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Benoît Mandelbrot - Wikipedia

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</div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Benoît 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="Ga naar een artikel in een andere taal. Beschikbaar in 66 talen" > <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 talen</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 – Zwitserduits" lang="gsw" hreflang="gsw" data-title="Benoît Mandelbrot" data-language-autonym="Alemannisch" data-language-local-name="Zwitserduits" 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 – Amhaars" lang="am" hreflang="am" data-title="ማንዴልብሮት" data-language-autonym="አማርኛ" data-language-local-name="Amhaars" class="interlanguage-link-target"><span>አማርኛ</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 – Aragonees" lang="an" hreflang="an" data-title="Benoît Mandelbrot" data-language-autonym="Aragonés" data-language-local-name="Aragonees" class="interlanguage-link-target"><span>Aragonés</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 – Arabisch" lang="ar" hreflang="ar" data-title="بينوا ماندلبروت" data-language-autonym="العربية" data-language-local-name="Arabisch" class="interlanguage-link-target"><span>العربية</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 – Egyptisch Arabisch" lang="arz" hreflang="arz" data-title="بينوا ماندلبروت" data-language-autonym="مصرى" data-language-local-name="Egyptisch Arabisch" class="interlanguage-link-target"><span>مصرى</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 – Asturisch" lang="ast" hreflang="ast" data-title="Benoît Mandelbrot" data-language-autonym="Asturianu" data-language-local-name="Asturisch" 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 – Azerbeidzjaans" lang="az" hreflang="az" data-title="Benua Mandelbrot" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbeidzjaans" 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-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 – Bulgaars" lang="bg" hreflang="bg" data-title="Беноа Манделброт" data-language-autonym="Български" data-language-local-name="Bulgaars" class="interlanguage-link-target"><span>Български</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 – Bengaals" lang="bn" hreflang="bn" data-title="বনোয়া মঁদেলব্রো" data-language-autonym="বাংলা" data-language-local-name="Bengaals" class="interlanguage-link-target"><span>বাংলা</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 – Bosnisch" lang="bs" hreflang="bs" data-title="Benoît Mandelbrot" data-language-autonym="Bosanski" data-language-local-name="Bosnisch" 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 – Catalaans" lang="ca" hreflang="ca" data-title="Benoît Mandelbrot" data-language-autonym="Català" data-language-local-name="Catalaans" 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 – Tsjechisch" lang="cs" hreflang="cs" data-title="Benoît Mandelbrot" data-language-autonym="Čeština" data-language-local-name="Tsjechisch" 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 – Deens" lang="da" hreflang="da" data-title="Benoît Mandelbrot" data-language-autonym="Dansk" data-language-local-name="Deens" 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 – Duits" lang="de" hreflang="de" data-title="Benoît Mandelbrot" data-language-autonym="Deutsch" data-language-local-name="Duits" class="interlanguage-link-target"><span>Deutsch</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 – Grieks" lang="el" hreflang="el" data-title="Μπενουά Μάντελμπροτ" data-language-autonym="Ελληνικά" data-language-local-name="Grieks" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Benoit_Mandelbrot" title="Benoit Mandelbrot – Engels" lang="en" hreflang="en" data-title="Benoit Mandelbrot" data-language-autonym="English" data-language-local-name="Engels" class="interlanguage-link-target"><span>English</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-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Beno%C3%AEt_Mandelbrot" title="Benoît