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id="toc-Symmetry" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Symmetry"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>Symmetry</span> </div> </a> <ul id="toc-Symmetry-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Spirals" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Spirals"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2</span> <span>Spirals</span> </div> </a> <ul id="toc-Spirals-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Chaos,_turbulence,_meanders_and_complexity" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Chaos,_turbulence,_meanders_and_complexity"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.3</span> <span>Chaos, turbulence, meanders and complexity</span> </div> </a> <ul id="toc-Chaos,_turbulence,_meanders_and_complexity-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Waves,_dunes" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Waves,_dunes"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.4</span> <span>Waves, dunes</span> </div> </a> <ul id="toc-Waves,_dunes-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Bubbles,_foam" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Bubbles,_foam"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.5</span> <span>Bubbles, foam</span> </div> </a> <ul id="toc-Bubbles,_foam-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Cracks" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Cracks"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.6</span> <span>Cracks</span> </div> </a> <ul id="toc-Cracks-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Spots,_stripes" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Spots,_stripes"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.7</span> <span>Spots, stripes</span> </div> </a> <ul id="toc-Spots,_stripes-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Art_and_architecture" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Art_and_architecture"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Art and architecture</span> </div> </a> <button aria-controls="toc-Art_and_architecture-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 Art and architecture subsection</span> </button> <ul id="toc-Art_and_architecture-sublist" class="vector-toc-list"> <li id="toc-Tilings" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Tilings"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Tilings</span> </div> </a> <ul id="toc-Tilings-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-In_architecture" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#In_architecture"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>In architecture</span> </div> </a> <ul id="toc-In_architecture-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Science_and_mathematics" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Science_and_mathematics"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Science and mathematics</span> </div> </a> <button aria-controls="toc-Science_and_mathematics-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 Science and mathematics subsection</span> </button> <ul id="toc-Science_and_mathematics-sublist" class="vector-toc-list"> <li id="toc-Real_patterns" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Real_patterns"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Real patterns</span> </div> </a> <ul id="toc-Real_patterns-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Fractals" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Fractals"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>Fractals</span> </div> </a> <ul id="toc-Fractals-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">4</span> <span>See also</span> </div> </a> <ul id="toc-See_also-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">5</span> <span>References</span> </div> </a> <ul id="toc-References-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">6</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_nature" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#In_nature"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.1</span> <span>In nature</span> </div> </a> <ul id="toc-In_nature-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-In_art_and_architecture" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#In_art_and_architecture"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.2</span> <span>In art and architecture</span> </div> </a> <ul id="toc-In_art_and_architecture-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-In_science_and_mathematics" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#In_science_and_mathematics"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.3</span> <span>In science and mathematics</span> </div> </a> <ul id="toc-In_science_and_mathematics-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-In_computing" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#In_computing"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.4</span> <span>In computing</span> </div> </a> <ul id="toc-In_computing-sublist" class="vector-toc-list"> </ul> </li> </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" title="Table of Contents" > <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">Pattern</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 36 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-36" 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">36 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/Patroon_(vorm)" title="Patroon (vorm) – Afrikaans" lang="af" hreflang="af" data-title="Patroon (vorm)" data-language-autonym="Afrikaans" data-language-local-name="Afrikaans" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%86%D9%85%D8%B7_(%D8%B4%D9%83%D9%84)" title="نمط (شكل) – Arabic" lang="ar" hreflang="ar" data-title="نمط (شكل)" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%9F%D0%B0%D1%82%D1%82%D0%B5%D1%80%D0%BD" title="Паттерн – Chuvash" lang="cv" hreflang="cv" data-title="Паттерн" data-language-autonym="Чӑвашла" data-language-local-name="Chuvash" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/M%C3%B8nster" title="Mønster – Danish" lang="da" hreflang="da" data-title="Mønster" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-ary mw-list-item"><a href="https://ary.wikipedia.org/wiki/%D9%BE%D8%A7%D8%B7%D9%8A%D8%B1%D9%86" title="پاطيرن – Moroccan Arabic" lang="ary" hreflang="ary" data-title="پاطيرن" data-language-autonym="الدارجة" data-language-local-name="Moroccan Arabic" class="interlanguage-link-target"><span>الدارجة</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Muster_(Struktur)" title="Muster (Struktur) – German" lang="de" hreflang="de" data-title="Muster (Struktur)" 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/Muster" title="Muster – Estonian" lang="et" hreflang="et" data-title="Muster" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Patr%C3%B3n_(estructura)" title="Patrón (estructura) – Spanish" lang="es" hreflang="es" data-title="Patrón (estructura)" 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/Reguleco" title="Reguleco – Esperanto" lang="eo" hreflang="eo" data-title="Reguleco" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%BE%D8%AA%D8%B1%D9%86_(%D9%86%D9%82%D8%B4%E2%80%8C%D9%85%D8%A7%DB%8C%D9%87%D8%8C_%D9%86%DA%AF%D8%A7%D8%B1%D9%87)" title="پترن (نقش‌مایه، نگاره) – Persian" lang="fa" hreflang="fa" data-title="پترن (نقش‌مایه، نگاره)" 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/R%C3%A9gularit%C3%A9_(perception)" title="Régularité (perception) – French" lang="fr" hreflang="fr" data-title="Régularité (perception)" 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/Patr%C3%BAn" title="Patrún – Irish" lang="ga" hreflang="ga" data-title="Patrún" data-language-autonym="Gaeilge" data-language-local-name="Irish" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%ED%8C%A8%ED%84%B4" title="패턴 – Korean" lang="ko" hreflang="ko" data-title="패턴" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Pola" title="Pola – Indonesian" lang="id" hreflang="id" data-title="Pola" 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-xh mw-list-item"><a href="https://xh.wikipedia.org/wiki/Ukufana_kwesakhiwo" title="Ukufana kwesakhiwo – Xhosa" lang="xh" hreflang="xh" data-title="Ukufana kwesakhiwo" data-language-autonym="IsiXhosa" data-language-local-name="Xhosa" class="interlanguage-link-target"><span>IsiXhosa</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Mynstur" title="Mynstur – Icelandic" lang="is" hreflang="is" data-title="Mynstur" 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/Pattern" title="Pattern – Italian" lang="it" hreflang="it" data-title="Pattern" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-jv mw-list-item"><a href="https://jv.wikipedia.org/wiki/Pola" title="Pola – Javanese" lang="jv" hreflang="jv" data-title="Pola" data-language-autonym="Jawa" data-language-local-name="Javanese" class="interlanguage-link-target"><span>Jawa</span></a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/Pattern" title="Pattern – Haitian Creole" lang="ht" hreflang="ht" data-title="Pattern" 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-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Pola" title="Pola – Malay" lang="ms" hreflang="ms" data-title="Pola" data-language-autonym="Bahasa Melayu" data-language-local-name="Malay" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Patroon_(vorm)" title="Patroon (vorm) – Dutch" lang="nl" hreflang="nl" data-title="Patroon (vorm)" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/M%C3%B8nster" title="Mønster – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Mønster" 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/M%C3%B8nster" title="Mønster – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Mønster" 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-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Padr%C3%A3o" title="Padrão – Portuguese" lang="pt" hreflang="pt" data-title="Padrão" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9F%D0%B0%D1%82%D1%82%D0%B5%D1%80%D0%BD" title="Паттерн – Russian" lang="ru" hreflang="ru" data-title="Паттерн" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Pattern" title="Pattern – Simple English" lang="en-simple" hreflang="en-simple" data-title="Pattern" 