wiki/Bruno_Rossi" title="Bruno Rossi">Bruno Rossi</a> / <a href="/wiki/Riccardo_Giacconi" title="Riccardo Giacconi">Riccardo Giacconi</a> (1987)</li> <li><a href="/wiki/Roger_Penrose" title="Roger Penrose">Roger Penrose</a> / <a href="/wiki/Stephen_Hawking" title="Stephen Hawking">Stephen Hawking</a> (1988)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="background:#d3d3d3;;width:1%">1990s</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Pierre-Gilles_de_Gennes" title="Pierre-Gilles de Gennes">Pierre-Gilles de Gennes</a> / <a href="/wiki/David_J._Thouless" title="David J. Thouless">David J. Thouless</a> (1990)</li> <li><a href="/wiki/Maurice_Goldhaber" title="Maurice Goldhaber">Maurice Goldhaber</a> / <a href="/wiki/Valentine_Telegdi" title="Valentine Telegdi">Valentine Telegdi</a> (1991)</li> <li><a href="/wiki/Joseph_Hooton_Taylor_Jr." title="Joseph Hooton Taylor Jr.">Joseph H. Taylor Jr.</a> (1992)</li> <li><a class="mw-selflink selflink">Benoît Mandelbrot</a> (1993)</li> <li><a href="/wiki/Vitaly_Ginzburg" title="Vitaly Ginzburg">Vitaly Ginzburg</a> / <a href="/wiki/Yoichiro_Nambu" title="Yoichiro Nambu">Yoichiro Nambu</a> (1994–95)</li> <li><a href="/wiki/John_Archibald_Wheeler" title="John Archibald Wheeler">John Wheeler</a> (1996–97)</li> <li><a href="/wiki/Yakir_Aharonov" title="Yakir Aharonov">Yakir Aharonov</a> / <a href="/wiki/Michael_Berry_(physicist)" title="Michael Berry (physicist)">Michael Berry</a> (1998)</li> <li><a href="/wiki/Dan_Shechtman" title="Dan Shechtman">Dan Shechtman</a> (1999)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="background:#d3d3d3;;width:1%">2000s</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Raymond_Davis_Jr." title="Raymond Davis Jr.">Raymond Davis Jr.</a> / <a href="/wiki/Masatoshi_Koshiba" title="Masatoshi Koshiba">Masatoshi Koshiba</a> (2000)</li> <li><a href="/wiki/Bertrand_Halperin" title="Bertrand Halperin">Bertrand Halperin</a> / <a href="/wiki/Anthony_James_Leggett" title="Anthony James Leggett">Anthony Leggett</a> (2002–03)</li> <li><a href="/wiki/Robert_Brout" title="Robert Brout">Robert Brout</a> / <a href="/wiki/Fran%C3%A7ois_Englert" title="François Englert">François Englert</a> / <a href="/wiki/Peter_Higgs" title="Peter Higgs">Peter Higgs</a> (2004)</li> <li><a href="/wiki/Daniel_Kleppner" title="Daniel Kleppner">Daniel Kleppner</a> (2005)</li> <li><a href="/wiki/Albert_Fert" title="Albert Fert">Albert Fert</a> / <a href="/wiki/Peter_Gr%C3%BCnberg" title="Peter Grünberg">Peter Grünberg</a> (2006–07)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="background:#d3d3d3;;width:1%">2010s</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/John_Clauser" title="John Clauser">John F. Clauser</a> / <a href="/wiki/Alain_Aspect" title="Alain Aspect">Alain Aspect</a> / <a href="/wiki/Anton_Zeilinger" title="Anton Zeilinger">Anton Zeilinger</a> (2010)</li> <li><a href="/wiki/Maximilian_Haider" title="Maximilian Haider">Maximilian Haider</a> / <a href="/wiki/Harald_Rose" title="Harald Rose">Harald Rose</a> / <a href="/wiki/Knut_Urban" title="Knut Urban">Knut Urban</a> (2011)</li> <li><a href="/wiki/Jacob_Bekenstein" title="Jacob Bekenstein">Jacob Bekenstein</a> (2012)</li> <li><a href="/wiki/Peter_Zoller" title="Peter Zoller">Peter Zoller</a> / <a href="/wiki/Juan_Ignacio_Cirac_Sasturain" title="Juan Ignacio Cirac Sasturain">Juan Ignacio Cirac</a> (2013)</li> <li><a href="/wiki/James_Bjorken" title="James Bjorken">James D. Bjorken</a> / <a href="/wiki/Robert_Kirshner" title="Robert Kirshner">Robert P. Kirshner</a> (2015)</li> <li><a href="/wiki/Yoseph_Imry" title="Yoseph Imry">Yoseph Imry</a> (2016)</li> <li><a href="/wiki/Michel_Mayor" title="Michel Mayor">Michel Mayor</a> / <a href="/wiki/Didier_Queloz" title="Didier Queloz">Didier Queloz</a> (2017)</li> <li><a href="/wiki/Charles_H._Bennett_(physicist)" title="Charles H. Bennett (physicist)">Charles H. Bennett</a> / <a href="/wiki/Gilles_Brassard" title="Gilles Brassard">Gilles Brassard</a> (2018)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="background:#d3d3d3;;width:1%">2020s</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Rafi_Bistritzer" title="Rafi Bistritzer">Rafi Bistritzer</a> / <a href="/wiki/Pablo_Jarillo-Herrero" title="Pablo Jarillo-Herrero">Pablo Jarillo-Herrero</a> / <a href="/wiki/Allan_H._MacDonald" title="Allan H. MacDonald">Allan H. MacDonald</a> (2020)</li> <li><a href="/wiki/Giorgio_Parisi" title="Giorgio Parisi">Giorgio Parisi</a> (2021)</li> <li><a href="/wiki/Anne_L%27Huillier" title="Anne L'Huillier">Anne L'Huillier</a> / <a href="/wiki/Paul_Corkum" title="Paul Corkum">Paul Corkum</a> / <a href="/wiki/Ferenc_Krausz" title="Ferenc Krausz">Ferenc Krausz</a> (2022)</li> <li><a href="/wiki/Martin_Rees" title="Martin Rees">Martin Rees</a> (2024)</li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="2" style="background:#d3d3d3;"><div> <ul><li><a href="/wiki/Wolf_Prize_in_Agriculture" title="Wolf Prize in Agriculture">Agriculture</a></li> <li><a href="/wiki/Wolf_Prize_in_Arts" title="Wolf Prize in Arts">Arts</a></li> <li><a href="/wiki/Wolf_Prize_in_Chemistry" title="Wolf Prize in Chemistry">Chemistry</a></li> <li><a href="/wiki/Wolf_Prize_in_Mathematics" title="Wolf Prize in Mathematics">Mathematics</a></li> <li><a href="/wiki/Wolf_Prize_in_Medicine" title="Wolf Prize in Medicine">Medicine</a></li> <li><b><a href="/wiki/Wolf_Prize_in_Physics" title="Wolf Prize in