Mandelbrot – Spaans" lang="es" hreflang="es" data-title="Benoît Mandelbrot" data-language-autonym="Español" data-language-local-name="Spaans" class="interlanguage-link-target"><span>Español</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 – Estisch" lang="et" hreflang="et" data-title="Benoît Mandelbrot" data-language-autonym="Eesti" data-language-local-name="Estisch" class="interlanguage-link-target"><span>Eesti</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 – Baskisch" lang="eu" hreflang="eu" data-title="Benoît Mandelbrot" data-language-autonym="Euskara" data-language-local-name="Baskisch" 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 – Perzisch" lang="fa" hreflang="fa" data-title="بنوآ مندلبرات" data-language-autonym="فارسی" data-language-local-name="Perzisch" class="interlanguage-link-target"><span>فارسی</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 – Fins" lang="fi" hreflang="fi" data-title="Benoît Mandelbrot" data-language-autonym="Suomi" data-language-local-name="Fins" class="interlanguage-link-target"><span>Suomi</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 – Frans" lang="fr" hreflang="fr" data-title="Benoît Mandelbrot" data-language-autonym="Français" data-language-local-name="Frans" 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 – Iers" lang="ga" hreflang="ga" data-title="Benoît Mandelbrot" data-language-autonym="Gaeilge" data-language-local-name="Iers" 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 – Galicisch" lang="gl" hreflang="gl" data-title="Benoît Mandelbrot" data-language-autonym="Galego" data-language-local-name="Galicisch" class="interlanguage-link-target"><span>Galego</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 – Hebreeuws" lang="he" hreflang="he" data-title="בנואה מנדלברוט" data-language-autonym="עברית" data-language-local-name="Hebreeuws" class="interlanguage-link-target"><span>עברית</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 – Kroatisch" lang="hr" hreflang="hr" data-title="Benoît Mandelbrot" data-language-autonym="Hrvatski" data-language-local-name="Kroatisch" class="interlanguage-link-target"><span>Hrvatski</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 – Haïtiaans Creools" lang="ht" hreflang="ht" data-title="Benoît Mandelbrot" data-language-autonym="Kreyòl ayisyen" data-language-local-name="Haïtiaans Creools" class="interlanguage-link-target"><span>Kreyòl ayisyen</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 – Hongaars" lang="hu" hreflang="hu" data-title="Benoît Mandelbrot" data-language-autonym="Magyar" data-language-local-name="Hongaars" class="interlanguage-link-target"><span>Magyar</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 – Indonesisch" lang="id" hreflang="id" data-title="Benoît Mandelbrot" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesisch" class="interlanguage-link-target"><span>Bahasa Indonesia</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-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Beno%C3%AEt_Mandelbrot" title="Benoît Mandelbrot – IJslands" lang="is" hreflang="is" data-title="Benoît Mandelbrot" data-language-autonym="Íslenska" data-language-local-name="IJslands" 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 – Italiaans" lang="it" hreflang="it" data-title="Benoît Mandelbrot" data-language-autonym="Italiano" data-language-local-name="Italiaans" class="interlanguage-link-target"><span>Italiano</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 – Japans" 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="Japans" class="interlanguage-link-target"><span>日本語</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 – Kazachs" lang="kk" hreflang="kk" data-title="Мандельброт Бенуа" data-language-autonym="Қазақша" data-language-local-name="Kazachs" class="interlanguage-link-target"><span>Қазақша</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 – Koreaans" lang="ko" hreflang="ko" data-title="브누아 