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-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D9%86%D9%88%DB%8E%D9%86%DB%95%DA%A9" title="نوێنەک – Central Kurdish" lang="ckb" hreflang="ckb" data-title="نوێنەک" data-language-autonym="کوردی" data-language-local-name="Central Kurdish" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Uzor" title="Uzor – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Uzor" 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/Kuosi" title="Kuosi – Finnish" lang="fi" hreflang="fi" data-title="Kuosi" 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/M%C3%B6nster_(regelbundenhet)" title="Mönster (regelbundenhet) – Swedish" lang="sv" hreflang="sv" data-title="Mönster (regelbundenhet)" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%A4%E0%AF%8B%E0%AE%B0%E0%AE%A3%E0%AE%AE%E0%AF%8D" title="தோரணம் – Tamil" lang="ta" hreflang="ta" data-title="தோரணம்" data-language-autonym="தமிழ்" data-language-local-name="Tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/%C3%96r%C3%BCnt%C3%BC" title="Örüntü – Turkish" lang="tr" hreflang="tr" data-title="Örüntü" 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%9F%D0%B0%D1%82%D0%B5%D1%80%D0%BD" title="Патерн – Ukrainian" lang="uk" hreflang="uk" data-title="Патерн" 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/M%E1%BA%ABu_(d%E1%BA%A1ng_th%E1%BB%A9c)" title="Mẫu (dạng thức) – Vietnamese" lang="vi" hreflang="vi" data-title="Mẫu (dạng thức)" 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-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E8%8A%B1%E8%87%A3" title="花臣 – Cantonese" lang="yue" hreflang="yue" data-title="花臣" 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%A8%A1%E5%BC%8F" title="模式 – Chinese" lang="zh" hreflang="zh" data-title="模式" 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/Q2083958#sitelinks-wikipedia" title="Edit interlanguage links" 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dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Regularity in sensory qualia or abstract ideas</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">For other uses, see <a href="/wiki/Pattern_(disambiguation)" class="mw-disambig" title="Pattern (disambiguation)">Pattern (disambiguation)</a>.</div> <style data-mw-deduplicate="TemplateStyles:r1273380762/mw-parser-output/.tmulti">.mw-parser-output .tmulti .multiimageinner{display:flex;flex-direction:column}.mw-parser-output .tmulti 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.trow>.thumbcaption{text-align:center}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .tmulti .multiimageinner span:not(.skin-invert-image):not(.skin-invert):not(.bg-transparent) img{background-color:white}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .tmulti .multiimageinner span:not(.skin-invert-image):not(.skin-invert):not(.bg-transparent) img{background-color:white}}</style><div class="thumb tmulti tright"><div class="thumbinner multiimageinner" style="width:442px;max-width:442px"><div class="trow"><div class="tsingle" style="width:231px;max-width:231px"><div class="thumbimage" style="height:90px;overflow:hidden"><span typeof="mw:File"><a href="/wiki/File:Ionic_frieze_from_the_Erechtheum,_dimensions_130_x_50_cm,_in_the_Glyptothek.jpg" class="mw-file-description"><img alt="" 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href="/wiki/File:Kleophrades_Painter_ARV_189_78bis_mission_to_Achilles.jpg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Kleophrades_Painter_ARV_189_78bis_mission_to_Achilles.jpg/205px-Kleophrades_Painter_ARV_189_78bis_mission_to_Achilles.jpg" decoding="async" width="205" height="91" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Kleophrades_Painter_ARV_189_78bis_mission_to_Achilles.jpg/308px-Kleophrades_Painter_ARV_189_78bis_mission_to_Achilles.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Kleophrades_Painter_ARV_189_78bis_mission_to_Achilles.jpg/410px-Kleophrades_Painter_ARV_189_78bis_mission_to_Achilles.jpg 2x" data-file-width="4272" data-file-height="1887" /></a></span></div></div></div><div class="trow"><div class="tsingle" style="width:120px;max-width:120px"><div class="thumbimage" style="height:202px;overflow:hidden"><span typeof="mw:File"><a href="/wiki/File:William_Morris_-_%22Pimpernel%22_-_Google_Art_Project.jpg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/e/eb/William_Morris_-_%22Pimpernel%22_-_Google_Art_Project.jpg/118px-William_Morris_-_%22Pimpernel%22_-_Google_Art_Project.jpg" decoding="async" width="118" height="202" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/eb/William_Morris_-_%22Pimpernel%22_-_Google_Art_Project.jpg/177px-William_Morris_-_%22Pimpernel%22_-_Google_Art_Project.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/eb/William_Morris_-_%22Pimpernel%22_-_Google_Art_Project.jpg/236px-William_Morris_-_%22Pimpernel%22_-_Google_Art_Project.jpg 2x" data-file-width="2510" data-file-height="4289" /></a></span></div></div><div class="tsingle" style="width:318px;max-width:318px"><div class="thumbimage" style="height:202px;overflow:hidden"><span typeof="mw:File"><a href="/wiki/File:Strawberrythief.jpg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/1/15/Strawberrythief.jpg/316px-Strawberrythief.jpg" decoding="async" width="316" height="203" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/15/Strawberrythief.jpg/474px-Strawberrythief.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/15/Strawberrythief.jpg/632px-Strawberrythief.jpg 2x" data-file-width="736" data-file-height="472" /></a></span></div></div></div><div class="trow"><div class="tsingle" style="width:253px;max-width:253px"><div class="thumbimage" style="height:122px;overflow:hidden"><span typeof="mw:File"><a href="/wiki/File:Settee_MET_SF2007_368_img4.jpg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f0/Settee_MET_SF2007_368_img4.jpg/251px-Settee_MET_SF2007_368_img4.jpg" decoding="async" width="251" height="122" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f0/Settee_MET_SF2007_368_img4.jpg/377px-Settee_MET_SF2007_368_img4.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f0/Settee_MET_SF2007_368_img4.jpg/502px-Settee_MET_SF2007_368_img4.jpg 2x" data-file-width="2049" data-file-height="999" /></a></span></div></div><div class="tsingle" style="width:185px;max-width:185px"><div class="thumbimage" style="height:122px;overflow:hidden"><span typeof="mw:File"><a href="/wiki/File:Nikoxenos_Painter_ARV_221_14_athletes_with_trainer_and_flute_player_-_satyrs_as_athletes_(05).jpg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3c/Nikoxenos_Painter_ARV_221_14_athletes_with_trainer_and_flute_player_-_satyrs_as_athletes_%2805%29.jpg/183px-Nikoxenos_Painter_ARV_221_14_athletes_with_trainer_and_flute_player_-_satyrs_as_athletes_%2805%29.jpg" decoding="async" width="183" height="122" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3c/Nikoxenos_Painter_ARV_221_14_athletes_with_trainer_and_flute_player_-_satyrs_as_athletes_%2805%29.jpg/275px-Nikoxenos_Painter_ARV_221_14_athletes_with_trainer_and_flute_player_-_satyrs_as_athletes_%2805%29.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3c/Nikoxenos_Painter_ARV_221_14_athletes_with_trainer_and_flute_player_-_satyrs_as_athletes_%2805%29.jpg/366px-Nikoxenos_Painter_ARV_221_14_athletes_with_trainer_and_flute_player_-_satyrs_as_athletes_%2805%29.jpg 2x" data-file-width="5472" data-file-height="3648" /></a></span></div></div></div><div class="trow"><div class="tsingle" style="width:440px;max-width:440px"><div class="thumbimage" style="height:147px;overflow:hidden"><span typeof="mw:File"><a href="/wiki/File:D.A._Sturdza_House,_Bucharest_(Romania)_32.jpg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/fb/D.A._Sturdza_House%2C_Bucharest_%28Romania%29_32.jpg/438px-D.A._Sturdza_House%2C_Bucharest_%28Romania%29_32.jpg" decoding="async" width="438" height="148" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/fb/D.A._Sturdza_House%2C_Bucharest_%28Romania%29_32.jpg/657px-D.A._Sturdza_House%2C_Bucharest_%28Romania%29_32.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/fb/D.A._Sturdza_House%2C_Bucharest_%28Romania%29_32.jpg/876px-D.A._Sturdza_House%2C_Bucharest_%28Romania%29_32.jpg 2x" data-file-width="3297" data-file-height="1112" /></a></span></div></div></div><div class="trow" style="display:flex"><div class="thumbcaption">Various examples of patterns</div></div></div></div> <p>A <b>pattern</b> is a regularity in the world, in human-made design,<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> or in <a href="/wiki/Abstraction" title="Abstraction">abstract</a> ideas. As such, the elements of a pattern repeat in a predictable manner. A <b>geometric pattern</b> is a kind of pattern formed of <a href="/wiki/Geometry" title="Geometry">geometric</a> <a href="/wiki/Shape" title="Shape">shapes</a> and typically repeated like a <a href="/wiki/Wallpaper" title="Wallpaper">wallpaper</a> design. </p><p>Any of the <a href="/wiki/Sense" title="Sense">senses</a> may directly observe patterns. Conversely, abstract patterns in <a href="/wiki/Science" title="Science">science</a>, <a href="/wiki/Mathematics" title="Mathematics">mathematics</a>, or <a href="/wiki/Language" title="Language">language</a> may be observable only by analysis. Direct observation in practice means seeing visual patterns, which are widespread in nature and in art. Visual <a href="/wiki/Patterns_in_nature" title="Patterns in nature">patterns in nature</a> are often <a href="/wiki/Chaos_theory" title="Chaos theory">chaotic</a>, rarely exactly repeating, and often involve <a href="/wiki/Fractals" class="mw-redirect" title="Fractals">fractals</a>. Natural patterns include <a href="/wiki/Spirals" class="mw-redirect" title="Spirals">spirals</a>, <a href="/wiki/Meander" title="Meander">meanders</a>, <a href="/wiki/Wave" title="Wave">waves</a>, <a href="/wiki/Foam" title="Foam">foams</a>, <a href="/wiki/Tessellation" title="Tessellation">tilings</a>, <a href="/wiki/Fracture" title="Fracture">cracks</a>, and those created by <a href="/wiki/Symmetry" title="Symmetry">symmetries</a> of <a href="/wiki/Rotation_symmetry" class="mw-redirect" title="Rotation symmetry">rotation</a> and <a href="/wiki/Reflection_symmetry" title="Reflection symmetry">reflection</a>. Patterns have an underlying <a href="/wiki/Mathematics" title="Mathematics">mathematical</a> structure;<sup id="cite_ref-:0_2-0" class="reference"><a href="#cite_note-:0-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page: 6">: 6 </span></sup> indeed, mathematics can be seen as the search for regularities, and the output of any function is a mathematical pattern. Similarly in the sciences, theories explain and predict regularities in the world. </p><p>In many areas of the <a href="/wiki/Decorative_arts" title="Decorative arts">decorative arts</a>, from ceramics and textiles to <a href="/wiki/Wallpaper" title="Wallpaper">wallpaper</a>, "pattern" is used for an ornamental design that is manufactured, perhaps for many different shapes of object. In art and architecture, decorations or <a href="/wiki/Motif_(visual_arts)" title="Motif (visual arts)">visual motifs</a> may be combined and repeated to form patterns designed to have a chosen effect on the viewer. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Nature">Nature</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Pattern&action=edit&section=1" title="Edit section: Nature"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Patterns_in_nature" title="Patterns in nature">Patterns in nature</a></div> <p>Nature provides examples of many kinds of pattern, including <a href="/wiki/Symmetry" title="Symmetry">symmetries</a>, trees and other structures with a <a href="/wiki/Fractal" title="Fractal">fractal</a> dimension, <a href="/wiki/Spirals" class="mw-redirect" title="Spirals">spirals</a>, <a href="/wiki/Meander" title="Meander">meanders</a>, <a href="/wiki/Wave" title="Wave">waves</a>, <a href="/wiki/Foam" title="Foam">foams</a>, <a href="/wiki/Tessellation" title="Tessellation">tilings</a>, <a href="/wiki/Fracture" title="Fracture">cracks</a> and stripes.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Symmetry">Symmetry</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Pattern&action=edit&section=2" title="Edit section: Symmetry"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:First_Snowfall_(38115232341).jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b4/First_Snowfall_%2838115232341%29.jpg/170px-First_Snowfall_%2838115232341%29.jpg" decoding="async" width="170" height="170" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b4/First_Snowfall_%2838115232341%29.jpg/255px-First_Snowfall_%2838115232341%29.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b4/First_Snowfall_%2838115232341%29.jpg/340px-First_Snowfall_%2838115232341%29.jpg 2x" data-file-width="3500" data-file-height="3500" /></a><figcaption><a href="/wiki/Snowflake" title="Snowflake">Snowflake</a> <a href="/wiki/Dihedral_symmetry" class="mw-redirect" title="Dihedral symmetry">sixfold symmetry</a></figcaption></figure> <p>Symmetry is widespread in living things. Animals that move usually have bilateral or <a href="/wiki/Reflection_symmetry" title="Reflection symmetry">mirror symmetry</a> as this favours movement.<sup id="cite_ref-:0_2-1" class="reference"><a href="#cite_note-:0-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Pages: 48–49">: 48–49 </span></sup> Plants often have radial or <a href="/wiki/Rotational_symmetry" title="Rotational symmetry">rotational symmetry</a>, as do many flowers, as well as animals which are largely static as adults, such as <a href="/wiki/Sea_anemone" title="Sea anemone">sea anemones</a>. Fivefold symmetry is found in the <a href="/wiki/Echinoderms" class="mw-redirect" title="Echinoderms">echinoderms</a>, including <a href="/wiki/Starfish" title="Starfish">starfish</a>, <a href="/wiki/Sea_urchin" title="Sea urchin">sea urchins</a>, and <a href="/wiki/Sea_lilies" class="mw-redirect" title="Sea lilies">sea lilies</a>.<sup id="cite_ref-:0_2-2" class="reference"><a href="#cite_note-:0-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Pages: 64–65">: 64–65 </span></sup> </p><p>Among non-living things, <a href="/wiki/Snowflake" title="Snowflake">snowflakes</a> have striking <a href="/wiki/Dihedral_symmetry" class="mw-redirect" title="Dihedral symmetry">sixfold symmetry</a>: each flake is unique, its structure recording the varying conditions during its crystallisation similarly on each of its six arms.<sup id="cite_ref-:0_2-3" class="reference"><a href="#cite_note-:0-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page: 52">: 52 </span></sup> <a href="/wiki/Crystal" title="Crystal">Crystals</a> have a highly specific set of possible <a href="/wiki/Crystal_habit" title="Crystal habit">crystal symmetries</a>; they can be cubic or <a href="/wiki/Octahedral" class="mw-redirect" title="Octahedral">octahedral</a>, but cannot have fivefold symmetry (unlike <a href="/wiki/Quasicrystals" class="mw-redirect" title="Quasicrystals">quasicrystals</a>).<sup id="cite_ref-:0_2-4" class="reference"><a href="#cite_note-:0-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Pages: 82–84">: 82–84 </span></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Spirals">Spirals</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Pattern&action=edit&section=3" title="Edit section: Spirals"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Aloe_polyphylla_spiral.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c4/Aloe_polyphylla_spiral.jpg/170px-Aloe_polyphylla_spiral.jpg" decoding="async" width="170" height="134" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c4/Aloe_polyphylla_spiral.jpg/255px-Aloe_polyphylla_spiral.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c4/Aloe_polyphylla_spiral.jpg/340px-Aloe_polyphylla_spiral.jpg 2x" data-file-width="800" data-file-height="631" /></a><figcaption><i><a href="/wiki/Aloe_polyphylla" title="Aloe polyphylla">Aloe polyphylla</a></i> <a href="/wiki/Phyllotaxis" title="Phyllotaxis">phyllotaxis</a></figcaption></figure> <p>Spiral patterns are found in the body plans of animals including <a href="/wiki/Molluscs" class="mw-redirect" title="Molluscs">molluscs</a> such as the <a href="/wiki/Nautilus" title="Nautilus">nautilus</a>, and in the <a href="/wiki/Phyllotaxis" title="Phyllotaxis">phyllotaxis</a> of many plants, both of leaves spiralling around stems, and in the multiple spirals found in flowerheads such as the <a href="/wiki/Sunflower" class="mw-redirect" title="Sunflower">sunflower</a> and fruit structures like the <a href="/wiki/Pineapple" title="Pineapple">pineapple</a>.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p> <div style="clear:both;" class=""></div> <div class="mw-heading mw-heading3"><h3 id="Chaos,_turbulence,_meanders_and_complexity"><span id="Chaos.2C_turbulence.2C_meanders_and_complexity"></span>Chaos, turbulence, meanders and complexity</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Pattern&action=edit&section=4" title="Edit section: Chaos, turbulence, meanders and complexity"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Vortex-street-1.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/2c/Vortex-street-1.jpg/130px-Vortex-street-1.jpg" decoding="async" width="130" height="233" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/2c/Vortex-street-1.jpg/195px-Vortex-street-1.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/2c/Vortex-street-1.jpg/260px-Vortex-street-1.jpg 2x" data-file-width="2549" data-file-height="4574" /></a><figcaption><a href="/wiki/Vortex_street" class="mw-redirect" title="Vortex street">Vortex street</a> turbulence</figcaption></figure> <p><a href="/wiki/Chaos_theory" title="Chaos theory">Chaos theory</a> predicts that while the laws of <a href="/wiki/Physics" title="Physics">physics</a> are <a href="/wiki/Deterministic" class="mw-redirect" title="Deterministic">deterministic</a>, there are events and patterns in nature that never exactly repeat because extremely small differences in starting conditions can lead to widely differing outcomes.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> The patterns in nature tend to be static due to dissipation on the emergence process, but when there is interplay between injection of energy and dissipation there can arise a complex dynamic.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> Many natural patterns are shaped by this complexity, including <a href="/wiki/Vortex_street" class="mw-redirect" title="Vortex street">vortex streets</a>,<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> other effects of turbulent flow such as <a href="/wiki/Meander" title="Meander">meanders</a> in rivers.<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> or nonlinear interaction of the system <sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p> <div style="clear:both;" class=""></div> <div class="mw-heading mw-heading3"><h3 id="Waves,_dunes"><span id="Waves.2C_dunes"></span>Waves, dunes</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Pattern&action=edit&section=5" title="Edit section: Waves, dunes"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Sand_dune_ripples.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Sand_dune_ripples.jpg/170px-Sand_dune_ripples.jpg" decoding="async" width="170" height="128" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Sand_dune_ripples.jpg/255px-Sand_dune_ripples.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Sand_dune_ripples.jpg/340px-Sand_dune_ripples.jpg 2x" data-file-width="1600" data-file-height="1200" /></a><figcaption><a href="/wiki/Dune" title="Dune">Dune</a> <a href="/wiki/Capillary_wave" title="Capillary wave">ripple</a></figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:M%C3%B6nster_-_Sand_-_Br%C3%A4dor_-_2021.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/85/M%C3%B6nster_-_Sand_-_Br%C3%A4dor_-_2021.jpg/170px-M%C3%B6nster_-_Sand_-_Br%C3%A4dor_-_2021.jpg" decoding="async" width="170" height="140" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/85/M%C3%B6nster_-_Sand_-_Br%C3%A4dor_-_2021.jpg/255px-M%C3%B6nster_-_Sand_-_Br%C3%A4dor_-_2021.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/85/M%C3%B6nster_-_Sand_-_Br%C3%A4dor_-_2021.jpg/340px-M%C3%B6nster_-_Sand_-_Br%C3%A4dor_-_2021.jpg 2x" data-file-width="1500" data-file-height="1234" /></a><figcaption>Dune ripples and boards form a symmetrical pattern.