Physics">Physics</a></b></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox" aria-labelledby="Japan_Prize_recipients" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Japan_Prize" title="Template:Japan Prize"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Japan_Prize" title="Template talk:Japan Prize"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Japan_Prize" title="Special:EditPage/Template:Japan Prize"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Japan_Prize_recipients" style="font-size:114%;margin:0 4em"><a href="/wiki/Japan_Prize" title="Japan Prize">Japan Prize</a> recipients</div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">1980s</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/John_R._Pierce" title="John R. Pierce">John R. Pierce</a> / <a href="/wiki/Ephraim_Katchalski-Katzir" class="mw-redirect" title="Ephraim Katchalski-Katzir">Ephraim Katchalski-Katzir</a> (1985)</li> <li><a href="/wiki/David_Turnbull_(materials_scientist)" title="David Turnbull (materials scientist)">David Turnbull</a> / <a href="/wiki/Willem_J._Kolff" class="mw-redirect" title="Willem J. Kolff">Willem J. Kolff</a> (1986)</li> <li><a href="/wiki/Henry_Beachell" title="Henry Beachell">Henry Beachell</a> / <a href="/wiki/Gurdev_Khush" title="Gurdev Khush">Gurdev Khush</a> / <a href="/wiki/Theodore_Maiman" title="Theodore Maiman">Theodore Maiman</a> (1987)</li> <li><a href="/wiki/Georges_Vendryes" title="Georges Vendryes">Georges Vendryes</a> / <a href="/wiki/Donald_Henderson" title="Donald Henderson">Donald Henderson</a> / <a href="/wiki/Isao_Arita" title="Isao Arita">Isao Arita</a> / <a href="/wiki/Frank_Fenner" title="Frank Fenner">Frank Fenner</a> / <a href="/wiki/Luc_Montagnier" title="Luc Montagnier">Luc Montagnier</a> / <a href="/wiki/Robert_Gallo" title="Robert Gallo">Robert Gallo</a> (1988)</li> <li><a href="/wiki/Frank_Sherwood_Rowland" class="mw-redirect" title="Frank Sherwood Rowland">Frank Sherwood Rowland</a> / <a href="/wiki/Elias_James_Corey" title="Elias James Corey">Elias James Corey</a> (1989)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">1990s</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Marvin_Minsky" title="Marvin Minsky">Marvin Minsky</a> / <a href="/wiki/W._Jason_Morgan" title="W. Jason Morgan">W. Jason Morgan</a> / <a href="/wiki/Dan_McKenzie_(geophysicist)" title="Dan McKenzie (geophysicist)">Dan McKenzie</a> / <a href="/wiki/Xavier_Le_Pichon" title="Xavier Le Pichon">Xavier Le Pichon</a> (1990)</li> <li><a href="/wiki/Jacques-Louis_Lions" title="Jacques-Louis Lions">Jacques-Louis Lions</a> / <a href="/wiki/John_J._Wild" title="John J. Wild">John J. Wild</a> (1991)</li> <li><a href="/wiki/Gerhard_Ertl" title="Gerhard Ertl">Gerhard Ertl</a> / <a href="/wiki/Ernest_John_Christopher_Polge" class="mw-redirect" title="Ernest John Christopher Polge">Ernest John Christopher Polge</a> (1992)</li> <li><a href="/wiki/Frank_Press" title="Frank Press">Frank Press</a> / <a href="/wiki/Kary_B._Mullis" class="mw-redirect" title="Kary B. Mullis">Kary B. Mullis</a> (1993)</li> <li><a href="/wiki/Bill_Pickering_(rocket_scientist)" title="Bill Pickering (rocket scientist)">William Hayward Pickering</a> / <a href="/wiki/Arvid_Carlsson" title="Arvid Carlsson">Arvid Carlsson</a> (1994)</li> <li><a href="/wiki/Nick_Holonyak" title="Nick Holonyak">Nick Holonyak</a> Jr. / <a href="/wiki/Edward_F._Knipling" title="Edward F. Knipling">Edward F. Knipling</a> (1995)</li> <li><a href="/wiki/Charles_K._Kao" title="Charles K. Kao">Charles K. Kao</a> / <a href="/wiki/Masao_Ito" title="Masao Ito">Masao Ito</a> (1996)</li> <li><a href="/wiki/Takashi_Sugimura" title="Takashi Sugimura">Takashi Sugimura</a> / <a href="/wiki/Bruce_Ames" title="Bruce Ames">Bruce Ames</a> / <a href="/wiki/Joseph_Engelberger" title="Joseph Engelberger">Joseph Engelberger</a> / <a href="/wiki/Hiroyuki_Yoshikawa" title="Hiroyuki Yoshikawa">Hiroyuki Yoshikawa</a> (1997)</li> <li><a href="/wiki/Leo_Esaki" title="Leo Esaki">Leo Esaki</a> / <a href="/wiki/Jozef_Schell" title="Jozef Schell">Jozef Schell</a> / <a href="/wiki/Marc_Van_Montagu" title="Marc Van Montagu">Marc Van Montagu</a> (1998)</li> <li><a href="/wiki/W._Wesley_Peterson" title="W. Wesley Peterson">W. Wesley Peterson</a> / <a href="/wiki/Jack_L._Strominger" title="Jack L. Strominger">Jack L. Strominger</a> / <a href="/wiki/Don_Craig_Wiley" title="Don Craig Wiley">Don Craig Wiley</a> (1999)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">2000s</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Ian_McHarg" title="Ian McHarg">Ian McHarg</a> / <a href="/wiki/Kimishige_Ishizaka" title="Kimishige Ishizaka">Kimishige Ishizaka</a> (2000)</li> <li><a href="/wiki/John_B._Goodenough" title="John B. Goodenough">John B. Goodenough</a> / <a href="/wiki/Timothy_R._Parsons" title="Timothy R. Parsons">Timothy R. Parsons</a> (2001)</li> <li><a href="/wiki/Tim_Berners-Lee" title="Tim Berners-Lee">Tim Berners-Lee</a> / <a href="/wiki/Anne_McLaren" title="Anne McLaren">Anne McLaren</a> / <a href="/wiki/Andrzej_Tarkowski" title="Andrzej Tarkowski">Andrzej Tarkowski</a> (2002)</li> <li><a class="mw-selflink selflink">Benoit Mandelbrot</a> / <a href="/wiki/James_A._Yorke" title="James A. Yorke">James A. Yorke</a> / <a href="/wiki/Seiji_Ogawa" title="Seiji Ogawa">Seiji Ogawa</a> (2003)</li> <li><a href="/wiki/Kenichi_Honda" title="Kenichi Honda">Kenichi Honda</a> / <a href="/wiki/Akira_Fujishima" title="Akira