망델브로" data-language-autonym="한국어" data-language-local-name="Koreaans" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Benedictus_Mandelbrot" title="Benedictus Mandelbrot – Latijn" lang="la" hreflang="la" data-title="Benedictus Mandelbrot" data-language-autonym="Latina" data-language-local-name="Latijn" class="interlanguage-link-target"><span>Latina</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 – Luxemburgs" lang="lb" hreflang="lb" data-title="Benoît Mandelbrot" data-language-autonym="Lëtzebuergesch" data-language-local-name="Luxemburgs" 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 – Litouws" lang="lt" hreflang="lt" data-title="Benoit Mandelbrot" data-language-autonym="Lietuvių" data-language-local-name="Litouws" class="interlanguage-link-target"><span>Lietuvių</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 – Lets" lang="lv" hreflang="lv" data-title="Benuā Mandelbrots" data-language-autonym="Latviešu" data-language-local-name="Lets" class="interlanguage-link-target"><span>Latviešu</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 – Malagassisch" lang="mg" hreflang="mg" data-title="Benoît Mandelbrot" data-language-autonym="Malagasy" data-language-local-name="Malagassisch" class="interlanguage-link-target"><span>Malagasy</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 – Nedersaksisch" lang="nds" hreflang="nds" data-title="Benoît Mandelbrot" data-language-autonym="Plattdüütsch" data-language-local-name="Nedersaksisch" class="interlanguage-link-target"><span>Plattdüütsch</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 – Noors - Nynorsk" lang="nn" hreflang="nn" data-title="Benoît Mandelbrot" data-language-autonym="Norsk nynorsk" data-language-local-name="Noors - Nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</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 – Noors - Bokmål" lang="nb" hreflang="nb" data-title="Benoît Mandelbrot" data-language-autonym="Norsk bokmål" data-language-local-name="Noors - Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</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 – Pools" lang="pl" hreflang="pl" data-title="Benoît Mandelbrot" data-language-autonym="Polski" data-language-local-name="Pools" class="interlanguage-link-target"><span>Polski</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 – Pasjtoe" lang="ps" hreflang="ps" data-title="بنوآ منډلبراټ" data-language-autonym="پښتو" data-language-local-name="Pasjtoe" class="interlanguage-link-target"><span>پښتو</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 – Portugees" lang="pt" hreflang="pt" data-title="Benoît Mandelbrot" data-language-autonym="Português" data-language-local-name="Portugees" 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 – Roemeens" lang="ro" hreflang="ro" data-title="Benoît Mandelbrot" data-language-autonym="Română" data-language-local-name="Roemeens" 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 – Russisch" lang="ru" hreflang="ru" data-title="Мандельброт, Бенуа" data-language-autonym="Русский" data-language-local-name="Russisch" class="interlanguage-link-target"><span>Русский</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 – Siciliaans" lang="scn" hreflang="scn" data-title="Benoît Mandelbrot" data-language-autonym="Sicilianu" data-language-local-name="Siciliaans" class="interlanguage-link-target"><span>Sicilianu</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 – Servo-Kroatisch" lang="sh" hreflang="sh" data-title="Benoît Mandelbrot" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Servo-Kroatisch" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</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 – Slowaaks" lang="sk" hreflang="sk" data-title="Benoît Mandelbrot" data-language-autonym="Slovenčina" data-language-local-name="Slowaaks" 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 – Sloveens" lang="sl" hreflang="sl" data-title="Benoît