</figcaption></figure> <p><a href="/wiki/Wave" title="Wave">Waves</a> are disturbances that carry energy as they move. <a href="/wiki/Mechanical_wave" title="Mechanical wave">Mechanical waves</a> propagate through a medium – air or water, making it <a href="/wiki/Oscillation" title="Oscillation">oscillate</a> as they pass by.<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Wind_wave" title="Wind wave">Wind waves</a> are <a href="/wiki/Surface_wave" title="Surface wave">surface waves</a> that create the chaotic patterns of the sea. As they pass over sand, such waves create patterns of ripples; similarly, as the wind passes over sand, it creates patterns of <a href="/wiki/Dune" title="Dune">dunes</a>.<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> </p> <div style="clear:both;" class=""></div> <div class="mw-heading mw-heading3"><h3 id="Bubbles,_foam"><span id="Bubbles.2C_foam"></span>Bubbles, foam</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Pattern&action=edit&section=6" title="Edit section: Bubbles, foam"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Foam_-_big.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f4/Foam_-_big.jpg/170px-Foam_-_big.jpg" decoding="async" width="170" height="223" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f4/Foam_-_big.jpg/255px-Foam_-_big.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f4/Foam_-_big.jpg/340px-Foam_-_big.jpg 2x" data-file-width="1278" data-file-height="1675" /></a><figcaption><a href="/wiki/Foam" title="Foam">Foam</a> of <a href="/wiki/Soap_bubble" title="Soap bubble">soap bubbles</a></figcaption></figure> <p><a href="/wiki/Foam" title="Foam">Foams</a> obey <a href="/wiki/Plateau%27s_laws" title="Plateau's laws">Plateau's laws</a>, which require films to be smooth and continuous, and to have a constant <a href="/wiki/Mean_curvature" title="Mean curvature">average curvature</a>. Foam and bubble patterns occur widely in nature, for example in <a href="/wiki/Radiolarian" class="mw-redirect" title="Radiolarian">radiolarians</a>, <a href="/wiki/Sponge" title="Sponge">sponge</a> <a href="/wiki/Spicule_(sponge)" class="mw-redirect" title="Spicule (sponge)">spicules</a>, and the skeletons of <a href="/wiki/Silicoflagellate" class="mw-redirect" title="Silicoflagellate">silicoflagellates</a> and <a href="/wiki/Sea_urchin" title="Sea urchin">sea urchins</a>.<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> </p> <div style="clear:both;" class=""></div> <div class="mw-heading mw-heading3"><h3 id="Cracks">Cracks</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Pattern&action=edit&section=7" title="Edit section: Cracks"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Cracked_earth_in_the_Rann_of_Kutch.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/7d/Cracked_earth_in_the_Rann_of_Kutch.jpg/170px-Cracked_earth_in_the_Rann_of_Kutch.jpg" decoding="async" width="170" height="113" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/7d/Cracked_earth_in_the_Rann_of_Kutch.jpg/255px-Cracked_earth_in_the_Rann_of_Kutch.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/7d/Cracked_earth_in_the_Rann_of_Kutch.jpg/340px-Cracked_earth_in_the_Rann_of_Kutch.jpg 2x" data-file-width="1440" data-file-height="957" /></a><figcaption>Shrinkage <a href="/wiki/Fracture" title="Fracture">Cracks</a></figcaption></figure> <p><a href="/wiki/Fracture" title="Fracture">Cracks</a> form in materials to relieve stress: with 120 degree joints in elastic materials, but at 90 degrees in inelastic materials. Thus the pattern of cracks indicates whether the material is elastic or not. Cracking patterns are widespread in nature, for example in rocks, mud, tree bark and the glazes of old paintings and ceramics.<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> </p> <div style="clear:both;" class=""></div> <div class="mw-heading mw-heading3"><h3 id="Spots,_stripes"><span id="Spots.2C_stripes"></span>Spots, stripes</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Pattern&action=edit&section=8" title="Edit section: Spots, stripes"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1273380762/mw-parser-output/.tmulti"><div class="thumb tmulti tright"><div class="thumbinner multiimageinner" style="width:432px;max-width:432px"><div class="trow"><div class="tsingle" style="width:149px;max-width:149px"><div class="thumbimage" style="height:147px;overflow:hidden"><span typeof="mw:File"><a href="/wiki/File:Giant_Pufferfish_skin_pattern_detail.jpg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Giant_Pufferfish_skin_pattern_detail.jpg/147px-Giant_Pufferfish_skin_pattern_detail.jpg" decoding="async" width="147" height="147" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Giant_Pufferfish_skin_pattern_detail.jpg/221px-Giant_Pufferfish_skin_pattern_detail.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/Giant_Pufferfish_skin_pattern_detail.jpg/294px-Giant_Pufferfish_skin_pattern_detail.jpg 2x" data-file-width="300" data-file-height="300" /></a></span></div><div class="thumbcaption"><a href="/wiki/Mbu_pufferfish" title="Mbu pufferfish">Mbu pufferfish</a> skin</div></div><div class="tsingle" style="width:279px;max-width:279px"><div class="thumbimage" style="height:147px;overflow:hidden"><span typeof="mw:File"><a href="/wiki/File:Animal_skin.jpg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c2/Animal_skin.jpg/277px-Animal_skin.jpg" decoding="async" width="277" height="147" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c2/Animal_skin.jpg/416px-Animal_skin.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c2/Animal_skin.jpg/554px-Animal_skin.jpg 2x" data-file-width="1049" data-file-height="557" /></a></span></div><div class="thumbcaption">Skins of a <a href="/wiki/South_African_giraffe" title="South African giraffe">South African giraffe</a> and <a href="/wiki/Burchell%27s_zebra" title="Burchell's zebra">Burchell's zebra</a></div></div></div></div></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Pattern_formation" title="Pattern formation">Pattern formation</a></div> <p><a href="/wiki/Alan_Turing" title="Alan Turing">Alan Turing</a>,<sup id="cite_ref-Turing_15-0" class="reference"><a href="#cite_note-Turing-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> and later the mathematical biologist <a href="/wiki/James_D._Murray" title="James D. Murray">James D. Murray</a><sup id="cite_ref-Murray2013_16-0" class="reference"><a href="#cite_note-Murray2013-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> and other scientists, described a mechanism that spontaneously creates spotted or striped patterns, for example in the skin of mammals or the plumage of birds: a <a href="/wiki/Reaction%E2%80%93diffusion" class="mw-redirect" title="Reaction–diffusion">reaction–diffusion</a> system involving two counter-acting chemical mechanisms, one that activates and one that inhibits a development, such as of dark pigment in the skin.<sup id="cite_ref-Ball159_17-0" class="reference"><a href="#cite_note-Ball159-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> These <a href="/wiki/Spatiotemporal_pattern" title="Spatiotemporal pattern">spatiotemporal patterns</a> slowly drift, the animals' appearance changing imperceptibly as Turing predicted. </p> <div class="mw-heading mw-heading2"><h2 id="Art_and_architecture">Art and architecture</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Pattern&action=edit&section=9" title="Edit section: Art and architecture"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Further information: <a href="/wiki/Mathematics_and_art" title="Mathematics and art">Mathematics and art</a> and <a href="/wiki/Mathematics_and_architecture" title="Mathematics and architecture">Mathematics and architecture</a></div> <div class="mw-heading mw-heading3"><h3 id="Tilings">Tilings</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Pattern&action=edit&section=10" title="Edit section: Tilings"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Enderun_library_Topkapi_42.JPG" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/82/Enderun_library_Topkapi_42.JPG/220px-Enderun_library_Topkapi_42.JPG" decoding="async" width="220" height="165" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/82/Enderun_library_Topkapi_42.JPG/330px-Enderun_library_Topkapi_42.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/82/Enderun_library_Topkapi_42.JPG/440px-Enderun_library_Topkapi_42.JPG 2x" data-file-width="1600" data-file-height="1200" /></a><figcaption>Elaborate ceramic tiles at <a href="/wiki/Topkapi_Palace" class="mw-redirect" title="Topkapi Palace">Topkapi Palace</a></figcaption></figure> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Further information: <a href="/wiki/Tessellation" title="Tessellation">Tessellation</a> and <a href="/wiki/Tile" title="Tile">Tile</a></div> <p>In visual art, pattern consists in regularity which in some way "organizes surfaces or structures in a consistent, regular manner." At its simplest, a pattern in art may be a geometric or other repeating shape in a <a href="/wiki/Painting" title="Painting">painting</a>, <a href="/wiki/Drawing" title="Drawing">drawing</a>, <a href="/wiki/Tapestry" title="Tapestry">tapestry</a>, ceramic <a href="/wiki/Tile" title="Tile">tiling</a> or <a href="/wiki/Carpet" title="Carpet">carpet</a>, but a pattern need not necessarily repeat exactly as long as it provides some form or organizing "skeleton" in the artwork.<sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> In mathematics, a <a href="/wiki/Tessellation" title="Tessellation">tessellation</a> is the tiling of a plane using one or more geometric shapes (which mathematicians call tiles), with no overlaps and no gaps.<sup id="cite_ref-Grunbaum_19-0" class="reference"><a href="#cite_note-Grunbaum-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="In_architecture">In architecture</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Pattern&action=edit&section=11" title="Edit section: In architecture"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Hampi1.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0a/Hampi1.jpg/170px-Hampi1.jpg" decoding="async" width="170" height="268" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/0/0a/Hampi1.jpg 1.5x" data-file-width="254" data-file-height="400" /></a><figcaption>Patterns in architecture: the Virupaksha temple at Hampi has a <a href="/wiki/Fractal" title="Fractal">fractal</a>-like structure where the parts resemble the whole.