Fujishima">Akira Fujishima</a> / Keith J. Sainsbury / <a href="/wiki/John_Lawton_(biologist)" title="John Lawton (biologist)">John H. Lawton</a> (2004)</li> <li><a href="/wiki/Makoto_Nagao" title="Makoto Nagao">Makoto Nagao</a> / <a href="/wiki/Masatoshi_Takeichi" title="Masatoshi Takeichi">Masatoshi Takeichi</a> / <a href="/wiki/Erkki_Ruoslahti" title="Erkki Ruoslahti">Erkki Ruoslahti</a> (2005)</li> <li><a href="/wiki/John_Houghton_(physicist)" title="John Houghton (physicist)">John Houghton</a> / <a href="/wiki/Akira_Endo_(biochemist)" title="Akira Endo (biochemist)">Akira Endo</a> (2006)</li> <li><a href="/wiki/Albert_Fert" title="Albert Fert">Albert Fert</a> / <a href="/wiki/Peter_Gr%C3%BCnberg" title="Peter Grünberg">Peter Grünberg</a> / <a href="/wiki/Peter_Shaw_Ashton" title="Peter Shaw Ashton">Peter Shaw Ashton</a> (2007)</li> <li><a href="/wiki/Vint_Cerf" title="Vint Cerf">Vint Cerf</a> / <a href="/wiki/Robert_Kahn_(computer_scientist)" title="Robert Kahn (computer scientist)">Robert E. Kahn</a> / <a href="/wiki/Victor_A._McKusick" title="Victor A. McKusick">Victor A. McKusick</a> (2008)</li> <li><a href="/wiki/Dennis_Meadows" title="Dennis Meadows">Dennis Meadows</a> / <a href="/wiki/David_E._Kuhl" title="David E. Kuhl">David E. Kuhl</a> (2009)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">2010s</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Shun-ichi_Iwasaki" title="Shun-ichi Iwasaki">Shun-ichi Iwasaki</a> / <a href="/wiki/Peter_Vitousek" title="Peter Vitousek">Peter Vitousek</a> (2010)</li> <li><a href="/wiki/Ken_Thompson" title="Ken Thompson">Ken Thompson</a> / <a href="/wiki/Dennis_Ritchie" title="Dennis Ritchie">Dennis Ritchie</a> / <a href="/wiki/Tadamitsu_Kishimoto" title="Tadamitsu Kishimoto">Tadamitsu Kishimoto</a> / <a href="/wiki/Toshio_Hirano" title="Toshio Hirano">Toshio Hirano</a> (2011)</li> <li><a href="/wiki/Janet_Rowley" title="Janet Rowley">Janet Rowley</a> / <a href="/wiki/Brian_Druker" title="Brian Druker">Brian Druker</a> / <a href="/wiki/Nicholas_Lydon" title="Nicholas Lydon">Nicholas Lydon</a> / <a href="/wiki/Masato_Sagawa" title="Masato Sagawa">Masato Sagawa</a> (2012)</li> <li><a href="/wiki/C._Grant_Willson" title="C. Grant Willson">C. Grant Willson</a> / <a href="/wiki/Jean_Fr%C3%A9chet" title="Jean Fréchet">Jean Fréchet</a> / <a href="/wiki/J._Frederick_Grassle" title="J. Frederick Grassle">John Frederick Grassle</a> (2013)</li> <li><a href="/wiki/Yasuharu_Suematsu" title="Yasuharu Suematsu">Yasuharu Suematsu</a> / <a href="/wiki/Charles_David_Allis" title="Charles David Allis">C. David Allis</a> (2014)</li> <li><a href="/wiki/Yutaka_Takahasi" title="Yutaka Takahasi">Yutaka Takahasi</a> / <a href="/wiki/Theodore_Friedmann" title="Theodore Friedmann">Theodore Friedmann</a> / <a href="/wiki/Alain_Fischer" title="Alain Fischer">Alain Fischer</a> (2015)</li> <li><a href="/wiki/Hideo_Hosono" title="Hideo Hosono">Hideo Hosono</a> / <a href="/wiki/Steven_D._Tanksley" title="Steven D. Tanksley">Steven D. Tanksley</a> (2016)</li> <li><a href="/wiki/Emmanuelle_Charpentier" title="Emmanuelle Charpentier">Emmanuelle Charpentier</a> / <a href="/wiki/Jennifer_Doudna" title="Jennifer Doudna">Jennifer Doudna</a> / <a href="/wiki/Adi_Shamir" title="Adi Shamir">Adi Shamir</a> (2017)</li> <li><a href="/wiki/Akira_Yoshino" title="Akira Yoshino">Akira Yoshino</a> / <a href="/wiki/Max_Dale_Cooper" title="Max Dale Cooper">Max Dale Cooper</a> / <a href="/wiki/Jacques_Miller" title="Jacques Miller">Jacques Miller</a> (2018)</li> <li><a href="/wiki/Yoshio_Okamoto" title="Yoshio Okamoto">Yoshio Okamoto</a> / <a href="/wiki/Rattan_Lal" title="Rattan Lal">Rattan Lal</a> (2019)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">2020s</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Robert_G._Gallager" title="Robert G. Gallager">Robert G. Gallager</a> / <a href="/wiki/Svante_P%C3%A4%C3%A4bo" title="Svante Pääbo">Svante Pääbo</a> (2020)</li> <li><a href="/wiki/Martin_Green_(professor)" title="Martin Green (professor)">Martin A. Green</a> / <a href="/wiki/Bert_Vogelstein" title="Bert Vogelstein">Bert Vogelstein</a> / <a href="/wiki/Robert_Weinberg_(biologist)" title="Robert Weinberg (biologist)">Robert A. Weinberg</a> (2021)</li> <li><a href="/wiki/Katalin_Karik%C3%B3" title="Katalin Karikó">Katalin Karikó</a> / <a href="/wiki/Drew_Weissman" title="Drew Weissman">Drew Weissman</a> / <a href="/wiki/Christopher_Field" title="Christopher Field">Christopher Field</a> (2022)</li> <li><a href="/wiki/Masataka_Nakazawa" title="Masataka Nakazawa">Masataka Nakazawa</a> / Kazuo Hagimoto / <a href="/wiki/Gero_Miesenb%C3%B6ck" title="Gero Miesenböck">Gero Miesenböck</a> / <a href="/wiki/Karl_Deisseroth" title="Karl Deisseroth">Karl Deisseroth</a> (2023)</li> <li><a href="/wiki/Brian_Hoskins" title="Brian Hoskins">Brian Hoskins</a> / <a href="/wiki/John_Michael_Wallace" title="John Michael Wallace">John Michael Wallace</a> / <a href="/wiki/Ronald_M._Evans" title="Ronald M. Evans">Ronald M. Evans</a> (2024)</li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox" aria-labelledby="Chaos_theory" style="padding:3px"><table class="nowraplinks mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="3"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Chaos_theory" title="Template:Chaos theory"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Chaos_theory" title="Template talk:Chaos