Mandelbrot" data-language-autonym="Slovenščina" data-language-local-name="Sloveens" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Benoit_Mandelbrot" title="Benoit Mandelbrot – Albanees" lang="sq" hreflang="sq" data-title="Benoit Mandelbrot" data-language-autonym="Shqip" data-language-local-name="Albanees" class="interlanguage-link-target"><span>Shqip</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 – Servisch" lang="sr" hreflang="sr" data-title="Беноа Манделброт" data-language-autonym="Српски / srpski" data-language-local-name="Servisch" class="interlanguage-link-target"><span>Српски / srpski</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 – Zweeds" lang="sv" hreflang="sv" data-title="Benoît Mandelbrot" data-language-autonym="Svenska" data-language-local-name="Zweeds" 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 – Turks" lang="tr" hreflang="tr" data-title="Benoit Mandelbrot" data-language-autonym="Türkçe" data-language-local-name="Turks" 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 – Oekraïens" lang="uk" hreflang="uk" data-title="Бенуа Мандельброт" data-language-autonym="Українська" data-language-local-name="Oekraïens" 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 – Vietnamees" lang="vi" hreflang="vi" data-title="Benoît Mandelbrot" data-language-autonym="Tiếng Việt" 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<div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Uiterlijk"> <div id="vector-appearance-pinned-container" class="vector-pinned-container"> <div id="vector-appearance" class="vector-appearance vector-pinnable-element"> <div class="vector-pinnable-header vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">Uiterlijk</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">naar zijbalk verplaatsen</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" 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//upload.wikimedia.org/wikipedia/commons/thumb/7/7b/Mandelbrot_p1130861.jpg/520px-Mandelbrot_p1130861.jpg 2x" data-file-width="2560" data-file-height="1920" /></a><figcaption>Benoît Mandelbrot</figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Bestand:Mandel_zoom_00_mandelbrot_set.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/21/Mandel_zoom_00_mandelbrot_set.jpg/260px-Mandel_zoom_00_mandelbrot_set.jpg" decoding="async" width="260" height="195" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/21/Mandel_zoom_00_mandelbrot_set.jpg/390px-Mandel_zoom_00_mandelbrot_set.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/21/Mandel_zoom_00_mandelbrot_set.jpg/520px-Mandel_zoom_00_mandelbrot_set.jpg 2x" data-file-width="2560" data-file-height="1920" /></a><figcaption>Grafische weergave van de <a href="/wiki/Mandelbrotverzameling" title="Mandelbrotverzameling">Mandelbrotverzameling</a></figcaption></figure> <p><b>Benoît B. Mandelbrot</b> (<a href="/wiki/Warschau" title="Warschau">Warschau</a>, <a href="/wiki/20_november" title="20 november">20 november</a> <a href="/wiki/1924" title="1924">1924</a> - <a href="/wiki/Cambridge_(Massachusetts)" title="Cambridge (Massachusetts)">Cambridge (Massachusetts)</a>, <a href="/wiki/14_oktober" title="14 oktober">14 oktober</a> <a href="/wiki/2010" title="2010">2010</a><sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">&#91;</span>1<span class="cite-bracket">&#93;</span></a></sup>) was een <a href="/wiki/Frankrijk" title="Frankrijk">Frans</a> <a href="/wiki/Wiskundige" title="Wiskundige">wiskundige</a> van <a href="/wiki/Polen" title="Polen">Poolse</a> afkomst. Hij is grotendeels verantwoordelijk voor de huidige interesse in <a href="/wiki/Fractal" title="Fractal">fractals</a> en liet zien dat fractals op een groot aantal verschillende terreinen kunnen worden toegepast, zowel in de wis- als in de natuurkunde. Zijn onderzoek bouwt voort op het werk van <a href="/wiki/Gaston_Maurice_Julia" class="mw-redirect" title="Gaston Maurice Julia">Gaston Maurice Julia</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Leven">Leven</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Beno%C3%AEt_Mandelbrot&amp;veaction=edit&amp;section=1" title="Bewerk