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Available in 12 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-12" 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">12 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%A8%D8%B1%D8%A7%D9%8A%D8%A7%D9%86_%D8%BA%D9%88%D8%AF%D9%88%D9%8A%D9%86" title="برايان غودوين – Arabic" lang="ar" hreflang="ar" data-title="برايان غودوين" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/Brian_Goodwin" title="Brian Goodwin – Minnan" lang="nan" hreflang="nan" data-title="Brian Goodwin" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="Minnan" class="interlanguage-link-target"><span>閩南語 / Bân-lâm-gú</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Brian_Goodwin" title="Brian Goodwin – German" lang="de" hreflang="de" data-title="Brian Goodwin" 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/Brian_Goodwin" title="Brian Goodwin – Estonian" lang="et" hreflang="et" data-title="Brian Goodwin" 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/Brian_Goodwin" title="Brian Goodwin – Spanish" lang="es" hreflang="es" data-title="Brian Goodwin" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Brian_Goodwin" title="Brian Goodwin – Indonesian" lang="id" hreflang="id" data-title="Brian Goodwin" 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-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/Brian_Goodwin" title="Brian Goodwin – Haitian Creole" lang="ht" hreflang="ht" data-title="Brian Goodwin" 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-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%83%96%E3%83%A9%E3%82%A4%E3%82%A2%E3%83%B3%E3%83%BB%E3%82%B0%E3%83%83%E3%83%89%E3%82%A6%E3%82%A3%E3%83%B3" title="ブライアン・グッドウィン – Japanese" lang="ja" hreflang="ja" data-title="ブライアン・グッドウィン" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Brian_Goodwin" title="Brian Goodwin – Portuguese" lang="pt" hreflang="pt" data-title="Brian Goodwin" 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%93%D1%83%D0%B4%D1%83%D0%B8%D0%BD,_%D0%91%D1%80%D0%B0%D0%B9%D0%B0%D0%BD" title="Гудуин, Брайан – Russian" lang="ru" hreflang="ru" data-title="Гудуин, Брайан" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Brian_Goodwin" title="Brian Goodwin – Finnish" lang="fi" hreflang="fi" data-title="Brian Goodwin" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E5%B8%83%E8%8E%B1%E6%81%A9%C2%B7%E5%8F%A4%E5%BE%B7%E6%B8%A9" title="布莱恩·古德温 – Chinese" lang="zh" hreflang="zh" data-title="布莱恩·古德温" 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 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dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Canadian mathematician and biologist (1931–2009)</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 the baseball player, see <a href="/wiki/Brian_Goodwin_(baseball)" title="Brian Goodwin (baseball)">Brian Goodwin (baseball)</a>. For the Scottish footballer, see <a href="/wiki/Brian_Goodwin_(footballer)" title="Brian Goodwin (footballer)">Brian Goodwin (footballer)</a>.</div> <style data-mw-deduplicate="TemplateStyles:r1251242444">.mw-parser-output .ambox{border:1px solid #a2a9b1;border-left:10px solid #36c;background-color:#fbfbfb;box-sizing:border-box}.mw-parser-output .ambox+link+.ambox,.mw-parser-output .ambox+link+style+.ambox,.mw-parser-output .ambox+link+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+style+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+link+.ambox{margin-top:-1px}html body.mediawiki .mw-parser-output .ambox.mbox-small-left{margin:4px 1em 4px 0;overflow:hidden;width:238px;border-collapse:collapse;font-size:88%;line-height:1.25em}.mw-parser-output .ambox-speedy{border-left:10px solid #b32424;background-color:#fee7e6}.mw-parser-output .ambox-delete{border-left:10px solid #b32424}.mw-parser-output .ambox-content{border-left:10px solid #f28500}.mw-parser-output .ambox-style{border-left:10px solid #fc3}.mw-parser-output .ambox-move{border-left:10px solid #9932cc}.mw-parser-output .ambox-protection{border-left:10px solid #a2a9b1}.mw-parser-output .ambox .mbox-text{border:none;padding:0.25em 