theory"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Chaos_theory" title="Special:EditPage/Template:Chaos theory"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Chaos_theory" style="font-size:114%;margin:0 4em"><a href="/wiki/Chaos_theory" title="Chaos theory">Chaos theory</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Concepts</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th id="Core" scope="row" class="navbox-group" style="width:1%"><div style="margin: 10px 0px">Core</div></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Attractor" title="Attractor">Attractor</a></li> <li><a href="/wiki/Bifurcation_theory" title="Bifurcation theory">Bifurcation</a></li> <li><a href="/wiki/Fractal" title="Fractal">Fractal</a></li> <li><a href="/wiki/Limit_set" title="Limit set">Limit set</a></li> <li><a href="/wiki/Lyapunov_exponent" title="Lyapunov exponent">Lyapunov exponent</a></li> <li><a href="/wiki/Orbit_(dynamics)" title="Orbit (dynamics)">Orbit</a></li> <li><a href="/wiki/Periodic_point" title="Periodic point">Periodic point</a></li> <li><a href="/wiki/Phase_space" title="Phase space">Phase space</a></li></ul> </div></td></tr><tr><td colspan="2" class="navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Anosov_diffeomorphism" title="Anosov diffeomorphism">Anosov diffeomorphism</a></li> <li><a href="/wiki/Arnold_tongue" title="Arnold tongue">Arnold tongue</a></li> <li><a href="/wiki/Axiom_A" title="Axiom A">axiom A dynamical system</a></li> <li><a href="/wiki/Bifurcation_diagram" title="Bifurcation diagram">Bifurcation diagram</a></li> <li><a href="/wiki/Box-counting_dimension" class="mw-redirect" title="Box-counting dimension">Box-counting dimension</a></li> <li><a href="/wiki/Correlation_dimension" title="Correlation dimension">Correlation dimension</a></li> <li><a href="/wiki/Conservative_system" title="Conservative system">Conservative system</a></li> <li><a href="/wiki/Ergodicity" title="Ergodicity">Ergodicity</a></li> <li><a href="/wiki/False_nearest_neighbors" class="mw-redirect" title="False nearest neighbors">False nearest neighbors</a></li> <li><a href="/wiki/Hausdorff_dimension" title="Hausdorff dimension">Hausdorff dimension</a></li> <li><a href="/wiki/Invariant_measure" title="Invariant measure">Invariant measure</a></li> <li><a href="/wiki/Lyapunov_stability" title="Lyapunov stability">Lyapunov stability</a></li> <li><a href="/wiki/Measure-preserving_dynamical_system" title="Measure-preserving dynamical system">Measure-preserving dynamical system</a></li> <li><a href="/wiki/Mixing_(mathematics)" title="Mixing (mathematics)">Mixing</a></li> <li><a href="/wiki/Poincar%C3%A9_section" class="mw-redirect" title="Poincaré section">Poincaré section</a></li> <li><a href="/wiki/Recurrence_plot" title="Recurrence plot">Recurrence plot</a></li> <li><a href="/wiki/SRB_measure" class="mw-redirect" title="SRB measure">SRB measure</a></li> <li><a href="/wiki/Stable_manifold" title="Stable manifold">Stable manifold</a></li> <li><a href="/wiki/Topological_conjugacy" title="Topological conjugacy">Topological conjugacy</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><div style="margin: 10px 0px">Theorems</div></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Ergodic_theory#Ergodic_theorems" title="Ergodic theory">Ergodic theorem</a></li> <li><a href="/wiki/Liouville%27s_theorem_(Hamiltonian)" title="Liouville's theorem (Hamiltonian)">Liouville's theorem</a></li> <li><a href="/wiki/Krylov%E2%80%93Bogolyubov_theorem" title="Krylov–Bogolyubov theorem">Krylov–Bogolyubov theorem</a></li> <li><a href="/wiki/Poincar%C3%A9%E2%80%93Bendixson_theorem" title="Poincaré–Bendixson theorem">Poincaré–Bendixson theorem</a></li> <li><a href="/wiki/Poincar%C3%A9_recurrence_theorem" title="Poincaré recurrence theorem">Poincaré recurrence theorem</a></li> <li><a href="/wiki/Stable_manifold_theorem" title="Stable manifold theorem">Stable manifold theorem</a></li> <li><a href="/wiki/Takens%27s_theorem" title="Takens's theorem">Takens's theorem</a></li></ul> </div></td></tr></tbody></table><div></div></td><td class="noviewer navbox-image" rowspan="6" style="width:1px;padding:0 0 0 2px"><div><span typeof="mw:File"><a href="/wiki/File:C%C3%B4ne_textileII.png" class="mw-file-description" title="Conus textile shell"><img alt="Conus textile shell" src="//upload.wikimedia.org/wikipedia/commons/thumb/a/ae/C%C3%B4ne_textileII.png/100px-C%C3%B4ne_textileII.png" decoding="async" width="100" height="180" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/ae/C%C3%B4ne_textileII.png/150px-C%C3%B4ne_textileII.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/ae/C%C3%B4ne_textileII.png/200px-C%C3%B4ne_textileII.png 2x" data-file-width="2344" data-file-height="4211" /></a></span> <p><br /> </p> <span typeof="mw:File"><a href="/wiki/File:Circle_map_poincare_recurrence.jpeg" class="mw-file-description" title="Circle map with black Arnold tongues"><img alt="Circle map with black Arnold tongues" src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1e/Circle_map_poincare_recurrence.jpeg/100px-Circle_map_poincare_recurrence.jpeg" decoding="async" width="100" height="200" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1e/Circle_map_poincare_recurrence.jpeg/150px-Circle_map_poincare_recurrence.jpeg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1e/Circle_map_poincare_recurrence.jpeg/200px-Circle_map_poincare_recurrence.jpeg 