dit kopje: Leven" class="mw-editsection-visualeditor"><span>bewerken</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Beno%C3%AEt_Mandelbrot&amp;action=edit&amp;section=1" title="De broncode bewerken van de sectie: Leven"><span>brontekst bewerken</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Mandelbrot werd geboren te <a href="/wiki/Warschau" title="Warschau">Warschau</a> in een intellectueel milieu als zoon van een handelaar in <a href="/wiki/Kleding" title="Kleding">kleding</a>. Zijn moeder was arts en zijn oom <a href="/wiki/Szolem_Mandelbrot" class="mw-redirect" title="Szolem Mandelbrot">Szolem Mandelbrot</a> was een beroemd wiskundige in <a href="/wiki/Parijs" title="Parijs">Parijs</a>. Het gezin verhuisde in <a href="/wiki/1936" title="1936">1936</a> naar Parijs, waar Mandelbrots beide ooms hem met wiskunde lieten kennismaken. </p><p>Mandelbrot volgde het <i>Lycée Rolin</i> in Parijs tot het uitbreken van de <a href="/wiki/Tweede_Wereldoorlog" title="Tweede Wereldoorlog">Tweede Wereldoorlog</a> toen het gezin naar <a href="/wiki/Tulle" title="Tulle">Tulle</a> (<a href="/wiki/Corr%C3%A8ze_(departement)" title="Corrèze (departement)">Corrèze</a>) verhuisde. In <a href="/wiki/1944" title="1944">1944</a> keerde hij terug naar Parijs waar hij aan de <i><a href="/wiki/%C3%89cole_Polytechnique" class="mw-redirect" title="École Polytechnique">École Polytechnique</a></i> studeerde bij Gaston Julia en <a href="/wiki/Paul_L%C3%A9vy" title="Paul Lévy">Paul Lévy</a>. Hij studeerde er in <a href="/wiki/1947" title="1947">1947</a> af. Vervolgens studeerde hij twee jaar <a href="/wiki/Ruimtevaart" title="Ruimtevaart">ruimtewetenschappen</a> aan het <a href="/wiki/California_Institute_of_Technology" title="California Institute of Technology">California Institute of Technology</a> (Caltech). Na zijn terugkeer naar Frankrijk promoveerde hij in <a href="/wiki/1952" title="1952">1952</a> aan de universiteit van Parijs. </p><p>Mandelbrot was van <a href="/wiki/1949" title="1949">1949</a> tot <a href="/wiki/1957" title="1957">1957</a> in dienst bij het <i><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></i> (CNRS). Tijdens deze periode werkte hij een jaar bij het <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</a>, met steun van <a href="/wiki/John_von_Neumann" title="John von Neumann">John von Neumann</a>. In <a href="/wiki/1955" title="1955">1955</a> trouwde hij met Aliette Kagan en verhuisde hij naar Genève. Het echtpaar verhuisde in <a href="/wiki/1958" title="1958">1958</a> naar de <a href="/wiki/Verenigde_Staten" title="Verenigde Staten">Verenigde Staten</a>, waar Mandelbrot bij het <i>Thomas J. Watson Research Centre</i> van <a href="/wiki/IBM" title="IBM">IBM</a> ging werken. Hij bleef de rest van zijn werkzame leven aan IBM verbonden en werd een <i>IBM Fellow</i> en later <i>Fellow Emeritus</i>. </p><p>Vanaf <a href="/wiki/1955" title="1955">1955</a> werkte Mandelbrot op diverse terreinen en publiceerde hij over zeer uiteenlopende zaken, zoals <a href="/wiki/Informatietheorie" title="Informatietheorie">informatietheorie</a>, <a href="/wiki/Economie_(wetenschap)" class="mw-redirect" title="Economie (wetenschap)">economie</a> en <a href="/wiki/Vloeistofdynamica" class="mw-redirect" title="Vloeistofdynamica">vloeistofdynamica</a>. Hij raakte ervan overtuigd dat deze onderwerpen allemaal hetzelfde achterliggende principe hadden, namelijk <a href="/wiki/Recursie" title="Recursie">recursieve structuren</a>. Om deze structuren te beschrijven bedacht Mandelbrot het begrip <i><a href="/wiki/Fractal" title="Fractal">fractal</a></i>. Hij publiceerde zijn ideeën in <i>Les objets fractals, forme, hasard et dimension</i> (<a href="/wiki/1975" title="1975">1975</a>), dat in <a href="/wiki/1977" title="1977">1977</a> in het Engels werd vertaald als <i>Fractals: form, chance and dimension</i>. </p><p>Toen hij in <a href="/wiki/1979" title="1979">1979</a> een