0.5em;width:100%}.mw-parser-output .ambox .mbox-image{border:none;padding:2px 0 2px 0.5em;text-align:center}.mw-parser-output .ambox .mbox-imageright{border:none;padding:2px 0.5em 2px 0;text-align:center}.mw-parser-output .ambox .mbox-empty-cell{border:none;padding:0;width:1px}.mw-parser-output .ambox .mbox-image-div{width:52px}@media(min-width:720px){.mw-parser-output .ambox{margin:0 10%}}@media print{body.ns-0 .mw-parser-output .ambox{display:none!important}}</style><table class="box-More_citations_needed plainlinks metadata ambox ambox-content ambox-Refimprove" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><a href="/wiki/File:Question_book-new.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/50px-Question_book-new.svg.png" decoding="async" width="50" height="39" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/75px-Question_book-new.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/100px-Question_book-new.svg.png 2x" data-file-width="512" data-file-height="399" /></a></span></div></td><td class="mbox-text"><div class="mbox-text-span">This article <b>needs additional citations for <a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability">verification</a></b>.<span class="hide-when-compact"> Please help <a href="/wiki/Special:EditPage/Brian_Goodwin" title="Special:EditPage/Brian Goodwin">improve this article</a> by <a href="/wiki/Help:Referencing_for_beginners" title="Help:Referencing for beginners">adding citations to reliable sources</a>. Unsourced material may be challenged and removed.<br /><small><span class="plainlinks"><i>Find sources:</i> <a rel="nofollow" class="external text" href="https://www.google.com/search?as_eq=wikipedia&q=%22Brian+Goodwin%22">"Brian Goodwin"</a> – <a rel="nofollow" class="external text" href="https://www.google.com/search?tbm=nws&q=%22Brian+Goodwin%22+-wikipedia&tbs=ar:1">news</a> <b>·</b> <a rel="nofollow" class="external text" href="https://www.google.com/search?&q=%22Brian+Goodwin%22&tbs=bkt:s&tbm=bks">newspapers</a> <b>·</b> <a rel="nofollow" class="external text" href="https://www.google.com/search?tbs=bks:1&q=%22Brian+Goodwin%22+-wikipedia">books</a> <b>·</b> <a rel="nofollow" class="external text" href="https://scholar.google.com/scholar?q=%22Brian+Goodwin%22">scholar</a> <b>·</b> <a rel="nofollow" class="external text" href="https://www.jstor.org/action/doBasicSearch?Query=%22Brian+Goodwin%22&acc=on&wc=on">JSTOR</a></span></small></span> <span class="date-container"><i>(<span class="date">December 2016</span>)</i></span><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> <p class="mw-empty-elt"> </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:BrianSmall.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4d/BrianSmall.png/220px-BrianSmall.png" decoding="async" width="220" height="255" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/4/4d/BrianSmall.png 1.5x" data-file-width="236" data-file-height="274" /></a><figcaption>Brian Goodwin in 1992</figcaption></figure> <p><b>Brian Carey Goodwin</b> (25 March 1931 – 15 July 2009) (<a href="/wiki/Sainte-Anne-de-Bellevue" title="Sainte-Anne-de-Bellevue">Sainte-Anne-de-Bellevue</a>, Quebec, Canada - <a href="/wiki/Dartington" title="Dartington">Dartington</a>, <a href="/wiki/Totnes" title="Totnes">Totnes</a>, Devon, UK) was a <a href="/wiki/Canadians" title="Canadians">Canadian</a> <a href="/wiki/Mathematician" title="Mathematician">mathematician</a> and <a href="/wiki/Biologist" title="Biologist">biologist</a>, a Professor Emeritus at the <a href="/wiki/Open_University" title="Open University">Open University</a> and a founder of <a href="/wiki/Theoretical_biology" class="mw-redirect" title="Theoretical biology">theoretical biology</a> and biomathematics. He introduced the use of complex systems and generative models in <a href="/wiki/Developmental_biology" title="Developmental biology">developmental biology</a>. He suggested that a <a href="/wiki/Reductionism" title="Reductionism">reductionist</a> view of nature fails to explain complex features, controversially proposing the <a href="/wiki/Structuralism_(biology)" title="Structuralism (biology)">structuralist</a> theory that <a href="/wiki/Morphogenetic_field" title="Morphogenetic field">morphogenetic fields</a> might substitute for <a href="/wiki/Natural_selection" title="Natural selection">natural selection</a> in driving <a href="/wiki/Evolution" title="Evolution">evolution</a>.