</figcaption></figure> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main articles: <a href="/wiki/Pattern_(architecture)" title="Pattern (architecture)">Pattern (architecture)</a> and <a href="/wiki/Mathematics_and_architecture" title="Mathematics and architecture">Mathematics and architecture</a></div> <p>In architecture, <a href="/wiki/Motif_(visual_arts)" title="Motif (visual arts)">motifs</a> are repeated in various ways to form patterns. Most simply, structures such as windows can be repeated horizontally and vertically (see leading picture). Architects can use and repeat decorative and structural elements such as <a href="/wiki/Column" title="Column">columns</a>, <a href="/wiki/Pediment" title="Pediment">pediments</a>, and <a href="/wiki/Lintel" title="Lintel">lintels</a>.<sup id="cite_ref-20" class="reference"><a href="#cite_note-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> Repetitions need not be identical; for example, temples in South India have a roughly pyramidal form, where elements of the pattern repeat in a <a href="/wiki/Fractal" title="Fractal">fractal</a>-like way at different sizes.<sup id="cite_ref-21" class="reference"><a href="#cite_note-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Evening_columns_Zeus_temple_Athens.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/75/Evening_columns_Zeus_temple_Athens.jpg/220px-Evening_columns_Zeus_temple_Athens.jpg" decoding="async" width="220" height="146" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/75/Evening_columns_Zeus_temple_Athens.jpg/330px-Evening_columns_Zeus_temple_Athens.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/75/Evening_columns_Zeus_temple_Athens.jpg/440px-Evening_columns_Zeus_temple_Athens.jpg 2x" data-file-width="4592" data-file-height="3056" /></a><figcaption>Patterns in Architecture: the columns of Zeus's temple in Athens</figcaption></figure> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Pattern_book" class="mw-redirect" title="Pattern book">pattern book</a></div> <div class="mw-heading mw-heading2"><h2 id="Science_and_mathematics">Science and mathematics</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Pattern&action=edit&section=12" title="Edit section: Science and mathematics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Fractal_fern_explained.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4b/Fractal_fern_explained.png/170px-Fractal_fern_explained.png" decoding="async" width="170" height="237" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4b/Fractal_fern_explained.png/255px-Fractal_fern_explained.png 1.5x, //upload.wikimedia.org/wikipedia/commons/4/4b/Fractal_fern_explained.png 2x" data-file-width="333" data-file-height="465" /></a><figcaption>Fractal model of a fern illustrating <a href="/wiki/Self-similar" class="mw-redirect" title="Self-similar">self-similarity</a></figcaption></figure> <p><a href="/wiki/Mathematics" title="Mathematics">Mathematics</a> is sometimes called the "Science of Pattern", in the sense of rules that can be applied wherever needed.<sup id="cite_ref-22" class="reference"><a href="#cite_note-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> For example, any <a href="/wiki/Sequence" title="Sequence">sequence</a> of numbers that may be modeled by a mathematical function can be considered a pattern. Mathematics can be taught as a collection of patterns.<sup id="cite_ref-23" class="reference"><a href="#cite_note-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup> </p><p><a href="/wiki/Gravity" title="Gravity">Gravity</a> is a source of ubiquitous scientific patterns or patterns of observation. The sun rising and falling pattern each day results from the rotation of the earth while in orbit around the sun. Likewise, the <a href="/wiki/Moon" title="Moon">moon's</a> path through the sky is due to its orbit of the earth. These examples, while perhaps trivial, are examples of the "unreasonable effectiveness of mathematics" which obtain due to the <a href="/wiki/Differential_equations" class="mw-redirect" title="Differential equations">differential equations</a> whose application within <a href="/wiki/Physics" title="Physics">physics</a> function to describe the most general <a href="/wiki/Empirical" class="mw-redirect" title="Empirical">empirical</a> patterns of the <a href="/wiki/Universe" title="Universe">universe</a>.<sup id="cite_ref-24" class="reference"><a href="#cite_note-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Real_patterns">Real patterns</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Pattern&action=edit&section=13" title="Edit section: Real patterns"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Daniel_Dennett" title="Daniel Dennett">Daniel Dennett</a>'s notion of <b>real patterns</b>, discussed in his 1991 paper of the same name,<sup id="cite_ref-25" class="reference"><a href="#cite_note-25"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup> provides an ontological framework aiming to discern the reality of patterns beyond mere human interpretation, by examining their predictive utility and the efficiency they provide in compressing information. For example, <a href="/wiki/Center_of_mass" title="Center of mass">centre of gravity</a> is a real pattern because it allows us to predict the movements of a bodies such as the earth around the sun, and it compresses all the information about all the particles in the sun and the earth that allows us to make those predictions. </p> <div class="mw-heading mw-heading3"><h3 id="Fractals">Fractals</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Pattern&action=edit&section=14" title="Edit section: Fractals"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Some mathematical rule-patterns can be visualised, and among these are those that explain <a href="/wiki/Patterns_in_nature" title="Patterns in nature">patterns in nature</a> including the mathematics of symmetry, waves, meanders, and fractals. <a href="/wiki/Fractal" title="Fractal">Fractals</a> are mathematical patterns that are scale invariant. This means that the shape of the pattern does not depend on how closely you look at it. <a href="/wiki/Self-similarity" title="Self-similarity">Self-similarity</a> is found in fractals. Examples of natural fractals are coast lines and tree shapes, which repeat their shape regardless of what magnification you view at. While self-similar patterns can appear indefinitely complex, the rules needed to describe or produce their <a href="/wiki/Pattern_formation" title="Pattern formation">formation</a> can be simple (e.g. <a href="/wiki/Lindenmayer_system" class="mw-redirect" title="Lindenmayer system">Lindenmayer systems</a> describing <a href="/wiki/Tree" title="Tree">tree</a> shapes).<sup id="cite_ref-Mandelbrot1983_26-0" class="reference"><a href="#cite_note-Mandelbrot1983-26"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup> </p><p>In <a href="/wiki/Pattern_theory" title="Pattern theory">pattern theory</a>, devised by <a href="/wiki/Ulf_Grenander" title="Ulf Grenander">Ulf Grenander</a>, mathematicians attempt to describe the world in terms of patterns. The goal is to lay out the world in a more computationally friendly manner.<sup id="cite_ref-27" class="reference"><a href="#cite_note-27"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup> </p><p>In the broadest sense, any regularity that can be explained by a scientific theory is a pattern. As in mathematics, science can be taught as a set of patterns.<sup id="cite_ref-28" class="reference"><a href="#cite_note-28"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup> </p><p>A recent study from Aesthetics and Psychological Effects of Fractal Based Design<sup id="cite_ref-29" class="reference"><a href="#cite_note-29"><span class="cite-bracket">[</span>29<span class="cite-bracket">]</span></a></sup> suggested that fractal patterns possess self-similar components that repeat at varying size scales. The perceptual experience of human-made environments can be impacted with inclusion of these natural patterns. Previous work has demonstrated consistent trends in preference for and complexity estimates of fractal patterns. However, limited information has been gathered on the impact of other visual judgments. Here we examine the aesthetic and perceptual experience of fractal ‘global-forest’ designs already installed in humanmade spaces and demonstrate how fractal pattern components are associated with positive psychological experiences that can be utilized to promote occupant wellbeing. These designs are composite fractal patterns consisting of individual fractal ‘tree-seeds’ which combine to create a ‘global fractal forest.’ The local ‘tree-seed’ patterns, global configuration of tree-seed locations, and overall resulting ‘global-forest’ patterns have fractal qualities. These designs span multiple mediums yet are all intended to lower occupant stress without detracting from the function and overall design of the space. In this series of studies, we first establish divergent relationships between various visual attributes, with pattern complexity, preference, and engagement ratings increasing with fractal complexity compared to ratings of refreshment and relaxation which stay the same or decrease with complexity. Subsequently, we determine that the local constituent fractal (‘tree-seed’) patterns contribute to the perception of the overall fractal design, and address how to balance aesthetic and psychological effects (such as individual experiences of perceived engagement and relaxation) in fractal design installations. This set of studies demonstrates that fractal preference is driven by a balance between increased arousal (desire for engagement and complexity) and decreased tension (desire for relaxation or refreshment). Installations of these composite mid-high complexity ‘global-forest’ patterns consisting of ‘tree-seed’ components balance these contrasting needs, and can serve as a practical implementation of biophilic patterns in human-made environments to promote occupant wellbeing. </p> <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=Pattern&action=edit&section=15" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <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: 