2x" data-file-width="450" data-file-height="900" /></a></span></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Theoretical<br />branches</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Bifurcation_theory" title="Bifurcation theory">Bifurcation theory</a></li> <li><a href="/wiki/Control_of_chaos" title="Control of chaos">Control of chaos</a></li> <li><a href="/wiki/Dynamical_system" title="Dynamical system">Dynamical system</a></li> <li><a href="/wiki/Ergodic_theory" title="Ergodic theory">Ergodic theory</a></li> <li><a href="/wiki/Quantum_chaos" title="Quantum chaos">Quantum chaos</a></li> <li><a href="/wiki/Stability_theory" title="Stability theory">Stability theory</a></li> <li><a href="/wiki/Synchronization_of_chaos" title="Synchronization of chaos">Synchronization of chaos</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Chaotic<br />maps (<a href="/wiki/List_of_chaotic_maps" title="List of chaotic maps">list</a>)</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><div style="margin: 10px 0px">Discrete</div></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Arnold%27s_cat_map" title="Arnold's cat map">Arnold's cat map</a></li> <li><a href="/wiki/Baker%27s_map" title="Baker's map">Baker's map</a></li> <li><a href="/wiki/Complex_quadratic_polynomial" title="Complex quadratic polynomial">Complex quadratic map</a></li> <li><a href="/wiki/Coupled_map_lattice" title="Coupled map lattice">Coupled map lattice</a></li> <li><a href="/wiki/Duffing_map" title="Duffing map">Duffing map</a></li> <li><a href="/wiki/Dyadic_transformation" title="Dyadic transformation">Dyadic transformation</a></li> <li><a href="/wiki/Dynamical_billiards" title="Dynamical billiards">Dynamical billiards</a> <ul><li><a href="/wiki/Outer_billiards" title="Outer billiards">outer</a></li></ul></li> <li><a href="/wiki/Exponential_map_(discrete_dynamical_systems)" title="Exponential map (discrete dynamical systems)">Exponential map</a></li> <li><a href="/wiki/Gauss_iterated_map" title="Gauss iterated map">Gauss map</a></li> <li><a href="/wiki/Gingerbreadman_map" title="Gingerbreadman map">Gingerbreadman map</a></li> <li><a href="/wiki/H%C3%A9non_map" title="Hénon map">Hénon map</a></li> <li><a href="/wiki/Horseshoe_map" title="Horseshoe map">Horseshoe map</a></li> <li><a href="/wiki/Ikeda_map" title="Ikeda map">Ikeda map</a></li> <li><a href="/wiki/Interval_exchange_transformation" title="Interval exchange transformation">Interval exchange map</a></li> <li><a href="/wiki/Irrational_rotation" title="Irrational rotation">Irrational rotation</a></li> <li><a href="/wiki/Kaplan%E2%80%93Yorke_map" title="Kaplan–Yorke map">Kaplan–Yorke map</a></li> <li><a href="/wiki/Langton%27s_ant" title="Langton's ant">Langton's ant</a></li> <li><a href="/wiki/Logistic_map" title="Logistic map">Logistic map</a></li> <li><a href="/wiki/Standard_map" title="Standard map">Standard map</a></li> <li><a href="/wiki/Tent_map" title="Tent map">Tent map</a></li> <li><a href="/wiki/Tinkerbell_map" title="Tinkerbell map">Tinkerbell map</a></li> <li><a href="/wiki/Zaslavskii_map" title="Zaslavskii map">Zaslavskii map</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><div style="margin: 10px 0px">Continuous</div></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Double_scroll_attractor" class="mw-redirect" title="Double scroll attractor">Double scroll attractor</a></li> <li><a href="/wiki/Duffing_equation" title="Duffing equation">Duffing equation</a></li> <li><a href="/wiki/Lorenz_system" title="Lorenz system">Lorenz system</a></li> <li><a href="/wiki/Lotka%E2%80%93Volterra_equations" title="Lotka–Volterra equations">Lotka–Volterra equations</a></li> <li><a href="/wiki/Mackey%E2%80%93Glass_equations" title="Mackey–Glass equations">Mackey–Glass equations</a></li> <li><a href="/wiki/Rabinovich%E2%80%93Fabrikant_equations" title="Rabinovich–Fabrikant equations">Rabinovich–Fabrikant equations</a></li> <li><a href="/wiki/R%C3%B6ssler_attractor" title="Rössler attractor">Rössler attractor</a></li> <li><a href="/wiki/Three-body_problem" title="Three-body problem">Three-body problem</a></li> <li><a href="/wiki/Van_der_Pol_oscillator" title="Van der Pol oscillator">Van der Pol oscillator</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Physical<br />systems</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Chua%27s_circuit" title="Chua's circuit">Chua's circuit</a></li> <li><a href="/wiki/Rayleigh%E2%80%93B%C3%A9nard_convection" title="Rayleigh–Bénard convection">Convection</a></li> <li><a href="/wiki/Double_pendulum" title="Double pendulum">Double pendulum</a></li> <li><a href="/wiki/Elastic_pendulum" title="Elastic pendulum">Elastic pendulum</a></li> <li><a href="/wiki/Fermi%E2%80%93Pasta%E2%80%93Ulam%E2%80%93Tsingou_problem" title="Fermi–Pasta–Ulam–Tsingou problem">FPUT problem</a></li> <li><a href="/wiki/H%C3%A9non%E2%80%93Heiles_system" title="Hénon–Heiles system">Hénon–Heiles system</a></li> <li><a href="/wiki/Kicked_rotator" title="Kicked rotator">Kicked rotator</a></li> <li><a href="/wiki/Multiscroll_attractor" title="Multiscroll attractor">Multiscroll attractor</a></li> <li><a href="/wiki/Population_dynamics" title="Population dynamics">Population dynamics</a></li> <li><a href="/wiki/Swinging_Atwood%27s_machine" title="Swinging Atwood's machine">Swinging Atwood's machine</a></li> <li><a href="/wiki/Tilt-A-Whirl" title="Tilt-A-Whirl">Tilt-A-Whirl</a></li> <li><a href="/wiki/Weather_forecasting" title="Weather