verlof van IBM doorbracht als <a href="/wiki/College_(universiteit)" title="College (universiteit)">gastdocent</a> aan <a href="/wiki/Harvard-universiteit" title="Harvard-universiteit">Harvard</a>, begon Mandelbrot fractals te bestuderen die <a href="/wiki/Juliaverzameling" title="Juliaverzameling">Juliaverzamelingen</a> worden genoemd. Deze zijn onveranderlijk bij sommige <a href="/wiki/Transformatie_(wiskunde)" title="Transformatie (wiskunde)">transformaties</a> van <a href="/wiki/Complex_getal" title="Complex getal">complexe getallen</a>. Mandelbrot bouwde voort op onderzoek van Julia en <a href="/wiki/Pierre_Fatou" title="Pierre Fatou">Pierre Fatou</a>, en gebruikte een computer om de Juliaverzamelingen van de vergelijking <i>z</i><sup>2</sup> + <i>c</i> af te beelden. Terwijl hij onderzocht hoe de <a href="/wiki/Topologie" title="Topologie">topologie</a> van deze Juliaverzamelingen afhing van de complexe parameter <i>c</i>, ontdekte hij de <a href="/wiki/Mandelbrotverzameling" title="Mandelbrotverzameling">Mandelbrotverzameling</a>, een fractal die nu zijn naam draagt. </p><p>In <a href="/wiki/1982" title="1982">1982</a> verscheen een uitgebreide en bijgewerkte versie van zijn ideeën in <i>The Fractal Geometry of Nature</i>. Dit invloedrijke werk bracht fractals onder de aandacht van de professionele wiskunde en het grote publiek. </p><p>Nadat hij in <a href="/wiki/1987" title="1987">1987</a> bij IBM werd gepensioneerd ging Mandelbrot aan <a href="/wiki/Yale_University" class="mw-redirect" title="Yale University">Yale University</a> verder, als <i>Sterling Professor of Mathematical Sciences</i>. In <a href="/wiki/2003" title="2003">2003</a> ontving hij de prestigieuze <a href="/wiki/Japanprijs" title="Japanprijs">Japanprijs</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Publicaties_(selectie)"><span id="Publicaties_.28selectie.29"></span>Publicaties (selectie)</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Beno%C3%AEt_Mandelbrot&amp;veaction=edit&amp;section=2" title="Bewerk dit kopje: Publicaties (selectie)" class="mw-editsection-visualeditor"><span>bewerken</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Beno%C3%AEt_Mandelbrot&amp;action=edit&amp;section=2" title="De broncode bewerken van de sectie: Publicaties (selectie)"><span>brontekst bewerken</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><style data-mw-deduplicate="TemplateStyles:r67679320">.mw-parser-output .taalaanduiding{font-family:sans-serif;font-size:85%;cursor:help;color:var(--color-subtle,#555)}.mw-parser-output .taalaanduiding span{border-bottom:1px dotted var(--color-subtle,#555)}</style><span class="taalaanduiding" title="Taal: Frans">(<span>fr</span>) </span> <i>Les Objets fractals. Forme, hasard et dimension</i>, 1973</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r67679320"><span class="taalaanduiding" title="Taal: Engels">(<span>en</span>) </span> <i>The Fractal Geometry of Nature</i>, 1982</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r67679320"><span class="taalaanduiding" title="Taal: Frans">(<span>fr</span>) </span> <i>Fractales, hasard et finance</i>, 1998</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r67679320"><span class="taalaanduiding" title="Taal: Engels">(<span>en</span>) </span> <i>The (Mis)Behaviour of Markets. A Fractal View of Risk, Ruin and Reward</i>, 2004</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r67679320"><span class="taalaanduiding" title="Taal: Engels">(<span>en</span>) </span> <i>The Fractalist. Memoir of a Scientific Maverick</i>, 2012 (postuum)</li></ul> <div class="mw-heading mw-heading2"><h2 id="Externe_links">Externe links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Beno%C3%AEt_Mandelbrot&amp;veaction=edit&amp;section=3" title="Bewerk dit kopje: Externe links" class="mw-editsection-visualeditor"><span>bewerken</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Beno%C3%AEt_Mandelbrot&amp;action=edit&amp;section=3" title="De broncode bewerken