20em;"> <ul><li><a href="/wiki/Archetype" title="Archetype">Archetype</a></li> <li><a href="/wiki/Cellular_automata" class="mw-redirect" title="Cellular automata">Cellular automata</a></li> <li><a href="/wiki/Die_(manufacturing)" title="Die (manufacturing)">Die (manufacturing)</a> (template)</li> <li><a href="/wiki/Form_constant" title="Form constant">Form constant</a></li> <li><a href="/wiki/Fractal" title="Fractal">Fractal</a></li> <li><a href="/wiki/Pattern_(casting)" title="Pattern (casting)">Pattern (casting)</a></li> <li><a href="/wiki/Pattern_coin" title="Pattern coin">Pattern coin</a></li> <li><a href="/wiki/Pattern_matching" title="Pattern matching">Pattern matching</a></li> <li><a href="/wiki/Pattern_(sewing)" title="Pattern (sewing)">Pattern (sewing)</a></li> <li><a href="/wiki/Pattern_recognition" title="Pattern recognition">Pattern recognition</a></li> <li><a href="/wiki/Patterns_in_nature" title="Patterns in nature">Patterns in nature</a></li> <li><a href="/wiki/Pedagogical_patterns" class="mw-redirect" title="Pedagogical patterns">Pedagogical patterns</a></li> <li><a href="/wiki/Software_design_pattern" title="Software design pattern">Software design pattern</a></li> <li><a href="/wiki/Template_method_pattern" title="Template method pattern">Template method pattern</a></li></ul> </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=Pattern&action=edit&section=16" title="Edit section: References"><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-columns references-column-width" style="column-width: 30em;"> <ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><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="CITEREFGarai2022" class="citation web cs1">Garai, Achraf (3 March 2022). <a rel="nofollow" class="external text" href="https://www.achrafgarai.com/what-are-design-patterns/">"What are design patterns?"</a>. <i>achrafgarai.com</i><span class="reference-accessdate">. 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Springer Science & Business Media. pp. <span class="nowrap">436–</span>450. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-662-08539-4" title="Special:BookSources/978-3-662-08539-4"><bdi>978-3-662-08539-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Mathematical+Biology&rft.pages=%3Cspan+class%3D%22nowrap%22%3E436-%3C%2Fspan%3E450&rft.pub=Springer+Science+%26+Business+Media&rft.date=2013-03-09&rft.isbn=978-3-662-08539-4&rft.aulast=Murray&rft.aufirst=James+D.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DK3LmCAAAQBAJ%26pg%3DPA436&rfr_id=info%3Asid%2Fen.wikipedia.org%3APattern" class="Z3988"></span></span> </li> <li id="cite_note-Ball159-17"><span class="mw-cite-backlink"><b><a href="#cite_ref-Ball159_17-0">^</a></b></span> <span class="reference-text">Ball, Philip. <i>Shapes</i>, 2009. pp. 159–167.<sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citing_sources#What_information_to_include" title="Wikipedia:Citing sources"><span title="A complete citation is needed. (February 2024)">full citation needed</span></a></i>]</sup></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="CITEREFJirousek,_Charlotte1995" class="citation web cs1">Jirousek, Charlotte (1995). <a rel="nofollow" class="external text" href="http://char.txa.cornell.edu/language/element/pattern/pattern.htm">"Art, Design, and Visual Thinking"</a>. <i>Pattern</i>. Cornell University<span class="reference-accessdate">. Retrieved <span class="nowrap">12 December</span> 2012</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Pattern&rft.atitle=Art%2C+Design%2C+and+Visual+Thinking&rft.date=1995&rft.au=Jirousek%2C+Charlotte&rft_id=http%3A%2F%2Fchar.txa.cornell.edu%2Flanguage%2Felement%2Fpattern%2Fpattern.htm&rfr_id=info%3Asid%2Fen.wikipedia.org%3APattern" class="Z3988"></span></span> </li> <li id="cite_note-Grunbaum-19"><span class="mw-cite-backlink"><b><a href="#cite_ref-Grunbaum_19-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGrünbaumShephard,_G._C.1987" class="citation book cs1">Grünbaum, Branko; Shephard, G. C. (1987). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/isbn_0716711931"><i>Tilings and Patterns</i></a></span>. New York: W. H. Freeman. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780716711933" title="Special:BookSources/9780716711933"><bdi>9780716711933</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Tilings+and+Patterns&rft.place=New+York&rft.pub=W.+H.+Freeman&rft.date=1987&rft.isbn=9780716711933&rft.aulast=Gr%C3%BCnbaum&rft.aufirst=Branko&rft.au=Shephard%2C+G.+C.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fisbn_0716711931&rfr_id=info%3Asid%2Fen.wikipedia.org%3APattern" class="Z3988"></span></span> </li> <li id="cite_note-20"><span class="mw-cite-backlink"><b><a href="#cite_ref-20">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAdams,_Laurie2001" class="citation book cs1">Adams, Laurie (2001). <i>A History of Western Art</i>. McGraw Hill. p. 99.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=A+History+of+Western+Art&rft.pages=99&rft.pub=McGraw+Hill&rft.date=2001&rft.au=Adams%2C+Laurie&rfr_id=info%3Asid%2Fen.wikipedia.org%3APattern" 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="CITEREFJackson,_William_Joseph2004" class="citation book cs1">Jackson, William Joseph (2004). <i>Heaven's Fractal Net: Retrieving Lost Visions in the Humanities</i>. 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"Mathematics as a Science of Patterns: Ontology and Reference". <i>Noûs</i>. <b>15</b> (4): <span class="nowrap">529–</span>550. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.2307%2F2214851">10.2307/2214851</a>. <a href="/wiki/JSTOR_(identifier)" class="mw-redirect" title="JSTOR (identifier)">JSTOR</a> <a rel="nofollow" class="external text" href="https://www.jstor.org/stable/2214851">2214851</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=No%C3%BBs&rft.atitle=Mathematics+as+a+Science+of+Patterns%3A+Ontology+and+Reference&rft.volume=15&rft.issue=4&rft.pages=%3Cspan+class%3D%22nowrap%22%3E529-%3C%2Fspan%3E550&rft.date=1981-11&rft_id=info%3Adoi%2F10.2307%2F2214851&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F2214851%23id-name%3DJSTOR&rft.au=Resnik%2C+Michael+D.&rfr_id=info%3Asid%2Fen.wikipedia.org%3APattern" 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="CITEREFBayne,_Richard_E2012" class="citation web cs1">Bayne, Richard E (2012). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20130207065047/http://www.coas.howard.edu/mathematics/faculty/bayne/patterns.html">"MATH 012 Patterns in Mathematics - spring 2012"</a>. Archived from <a rel="nofollow" class="external text" href="http://www.coas.howard.edu/mathematics/faculty/bayne/patterns.html">the original</a> on 7 February 2013<span class="reference-accessdate">. Retrieved <span class="nowrap">16 January</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=MATH+012+Patterns+in+Mathematics+-+spring+2012&rft.date=2012&rft.au=Bayne%2C+Richard+E&rft_id=http%3A%2F%2Fwww.coas.howard.edu%2Fmathematics%2Ffaculty%2Fbayne%2Fpatterns.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3APattern" 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 id="CITEREFSteen1988" class="citation journal cs1">Steen, Lynn (June 1988). <a rel="nofollow" class="external text" href="https://www.science.org/doi/pdf/10.1126/science.240.4852.611?casa_token=g0zogcehLMcAAAAA:Qfw2b-7J4GZ-ZaVQrlOtAcZD4QKI55dYBLAnJCb_BIZm-9bsTJirn326b3fv37SbluU-yJRBF1qQDto">"The Science of Patterns"</a>. <i>Science</i>. <b>240</b> (4852): <span class="nowrap">611–</span>616. <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.240.4852.611">10.1126/science.240.4852.611</a><span class="reference-accessdate">. Retrieved <span class="nowrap">2024-08-11</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Science&rft.atitle=The+Science+of+Patterns&rft.volume=240&rft.issue=4852&rft.pages=%3Cspan+class%3D%22nowrap%22%3E611-%3C%2Fspan%3E616&rft.date=1988-06&rft_id=info%3Adoi%2F10.1126%2Fscience.240.4852.611&rft.aulast=Steen&rft.aufirst=Lynn&rft_id=https%3A%2F%2Fwww.science.org%2Fdoi%2Fpdf%2F10.1126%2Fscience.240.4852.611%3Fcasa_token%3Dg0zogcehLMcAAAAA%3AQfw2b-7J4GZ-ZaVQrlOtAcZD4QKI55dYBLAnJCb_BIZm-9bsTJirn326b3fv37SbluU-yJRBF1qQDto&rfr_id=info%3Asid%2Fen.wikipedia.org%3APattern" class="Z3988"></span>The author attributes Eugene Wigner for the claim for the "unreasonable effectiveness of mathematics," a partial quote which continues "[t]he miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve."</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">Dennett, D. C. (1991). Real Patterns. <i>The Journal of Philosophy</i> <b>88</b>(1), 27–51.</span> </li> <li id="cite_note-Mandelbrot1983-26"><span class="mw-cite-backlink"><b><a href="#cite_ref-Mandelbrot1983_26-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMandelbrot1983" class="citation book cs1"><a href="/wiki/Benoit_Mandelbrot" title="Benoit Mandelbrot">Mandelbrot, Benoit B.</a> (1983). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=0R2LkE3N7-oC"><i>The fractal geometry of nature</i></a>. Macmillan. <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.pub=Macmillan&rft.date=1983&rft.isbn=978-0-7167-1186-5&rft.aulast=Mandelbrot&rft.aufirst=Benoit+B.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3D0R2LkE3N7-oC&rfr_id=info%3Asid%2Fen.wikipedia.org%3APattern" 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="CITEREFGrenander,_UlfMiller,_Michael2007" class="citation book cs1">Grenander, Ulf; Miller, Michael (2007). <i>Pattern Theory: From Representation to Inference</i>. Oxford University Press.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Pattern+Theory%3A+From+Representation+to+Inference&rft.pub=Oxford+University+Press&rft.date=2007&rft.au=Grenander%2C+Ulf&rft.au=Miller%2C+Michael&rfr_id=info%3Asid%2Fen.wikipedia.org%3APattern" 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 class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.cfa.harvard.edu/smg/Website/UCP/">"Causal Patterns in Science"</a>. Harvard Graduate School of Education. 