forecasting">Weather</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Chaos<br />theorists</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Michael_Berry_(physicist)" title="Michael Berry (physicist)">Michael Berry</a></li> <li><a href="/wiki/Rufus_Bowen" title="Rufus Bowen">Rufus Bowen</a></li> <li><a href="/wiki/Mary_Cartwright" title="Mary Cartwright">Mary Cartwright</a></li> <li><a href="/wiki/Chen_Guanrong" title="Chen Guanrong">Chen Guanrong</a></li> <li><a href="/wiki/Leon_O._Chua" title="Leon O. Chua">Leon O. Chua</a></li> <li><a href="/wiki/Mitchell_Feigenbaum" title="Mitchell Feigenbaum">Mitchell Feigenbaum</a></li> <li><a href="/wiki/Peter_Grassberger" title="Peter Grassberger">Peter Grassberger</a></li> <li><a href="/wiki/Celso_Grebogi" title="Celso Grebogi">Celso Grebogi</a></li> <li><a href="/wiki/Martin_Gutzwiller" title="Martin Gutzwiller">Martin Gutzwiller</a></li> <li><a href="/wiki/Brosl_Hasslacher" title="Brosl Hasslacher">Brosl Hasslacher</a></li> <li><a href="/wiki/Michel_H%C3%A9non" title="Michel Hénon">Michel Hénon</a></li> <li><a href="/wiki/Svetlana_Jitomirskaya" title="Svetlana Jitomirskaya">Svetlana Jitomirskaya</a></li> <li><a href="/wiki/Bryna_Kra" title="Bryna Kra">Bryna Kra</a></li> <li><a href="/wiki/Edward_Norton_Lorenz" title="Edward Norton Lorenz">Edward Norton Lorenz</a></li> <li><a href="/wiki/Aleksandr_Lyapunov" title="Aleksandr Lyapunov">Aleksandr Lyapunov</a></li> <li><a class="mw-selflink selflink">Benoît Mandelbrot</a></li> <li><a href="/wiki/Hee_Oh" title="Hee Oh">Hee Oh</a></li> <li><a href="/wiki/Edward_Ott" title="Edward Ott">Edward Ott</a></li> <li><a href="/wiki/Henri_Poincar%C3%A9" title="Henri Poincaré">Henri Poincaré</a></li> <li><a href="/wiki/Itamar_Procaccia" title="Itamar Procaccia">Itamar Procaccia</a></li> <li><a href="/wiki/Mary_Rees" title="Mary Rees">Mary Rees</a></li> <li><a href="/wiki/Otto_R%C3%B6ssler" title="Otto Rössler">Otto Rössler</a></li> <li><a href="/wiki/David_Ruelle" title="David Ruelle">David Ruelle</a></li> <li><a href="/wiki/Caroline_Series" title="Caroline Series">Caroline Series</a></li> <li><a href="/wiki/Yakov_Sinai" title="Yakov Sinai">Yakov Sinai</a></li> <li><a href="/wiki/Oleksandr_Mykolayovych_Sharkovsky" class="mw-redirect" title="Oleksandr Mykolayovych Sharkovsky">Oleksandr Mykolayovych Sharkovsky</a></li> <li><a href="/wiki/Nina_Snaith" title="Nina Snaith">Nina Snaith</a></li> <li><a href="/wiki/Floris_Takens" title="Floris Takens">Floris Takens</a></li> <li><a href="/wiki/Audrey_Terras" title="Audrey Terras">Audrey Terras</a></li> <li><a href="/wiki/Mary_Tsingou" title="Mary Tsingou">Mary Tsingou</a></li> <li><a href="/wiki/Marcelo_Viana" title="Marcelo Viana">Marcelo Viana</a></li> <li><a href="/wiki/Amie_Wilkinson" title="Amie Wilkinson">Amie Wilkinson</a></li> <li><a href="/wiki/James_A._Yorke" title="James A. Yorke">James A. Yorke</a></li> <li><a href="/wiki/Lai-Sang_Young" title="Lai-Sang Young">Lai-Sang Young</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Related<br />articles</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Butterfly_effect" title="Butterfly effect">Butterfly effect</a></li> <li><a href="/wiki/Complexity" title="Complexity">Complexity</a></li> <li><a href="/wiki/Edge_of_chaos" title="Edge of chaos">Edge of chaos</a></li> <li><a href="/wiki/Predictability" title="Predictability">Predictability</a></li> <li><a href="/wiki/Santa_Fe_Institute" title="Santa Fe Institute">Santa Fe Institute</a></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox" aria-labelledby="Fractals" style="padding:3px"><table class="nowraplinks mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Fractals" title="Template:Fractals"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Fractals" title="Template talk:Fractals"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Fractals" title="Special:EditPage/Template:Fractals"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Fractals" style="font-size:114%;margin:0 4em"><a href="/wiki/Fractal" title="Fractal">Fractals</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Characteristics</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Fractal_dimension" title="Fractal dimension">Fractal dimensions</a> <ul><li><a href="/wiki/Assouad_dimension" title="Assouad dimension">Assouad</a></li> <li><a href="/wiki/Minkowski%E2%80%93Bouligand_dimension" title="Minkowski–Bouligand dimension">Box-counting</a> <ul><li><a href="/wiki/Higuchi_dimension" title="Higuchi dimension">Higuchi</a></li></ul></li> <li><a href="/wiki/Correlation_dimension" title="Correlation dimension">Correlation</a></li> <li><a href="/wiki/Hausdorff_dimension" title="Hausdorff dimension">Hausdorff</a></li> <li><a href="/wiki/Packing_dimension" title="Packing dimension">Packing</a></li> <li><a href="/wiki/Lebesgue_covering_dimension" title="Lebesgue covering dimension">Topological</a></li></ul></li> <li><a href="/wiki/Recursion" title="Recursion">Recursion</a></li> <li><a href="/wiki/Self-similarity" title="Self-similarity">Self-similarity</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Iterated_function_system" title="Iterated function system">Iterated function <br />system</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Barnsley_fern" title="Barnsley fern">Barnsley fern</a></li> <li><a href="/wiki/Cantor_set" title="Cantor set">Cantor set</a></li> <li><a href="/wiki/Koch_snowflake" title="Koch snowflake">Koch