van de sectie: Externe links"><span>brontekst bewerken</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="http://archive.wikiwix.com/cache/20110224015218/http://www.math.yale.edu/mandelbrot/">Mandelbrots pagina bij Yale</a> (Engelstalig)</li> <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20101028163539/http://www.ted.com/talks/lang/dut/benoit_mandelbrot_fractals_the_art_of_roughness.html">Video</a> van de lezing van Mandelbrot op <a href="/wiki/TED_(conferentie)" title="TED (conferentie)">TED 2010</a></li></ul> <div class="toccolours appendix" role="presentation" style="font-size:90%; margin:1em 0 -0.5em; clear:both;"> <div><span style="font-weight:bold">Bronnen, noten en/of referenties</span></div> <ul><li><i>The Fractal Geometry of Nature</i>, by Benoît Mandelbrot; W H Freeman &amp; Co, 1982; <a href="/wiki/Speciaal:Boekbronnen/0716711869" class="internal mw-magiclink-isbn">ISBN 0-7167-1186-9</a></li> <li><i>The (Mis)Behavior of Markets: A Fractal View of Risk, Ruin, and Reward</i>, by Benoit Mandelbrot and Richard L. Hudson; Basic Books, 2004; <a href="/wiki/Speciaal:Boekbronnen/0465043550" class="internal mw-magiclink-isbn">ISBN 0-465-04355-0</a></li></ul> <div class="reflist" style="list-style-type: decimal;"><div class="mw-references-wrap"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><a href="#cite_ref-1">↑</a></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://www.nytimes.com/2010/10/17/us/17mandelbrot.html?partner=rss&amp;emc=rss">Benoit Mandelbrot, Mathematician, Dies at 85</a>, NYTimes.com, 16 oktober 2010</span> </li> </ol></div></div> </div> <div class="interProject commons mw-list-item" style="display:none;"><a href="https://commons.wikimedia.org/wiki/Category:Beno%C3%AEt_Mandelbrot#mw-subcategories" class="extiw" title="commons:Category:Benoît Mandelbrot">Mediabestanden</a></div> <div class="interProjectTemplate interProject-groot toccolours" style="display:flex; gap:1em; align-items:center; clear:both; margin:1em 0 -0.5em 0;"> <div style="min-width:max-content;"><span class="noviewer noresize" typeof="mw:File"><a href="/wiki/Bestand:Commons-logo.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/25px-Commons-logo.svg.png" decoding="async" width="25" height="34" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/38px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/50px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></a></span></div> <div>Zie de categorie <i><b><a href="https://commons.wikimedia.org/wiki/Category:Beno%C3%AEt_Mandelbrot#mw-subcategories" class="extiw" title="commons:Category:Benoît Mandelbrot">Benoît Mandelbrot</a></b></i> van <a href="/wiki/Wikimedia_Commons" title="Wikimedia Commons">Wikimedia Commons</a> voor mediabestanden over dit onderwerp.</div> </div> <!-- NewPP limit report Parsed by mw‐web.eqiad.main‐6b6c9bdc8b‐r5vlk Cached time: 20241102160926 Cache expiry: 2592000 Reduced expiry: false Complications: [] CPU time usage: 0.086 seconds Real time usage: 0.126 seconds Preprocessor visited node count: 280/1000000 Post‐expand include size: 3263/2097152 bytes Template argument size: 861/2097152 bytes Highest expansion depth: 10/100 Expensive parser function count: 0/500 Unstrip recursion depth: 0/20 Unstrip post‐expand size: 2089/5000000 bytes Lua time usage: 0.005/10.000 seconds Lua memory usage: 637749/52428800 bytes Number of Wikibase entities loaded: 1/400 --> <!-- Transclusion expansion time report (%,ms,calls,template) 100.00% 87.544 1 -total 62.30% 54.542 1 Sjabloon:Commonscat 57.10% 49.989 1 Sjabloon:Zusterproject_box 19.82% 17.351 1 Sjabloon:Appendix 17.49% 15.311 1 Sjabloon:References 12.65% 11.078 2 Sjabloon:Fr 9.52% 8.338 2 Sjabloon:First_non_empty 7.91% 6.924 2 Sjabloon:Taalaanduiding 4.69% 4.102 3 Sjabloon:En 2.12% 1.859 1 Sjabloon:InterProject --> <!-- Saved in parser cache with key nlwiki:pcache:idhash:127060-0!canonical and timestamp 20241102160926 and revision id 64894116. 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