2008<span class="reference-accessdate">. Retrieved <span class="nowrap">16 January</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=Causal+Patterns+in+Science&rft.pub=Harvard+Graduate+School+of+Education&rft.date=2008&rft_id=http%3A%2F%2Fwww.cfa.harvard.edu%2Fsmg%2FWebsite%2FUCP%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3APattern" 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="CITEREFRoblesRobertsViengkhamSmith2021" class="citation journal cs1">Robles, Kelly E.; Roberts, Michelle; Viengkham, Catherine; Smith, Julian H.; Rowland, Conor; Moslehi, Saba; Stadlober, Sabrina; Lesjak, Anastasija; Lesjak, Martin; Taylor, Richard P.; Spehar, Branka; Sereno, Margaret E. (2021). <a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8416160">"Aesthetics and Psychological Effects of Fractal Based Design"</a>. <i>Frontiers in Psychology</i>. <b>12</b>. <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/10.3389%2Ffpsyg.2021.699962">10.3389/fpsyg.2021.699962</a></span>. <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/1664-1078">1664-1078</a>. <a href="/wiki/PMC_(identifier)" class="mw-redirect" title="PMC (identifier)">PMC</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8416160">8416160</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/34484047">34484047</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Frontiers+in+Psychology&rft.atitle=Aesthetics+and+Psychological+Effects+of+Fractal+Based+Design&rft.volume=12&rft.date=2021&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC8416160%23id-name%3DPMC&rft.issn=1664-1078&rft_id=info%3Apmid%2F34484047&rft_id=info%3Adoi%2F10.3389%2Ffpsyg.2021.699962&rft.aulast=Robles&rft.aufirst=Kelly+E.&rft.au=Roberts%2C+Michelle&rft.au=Viengkham%2C+Catherine&rft.au=Smith%2C+Julian+H.&rft.au=Rowland%2C+Conor&rft.au=Moslehi%2C+Saba&rft.au=Stadlober%2C+Sabrina&rft.au=Lesjak%2C+Anastasija&rft.au=Lesjak%2C+Martin&rft.au=Taylor%2C+Richard+P.&rft.au=Spehar%2C+Branka&rft.au=Sereno%2C+Margaret+E.&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC8416160&rfr_id=info%3Asid%2Fen.wikipedia.org%3APattern" class="Z3988"></span></span> </li> </ol></div> <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=Pattern&action=edit&section=17" title="Edit section: Bibliography"><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 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</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"><a href="/wiki/File:Wikiquote-logo.svg" class="mw-file-description"><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" /></a></span></div> <div class="side-box-text plainlist">Wikiquote has quotations related to <i><b><a href="https://en.wikiquote.org/wiki/Special:Search/Pattern" class="extiw" title="q:Special:Search/Pattern">Pattern</a></b></i>.</div></div> </div> <div class="mw-heading mw-heading3"><h3 id="In_nature">In nature</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Pattern&action=edit&section=18" title="Edit section: In nature"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>Adam, John A. <i>Mathematics in Nature: Modeling Patterns in the Natural World</i>. Princeton, 2006.</li> <li><a href="/wiki/Philip_Ball" title="Philip Ball">Ball, Philip</a> <i>The Self-made Tapestry: Pattern Formation in Nature</i>. Oxford, 2001.</li> <li><a href="/wiki/Bernhard_Edmaier" title="Bernhard Edmaier">Edmaier, Bernhard</a> <i>Patterns of the Earth</i>. <a href="/wiki/Phaidon_Press" title="Phaidon Press">Phaidon Press</a>, 2007.</li> <li><a href="/wiki/Ernst_Haeckel" title="Ernst Haeckel">Haeckel, Ernst</a> <i><a href="/wiki/Art_Forms_of_Nature" class="mw-redirect" title="Art Forms of Nature">Art Forms of Nature</a></i>. Dover, 1974.</li> <li>Stevens, Peter S. <i>Patterns in Nature</i>. Penguin, 1974.</li> <li><a href="/wiki/Ian_Stewart_(mathematician)" title="Ian Stewart (mathematician)">Stewart, Ian</a>. <i>What Shape is a Snowflake? Magical Numbers in Nature</i>. <a href="/wiki/Weidenfeld_%26_Nicolson" title="Weidenfeld & Nicolson">Weidenfeld & Nicolson</a>, 2001.</li> <li><a href="/wiki/D%27Arcy_Wentworth_Thompson" title="D'Arcy Wentworth Thompson">Thompson, D'Arcy W.</a> <i><a rel="nofollow" class="external text" href="https://archive.org/details/ongrowthform00thom">On Growth and Form</a></i>. 1942 2nd ed. (1st ed., 1917). <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/0-486-67135-6" title="Special:BookSources/0-486-67135-6">0-486-67135-6</a></li></ul> <div class="mw-heading mw-heading3"><h3 id="In_art_and_architecture">In art and architecture</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Pattern&action=edit&section=19" title="Edit section: In art and architecture"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Christopher_Alexander" title="Christopher Alexander">Alexander, C.</a> <i>A Pattern Language: Towns, Buildings, Construction</i>. Oxford, 1977.</li> <li>de Baeck, P. <i>Patterns</i>. Booqs, 2009.</li> <li>Garcia, M. <i>The Patterns of Architecture</i>. Wiley, 2009.</li> <li>Kiely, O. <i>Pattern</i>. Conran Octopus, 2010.</li> <li>Pritchard, S. <i>V&A Pattern: The Fifties</i>. V&A Publishing, 2009.</li></ul> <div class="mw-heading mw-heading3"><h3 id="In_science_and_mathematics">In science and mathematics</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Pattern&action=edit&section=20" title="Edit section: In science and mathematics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>Adam, J. A. <i>Mathematics in Nature: Modeling Patterns in the Natural World</i>. Princeton, 2006.</li> <li>Resnik, M. D. <i>Mathematics as a Science of Patterns</i>. Oxford, 1999.</li></ul> <div class="mw-heading mw-heading3"><h3 id="In_computing">In computing</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Pattern&action=edit&section=21" title="Edit section: In computing"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>Gamma, E., Helm, R., Johnson, R., Vlissides, J. <i><a href="/wiki/Design_Patterns" title="Design Patterns">Design Patterns</a></i>. Addison-Wesley, 1994.</li> <li>Bishop, C. M. <i>Pattern Recognition and Machine Learning</i>. 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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/Abstract_object_theory" title="Abstract object theory">Abstract object theory</a></li> <li><a href="/wiki/Action_theory_(philosophy)" title="Action theory (philosophy)">Action theory</a></li> <li><a href="/wiki/Anti-realism" title="Anti-realism">Anti-realism</a></li> <li><a href="/wiki/Determinism" title="Determinism">Determinism</a></li> <li><a href="/wiki/Mind%E2%80%93body_dualism" title="Mind–body dualism">Dualism</a></li> <li><a href="/wiki/Enactivism" title="Enactivism">Enactivism</a></li> <li><a href="/wiki/Essentialism" title="Essentialism">Essentialism</a></li> <li><a href="/wiki/Existentialism" title="Existentialism">Existentialism</a></li> <li><a href="/wiki/Free_will" title="Free will">Free will</a></li> <li><a href="/wiki/Idealism" title="Idealism">Idealism</a></li> <li><a href="/wiki/Libertarianism_(metaphysics)" title="Libertarianism 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title="Spiritualism (philosophy)">Spiritualism</a></li> <li><a href="/wiki/Subjectivism" title="Subjectivism">Subjectivism</a></li> <li><a href="/wiki/Substance_theory" title="Substance theory">Substance theory</a></li> <li><a href="/wiki/Theory_of_forms" title="Theory of forms">Theory of forms</a></li> <li><a href="/wiki/Truthmaker_theory" title="Truthmaker theory">Truthmaker theory</a></li> <li><a href="/wiki/Type_theory" title="Type theory">Type theory</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Concepts</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/Abstract_and_concrete" title="Abstract and concrete">Abstract object</a></li> <li><a href="/wiki/Anima_mundi" title="Anima mundi">Anima mundi</a></li> <li><a href="/wiki/Category_of_being" class="mw-redirect" title="Category of being">Category of being</a></li> <li><a href="/wiki/Causality" title="Causality">Causality</a></li> <li><a href="/wiki/Causal_closure" title="Causal closure">Causal closure</a></li> <li><i><a href="/wiki/Cogito,_ergo_sum" title="Cogito, ergo sum">Cogito, ergo sum</a></i></li> <li><a href="/wiki/Concept" title="Concept">Concept</a></li> <li><a href="/wiki/Embodied_cognition" title="Embodied cognition">Embodied cognition</a></li> <li><a href="/wiki/Entity" title="Entity">Entity</a></li> <li><a href="/wiki/Essence" title="Essence">Essence</a></li> <li><a href="/wiki/Existence" title="Existence">Existence</a></li> <li><a href="/wiki/Experience" title="Experience">Experience</a></li> <li><a href="/wiki/Hypostatic_abstraction" title="Hypostatic abstraction">Hypostatic abstraction</a></li> <li><a href="/wiki/Idea" title="Idea">Idea</a></li> <li><a href="/wiki/Identity_(philosophy)" title="Identity (philosophy)">Identity</a></li> <li><a href="/wiki/Information" title="Information">Information</a> <ul><li><a href="/wiki/Data" title="Data">Data</a></li></ul></li> <li><a href="/wiki/Insight" title="Insight">Insight</a></li> <li><a href="/wiki/Intelligence" title="Intelligence">Intelligence</a></li> <li><a href="/wiki/Intention" title="Intention">Intention</a></li> <li><a href="/wiki/Linguistic_modality" class="mw-redirect" title="Linguistic modality">Linguistic modality</a></li> <li><a href="/wiki/Philosophy_of_matter" title="Philosophy of matter">Matter</a></li> <li><a href="/wiki/Meaning_(existential)" title="Meaning (existential)">Meaning</a></li> <li><a href="/wiki/Mental_representation" title="Mental representation">Mental representation</a></li> <li><a href="/wiki/Mind" title="Mind">Mind</a></li> <li><a href="/wiki/Motion" title="Motion">Motion</a></li> <li><a href="/wiki/Nature_(philosophy)" title="Nature (philosophy)">Nature</a></li> <li><a href="/wiki/Metaphysical_necessity" title="Metaphysical necessity">Necessity</a></li> <li><a href="/wiki/Object_(philosophy)" class="mw-redirect" title="Object (philosophy)">Object</a></li> <li><a href="/wiki/Ontology" title="Ontology">Ontology</a></li> <li><a class="mw-selflink selflink">Pattern</a></li> <li><a href="/wiki/Perception" title="Perception">Perception</a></li> <li><a href="/wiki/Physical_object" title="Physical object">Physical object</a></li> <li><a href="/wiki/Principle" title="Principle">Principle</a></li> <li><a href="/wiki/Property_(philosophy)" title="Property (philosophy)">Property</a></li> <li><a href="/wiki/Qualia" title="Qualia">Qualia</a></li> <li><a href="/wiki/Quality_(philosophy)" title="Quality (philosophy)">Quality</a></li> <li><a href="/wiki/Reality" title="Reality">Reality</a></li> <li><a href="/wiki/Relations_(philosophy)" class="mw-redirect" title="Relations (philosophy)">Relation</a></li> <li><a href="/wiki/Self" title="Self">Self</a></li> <li><a href="/wiki/Soul" title="Soul">Soul</a></li> <li><a href="/wiki/Subject_(philosophy)" class="mw-redirect" title="Subject (philosophy)">Subject</a></li> <li><a href="/wiki/Substantial_form" title="Substantial form">Substantial form</a></li> <li><a href="/wiki/Thought" title="Thought">Thought</a></li> <li><a href="/wiki/Time" title="Time">Time</a></li> <li><a href="/wiki/Truth" title="Truth">Truth</a></li> <li><a href="/wiki/Type%E2%80%93token_distinction" title="Type–token distinction">Type–token distinction</a></li> <li><a href="/wiki/Universal_(metaphysics)" title="Universal (metaphysics)">Universal</a></li> <li><a href="/wiki/Unobservable" title="Unobservable">Unobservable</a></li> <li><a href="/wiki/Value_(ethics)" title="Value (ethics)">Value</a></li> <li><i><a href="/wiki/Index_of_metaphysics_articles" title="Index of metaphysics articles">more ...