snowflake</a></li> <li><a href="/wiki/Menger_sponge" title="Menger sponge">Menger sponge</a></li> <li><a href="/wiki/Sierpi%C5%84ski_carpet" title="Sierpiński carpet">Sierpiński carpet</a></li> <li><a href="/wiki/Sierpi%C5%84ski_triangle" title="Sierpiński triangle">Sierpiński triangle</a></li> <li><a href="/wiki/Apollonian_gasket" title="Apollonian gasket">Apollonian gasket</a></li> <li><a href="/wiki/Fibonacci_word_fractal" title="Fibonacci word fractal">Fibonacci word</a></li> <li><a href="/wiki/Space-filling_curve" title="Space-filling curve">Space-filling curve</a> <ul><li><a href="/wiki/Blancmange_curve" title="Blancmange curve">Blancmange curve</a></li> <li><a href="/wiki/De_Rham_curve" title="De Rham curve">De Rham curve</a> <ul><li><a href="/wiki/Minkowski_sausage" title="Minkowski sausage">Minkowski</a></li></ul></li> <li><a href="/wiki/Dragon_curve" title="Dragon curve">Dragon curve</a></li> <li><a href="/wiki/Hilbert_curve" title="Hilbert curve">Hilbert curve</a></li> <li><a href="/wiki/Koch_snowflake" title="Koch snowflake">Koch curve</a></li> <li><a href="/wiki/L%C3%A9vy_C_curve" title="Lévy C curve">Lévy C curve</a></li> <li><a href="/wiki/Moore_curve" title="Moore curve">Moore curve</a></li> <li><a href="/wiki/Peano_curve" title="Peano curve">Peano curve</a></li> <li><a href="/wiki/Sierpi%C5%84ski_curve" title="Sierpiński curve">Sierpiński curve</a></li> <li><a href="/wiki/Z-order_curve" title="Z-order curve">Z-order curve</a></li></ul></li> <li><a href="/wiki/Fractal_string" title="Fractal string">String</a></li> <li><a href="/wiki/T-square_(fractal)" title="T-square (fractal)">T-square</a></li> <li><a href="/wiki/N-flake" title="N-flake">n-flake</a></li> <li><a href="/wiki/Vicsek_fractal" title="Vicsek fractal">Vicsek fractal</a></li> <li><a href="/wiki/Gosper_curve" title="Gosper curve">Gosper curve</a></li> <li><a href="/wiki/Pythagoras_tree_(fractal)" title="Pythagoras tree (fractal)">Pythagoras tree</a></li> <li><a href="/wiki/Weierstrass_function" title="Weierstrass function">Weierstrass function</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Attractor#Strange_attractor" title="Attractor">Strange attractor</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Multifractal_system" title="Multifractal system">Multifractal system</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/L-system" title="L-system">L-system</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Fractal_canopy" title="Fractal canopy">Fractal canopy</a></li> <li><a href="/wiki/Space-filling_curve" title="Space-filling curve">Space-filling curve</a> <ul><li><a href="/wiki/H_tree" title="H tree">H tree</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Fractal#Common_techniques_for_generating_fractals" title="Fractal">Escape-time <br />fractals</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Burning_Ship_fractal" title="Burning Ship fractal">Burning Ship fractal</a></li> <li><a href="/wiki/Julia_set" title="Julia set">Julia set</a> <ul><li><a href="/wiki/Filled_Julia_set" title="Filled Julia set">Filled</a></li> <li><a href="/wiki/Newton_fractal" title="Newton fractal">Newton fractal</a></li> <li><a href="/wiki/Douady_rabbit" title="Douady rabbit">Douady rabbit</a></li></ul></li> <li><a href="/wiki/Lyapunov_fractal" title="Lyapunov fractal">Lyapunov fractal</a></li> <li><a href="/wiki/Mandelbrot_set" title="Mandelbrot set">Mandelbrot set</a> <ul><li><a href="/wiki/Misiurewicz_point" title="Misiurewicz point">Misiurewicz point</a></li></ul></li> <li><a href="/wiki/Multibrot_set" title="Multibrot set">Multibrot set</a></li> <li><a href="/wiki/Newton_fractal" title="Newton fractal">Newton fractal</a></li> <li><a href="/wiki/Tricorn_(mathematics)" title="Tricorn (mathematics)">Tricorn</a></li> <li><a href="/wiki/Mandelbox" title="Mandelbox">Mandelbox</a></li> <li><a href="/wiki/Mandelbulb" title="Mandelbulb">Mandelbulb</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Rendering_(computer_graphics)" title="Rendering (computer graphics)">Rendering</a> techniques</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Buddhabrot" title="Buddhabrot">Buddhabrot</a></li> <li><a href="/wiki/Orbit_trap" title="Orbit trap">Orbit trap</a></li> <li><a href="/wiki/Pickover_stalk" title="Pickover stalk">Pickover stalk</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Chaos_game" title="Chaos game">Random</a> fractals</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Brownian_motion" title="Brownian motion">Brownian motion</a> <ul><li><a href="/wiki/Diffusion-limited_aggregation" title="Diffusion-limited aggregation">Brownian tree</a></li> <li><a href="/wiki/Brownian_motor" title="Brownian motor">Brownian motor</a></li></ul></li> <li><a href="/wiki/Fractal_landscape" title="Fractal landscape">Fractal landscape</a></li> <li><a href="/wiki/L%C3%A9vy_flight" title="Lévy flight">Lévy flight</a></li> <li><a href="/wiki/Percolation_theory" title="Percolation theory">Percolation theory</a></li> <li><a href="/wiki/Self-avoiding_walk" title="Self-avoiding walk">Self-avoiding walk</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">People</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Michael_Barnsley" title="Michael Barnsley">Michael Barnsley</a></li> <li><a href="/wiki/Georg_Cantor" title="Georg Cantor">Georg Cantor</a></li> <li><a href="/wiki/Bill_Gosper" title="Bill Gosper">Bill Gosper</a></li> <li><a href="/wiki/Felix_Hausdorff" title="Felix