</a></i></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/List_of_metaphysicians" title="List of metaphysicians">Metaphysicians</a></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/Parmenides" title="Parmenides">Parmenides</a></li> <li><a href="/wiki/Plato" title="Plato">Plato</a></li> <li><a href="/wiki/Aristotle" title="Aristotle">Aristotle</a></li> <li><a href="/wiki/Lucretius" title="Lucretius">Lucretius</a></li> <li><a href="/wiki/Proclus" title="Proclus">Proclus</a></li> <li><a href="/wiki/Plotinus" title="Plotinus">Plotinus</a></li> <li><a href="/wiki/Avicenna" title="Avicenna">Avicenna</a></li> <li><a href="/wiki/Duns_Scotus" title="Duns Scotus">Scotus</a></li> <li><a href="/wiki/Thomas_Aquinas" title="Thomas Aquinas">Aquinas</a></li> <li><a href="/wiki/Francisco_Su%C3%A1rez" title="Francisco Suárez">Suárez</a></li> <li><a href="/wiki/Ren%C3%A9_Descartes" title="René Descartes">Descartes</a></li> <li><a href="/wiki/Baruch_Spinoza" title="Baruch Spinoza">Spinoza</a></li> <li><a href="/wiki/John_Locke" title="John Locke">Locke</a></li> <li><a href="/wiki/Nicolas_Malebranche" title="Nicolas Malebranche">Malebranche</a></li> <li><a href="/wiki/Isaac_Newton" title="Isaac Newton">Newton</a></li> <li><a href="/wiki/Gottfried_Wilhelm_Leibniz" title="Gottfried Wilhelm Leibniz">Leibniz</a></li> <li><a href="/wiki/Christian_Wolff_(philosopher)" title="Christian Wolff (philosopher)">Wolff</a></li> <li><a href="/wiki/Thomas_Reid" title="Thomas Reid">Reid</a></li> <li><a href="/wiki/George_Berkeley" title="George Berkeley">Berkeley</a></li> <li><a href="/wiki/David_Hume" title="David Hume">Hume</a></li> <li><a href="/wiki/Immanuel_Kant" title="Immanuel Kant">Kant</a></li> <li><a href="/wiki/Georg_Wilhelm_Friedrich_Hegel" title="Georg Wilhelm Friedrich Hegel">Hegel</a></li> <li><a href="/wiki/Arthur_Schopenhauer" title="Arthur Schopenhauer">Schopenhauer</a></li> <li><a href="/wiki/Bernard_Bolzano" title="Bernard Bolzano">Bolzano</a></li> <li><a href="/wiki/S%C3%B8ren_Kierkegaard" title="Søren Kierkegaard">Kierkegaard</a></li> <li><a href="/wiki/Hermann_Lotze" title="Hermann Lotze">Lotze</a></li> <li><a href="/wiki/Charles_Sanders_Peirce" title="Charles Sanders Peirce">Peirce</a></li> <li><a href="/wiki/Friedrich_Nietzsche" title="Friedrich Nietzsche">Nietzsche</a></li> <li><a href="/wiki/Alexius_Meinong" title="Alexius Meinong">Meinong</a></li> <li><a href="/wiki/Henri_Bergson" title="Henri Bergson">Bergson</a></li> <li><a href="/wiki/Alfred_North_Whitehead" title="Alfred North Whitehead">Whitehead</a></li> <li><a href="/wiki/Bertrand_Russell" title="Bertrand Russell">Russell</a></li> <li><a href="/wiki/G._E._Moore" title="G. E. Moore">Moore</a></li> <li><a href="/wiki/R._G._Collingwood" title="R. G. Collingwood">Collingwood</a></li> <li><a href="/wiki/Ludwig_Wittgenstein" title="Ludwig Wittgenstein">Wittgenstein</a></li> <li><a href="/wiki/Martin_Heidegger" title="Martin Heidegger">Heidegger</a></li> <li><a href="/wiki/Rudolf_Carnap" title="Rudolf Carnap">Carnap</a></li> <li><a href="/wiki/Gilbert_Ryle" title="Gilbert Ryle">Ryle</a></li> <li><a href="/wiki/Jean-Paul_Sartre" title="Jean-Paul Sartre">Sartre</a></li> <li><a href="/wiki/Willard_Van_Orman_Quine" title="Willard Van Orman Quine">Quine</a></li> <li><a href="/wiki/Donald_Davidson_(philosopher)" title="Donald Davidson (philosopher)">Davidson</a></li> <li><a href="/wiki/P._F._Strawson" title="P. F. Strawson">Strawson</a></li> <li><a href="/wiki/G._E._M._Anscombe" title="G. E. M. Anscombe">Anscombe</a></li> <li><a href="/wiki/Gilles_Deleuze" title="Gilles Deleuze">Deleuze</a></li> <li><a href="/wiki/Michael_Dummett" title="Michael Dummett">Dummett</a></li> <li><a href="/wiki/David_Malet_Armstrong" title="David Malet Armstrong">Armstrong</a></li> <li><a href="/wiki/Hilary_Putnam" title="Hilary Putnam">Putnam</a></li> <li><a href="/wiki/Alvin_Plantinga" title="Alvin Plantinga">Plantinga</a></li> <li><a href="/wiki/Saul_Kripke" title="Saul Kripke">Kripke</a></li> <li><a href="/wiki/David_Lewis_(philosopher)" title="David Lewis (philosopher)">Lewis</a></li> <li><a href="/wiki/Jean_Baudrillard" title="Jean Baudrillard">Baudrillard</a></li> <li><a href="/wiki/Derek_Parfit" title="Derek Parfit">Parfit</a></li> <li><i><a href="/wiki/List_of_metaphysicians" title="List of metaphysicians">more ...</a></i></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Notable works</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><i><a href="/wiki/Sophist_(dialogue)" title="Sophist (dialogue)">Sophist</a></i> <span style="font-size:85%;">(c. 350 BC)</span></li> <li><i><a href="/wiki/Timaeus_(dialogue)" title="Timaeus (dialogue)">Timaeus</a></i> <span style="font-size:85%;">(c. 350 BC)</span></li> <li><i><a href="/wiki/Ny%C4%81ya_S%C5%ABtras" title="Nyāya Sūtras">Nyāya Sūtras</a></i> <span style="font-size:85%;">(c. 200 BC)</span></li> <li><i><a href="/wiki/De_rerum_natura" title="De rerum natura">De rerum natura</a></i> <span style="font-size:85%;">(c. 80 BC)</span></li> <li><i><a href="/wiki/Metaphysics_(Aristotle)" title="Metaphysics (Aristotle)">Metaphysics</a></i> <span style="font-size:85%;">(c. 50)</span></li> <li><i><a href="/wiki/Enneads" title="Enneads">Enneads</a></i> <span style="font-size:85%;">(c. 270)</span></li> <li><i><a href="/wiki/Daneshnameh-ye_Alai" class="mw-redirect" title="Daneshnameh-ye Alai">Daneshnameh-ye Alai</a></i> <span style="font-size:85%;">(c. 1000)</span></li> <li><i><a href="/wiki/Meditations_on_First_Philosophy" title="Meditations on First Philosophy">Meditations on First Philosophy</a></i> <span style="font-size:85%;">(1641)</span></li> <li><i><a href="/wiki/Ethics_(Spinoza_book)" class="mw-redirect" title="Ethics (Spinoza book)">Ethics</a></i> <span style="font-size:85%;">(1677)</span></li> <li><i><a href="/wiki/A_Treatise_Concerning_the_Principles_of_Human_Knowledge" title="A Treatise Concerning the Principles of Human Knowledge">A Treatise Concerning the Principles of Human Knowledge</a></i> <span style="font-size:85%;">(1710)</span></li> <li><i><a href="/wiki/Monadology" title="Monadology">Monadology</a></i> <span style="font-size:85%;">(1714)</span></li> <li><i><a href="/wiki/Critique_of_Pure_Reason" title="Critique of Pure Reason">Critique of Pure Reason</a></i> <span style="font-size:85%;">(1781)</span></li> <li><i><a href="/wiki/Prolegomena_to_Any_Future_Metaphysics" title="Prolegomena to Any Future Metaphysics">Prolegomena to Any Future Metaphysics</a></i> <span style="font-size:85%;">(1783)</span></li> <li><i><a href="/wiki/The_Phenomenology_of_Spirit" title="The Phenomenology of Spirit">The Phenomenology of Spirit</a></i> <span style="font-size:85%;">(1807)</span></li> <li><i><a href="/wiki/The_World_as_Will_and_Representation" title="The World as Will and Representation">The World as Will and Representation</a></i> <span style="font-size:85%;">(1818)</span></li> <li><i><a href="/wiki/Concluding_Unscientific_Postscript_to_Philosophical_Fragments" title="Concluding Unscientific Postscript to Philosophical Fragments">Concluding Unscientific Postscript to Philosophical Fragments</a></i> <span style="font-size:85%;">(1846)</span></li> <li><i><a href="/wiki/Being_and_Time" title="Being and Time">Being and Time</a></i> <span style="font-size:85%;">(1927)</span></li> <li><i><a href="/wiki/Being_and_Nothingness" title="Being and Nothingness">Being and Nothingness</a></i> <span style="font-size:85%;">(1943)</span></li> <li><i><a href="/wiki/Simulacra_and_Simulation" title="Simulacra and Simulation">Simulacra and Simulation</a></i> <span style="font-size:85%;">(1981)</span></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Related topics</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/Axiology" class="mw-redirect" title="Axiology">Axiology</a></li> <li><a href="/wiki/Cosmology" title="Cosmology">Cosmology</a></li> <li><a href="/wiki/Epistemology" title="Epistemology">Epistemology</a></li> <li><a href="/wiki/Feminist_metaphysics" title="Feminist metaphysics">Feminist metaphysics</a></li> <li><a href="/wiki/Interpretations_of_quantum_mechanics" title="Interpretations of quantum mechanics">Interpretations of quantum mechanics</a></li> <li><a href="/wiki/Mereology" title="Mereology">Mereology</a></li> <li><a href="/wiki/Meta_(prefix)" title="Meta (prefix)">Meta-</a></li> <li><a href="/wiki/Phenomenology_(philosophy)" title="Phenomenology (philosophy)">Phenomenology</a></li> <li><a href="/wiki/Philosophy_of_mind" title="Philosophy of mind">Philosophy of mind</a></li> <li><a href="/wiki/Philosophy_of_psychology" title="Philosophy of psychology">Philosophy of psychology</a></li> <li><a href="/wiki/Philosophy_of_self" title="Philosophy of self">Philosophy of self</a></li> <li><a href="/wiki/Philosophy_of_space_and_time" title="Philosophy of space and time">Philosophy of space and time</a></li> <li><a href="/wiki/Teleology" title="Teleology">Teleology</a></li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div> <ul><li><span class="noviewer" typeof="mw:File"><span title="Category"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/16px-Symbol_category_class.svg.png" decoding="async" width="16" height="16" class="mw-file-element" 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