Hausdorff">Felix Hausdorff</a></li> <li><a href="/wiki/Desmond_Paul_Henry" title="Desmond Paul Henry">Desmond Paul Henry</a></li> <li><a href="/wiki/Gaston_Julia" title="Gaston Julia">Gaston Julia</a></li> <li><a href="/wiki/Niels_Fabian_Helge_von_Koch" title="Niels Fabian Helge von Koch">Niels Fabian Helge von Koch</a></li> <li><a href="/wiki/Paul_L%C3%A9vy_(mathematician)" title="Paul Lévy (mathematician)">Paul Lévy</a></li> <li><a href="/wiki/Aleksandr_Lyapunov" title="Aleksandr Lyapunov">Aleksandr Lyapunov</a></li> <li><a class="mw-selflink selflink">Benoit Mandelbrot</a></li> <li><a href="/wiki/Hamid_Naderi_Yeganeh" title="Hamid Naderi Yeganeh">Hamid Naderi Yeganeh</a></li> <li><a href="/wiki/Lewis_Fry_Richardson" title="Lewis Fry Richardson">Lewis Fry Richardson</a></li> <li><a href="/wiki/Wac%C5%82aw_Sierpi%C5%84ski" title="Wacław Sierpiński">Wacław Sierpiński</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Coastline_paradox" title="Coastline paradox">Coastline paradox</a></li> <li><a href="/wiki/Fractal_art" title="Fractal art">Fractal art</a></li> <li><a href="/wiki/List_of_fractals_by_Hausdorff_dimension" title="List of fractals by Hausdorff dimension">List of fractals by Hausdorff dimension</a></li> <li><i><a href="/wiki/The_Fractal_Geometry_of_Nature" title="The Fractal Geometry of Nature">The Fractal Geometry of Nature</a></i> (1982 book)</li> <li><i><a href="/wiki/The_Beauty_of_Fractals" title="The Beauty of Fractals">The Beauty of Fractals</a></i> (1986 book)</li> <li><i><a href="/wiki/Chaos:_Making_a_New_Science" title="Chaos: Making a New Science">Chaos: Making a New Science</a></i> (1987 book)</li> <li><a href="/wiki/Kaleidoscope" title="Kaleidoscope">Kaleidoscope</a></li> <li><a href="/wiki/Chaos_theory" title="Chaos theory">Chaos theory</a></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"><style data-mw-deduplicate="TemplateStyles:r1038841319">.mw-parser-output .tooltip-dotted{border-bottom:1px dotted;cursor:help}</style></div><div role="navigation" class="navbox authority-control" aria-labelledby="Authority_control_databases_frameless&#124;text-top&#124;10px&#124;alt=Edit_this_at_Wikidata&#124;link=https&#58;//www.wikidata.org/wiki/Q101740#identifiers&#124;class=noprint&#124;Edit_this_at_Wikidata" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" 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style="width:1%">National</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://d-nb.info/gnd/118974203">Germany</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://id.loc.gov/authorities/n81107154">United States</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://catalogue.bnf.fr/ark:/12148/cb11914221j">France</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://data.bnf.fr/ark:/12148/cb11914221j">BnF data</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://id.ndl.go.jp/auth/ndlna/00448659">Japan</a></span></li><li><span class="uid"><span class="rt-commentedText tooltip tooltip-dotted" title="Mandelbrot, Benoît B."><a rel="nofollow" class="external text" href="https://opac.sbn.it/nome/CFIV074635">Italy</a></span></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://nla.gov.au/anbd.aut-an35685251">Australia</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://aleph.nkp.cz/F/?func=find-c&local_base=aut&ccl_term=ica=xx0012614&CON_LNG=ENG">Czech Republic</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="http://aleph.rsl.ru/F?func=find-b&find_code=SYS&adjacent=Y&local_base=RSL11&request=000135469&CON_LNG=ENG">Russia</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="http://catalogo.bne.es/uhtbin/authoritybrowse.cgi?action=display&authority_id=XX973828">Spain</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="http://id.bnportugal.gov.pt/aut/catbnp/38377">Portugal</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="http://data.bibliotheken.nl/id/thes/p069512167">Netherlands</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://authority.bibsys.no/authority/rest/authorities/html/90065702">Norway</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://kopkatalogs.lv/F?func=direct&local_base=lnc10&doc_number=000058589&P_CON_LNG=ENG">Latvia</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="http://katalog.nsk.hr/F/?func=direct&doc_number=000327195&local_base=nsk10">Croatia</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://catalogue.nlg.gr/cgi-bin/koha/opac-authoritiesdetail.pl?authid=183483">Greece</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://lod.nl.go.kr/resource/KAC201006355">Korea</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" 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href="https://ci.nii.ac.jp/author/DA00187535?l=en">CiNii</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://www.mathgenealogy.org/id.php?id=60791">Mathematics Genealogy Project</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://zbmath.org/authors/?q=ai:mandelbrot.benoit-b">zbMATH</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://dblp.org/pid/04/2558">DBLP</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://mathscinet.ams.org/mathscinet/MRAuthorID/119060">MathSciNet</a></span></li></ul></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">People</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://trove.nla.gov.au/people/1041889">Trove</a></span></li><li><span 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