<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> He was also a visible member of the <a href="/wiki/The_Third_Culture" title="The Third Culture">Third Culture</a> movement.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Biography">Biography</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Brian_Goodwin&action=edit&section=1" title="Edit section: Biography"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Brian Goodwin was born in <a href="/wiki/Montreal" title="Montreal">Montreal</a>, <a href="/wiki/Quebec" title="Quebec">Quebec</a>, Canada in 1931. He studied biology at <a href="/wiki/McGill_University" title="McGill University">McGill University</a> and then emigrated to the <a href="/wiki/United_Kingdom" title="United Kingdom">UK</a>, under a <a href="/wiki/Rhodes_Scholarship" title="Rhodes Scholarship">Rhodes Scholarship</a> for studying mathematics at Oxford. He got his PhD at the <a href="/wiki/University_of_Edinburgh" title="University of Edinburgh">University of Edinburgh</a> presenting the thesis <i>"Studies in the general theory of development and evolution"</i><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> under the supervision of <a href="/wiki/Conrad_Hal_Waddington" class="mw-redirect" title="Conrad Hal Waddington">Conrad Hal Waddington</a>. He then moved to <a href="/wiki/Sussex_University" class="mw-redirect" title="Sussex University">Sussex University</a> until 1983 when he became a full <a href="/wiki/Professor" title="Professor">professor</a> at the <a href="/wiki/Open_University" title="Open University">Open University</a> in <a href="/wiki/Milton_Keynes" title="Milton Keynes">Milton Keynes</a> until retirement in 1992. He became a major figure in the early development of <a href="/wiki/Mathematical_biology" class="mw-redirect" title="Mathematical biology">mathematical biology</a>, along with other researchers. He was one of the attendants to the famous meetings that took place between 1965 and 1968 in Villa Serbelloni, hosted by the <a href="/wiki/Rockefeller_Foundation" title="Rockefeller Foundation">Rockefeller Foundation</a>, under the topic "Towards a theoretical Biology". </p><p>Thereafter, he taught at the <a href="/wiki/Schumacher_College" title="Schumacher College">Schumacher College</a> in <a href="/wiki/Devon" title="Devon">Devon</a>, <a href="/wiki/United_Kingdom" title="United Kingdom">UK</a>, where he was instrumental in starting the college's MSc in Holistic Science. He was made a Founding Fellow of Schumacher College shortly before his death. Goodwin also had a research position at <a href="/wiki/MIT" class="mw-redirect" title="MIT">MIT</a> and was a long time visitor of several institutions including the <a href="/wiki/UNAM" class="mw-redirect" title="UNAM">UNAM</a> in Mexico City. He was a founding member of the <a href="/wiki/Santa_Fe_Institute" title="Santa Fe Institute">Santa Fe Institute</a> in <a href="/wiki/New_Mexico" title="New Mexico">New Mexico</a> where he also served as a member of the science board for several years.<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><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> </p><p>Brian Goodwin died in hospital in 2009, after surgery resulting from a fall from his bicycle.<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> Goodwin is survived by his third wife, Christel, and his daughter, Lynn. </p> <div class="mw-heading mw-heading2"><h2 id="Gene_networks_and_development">Gene networks and development</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Brian_Goodwin&action=edit&section=2" title="Edit section: Gene networks and development"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Shortly after <a href="/wiki/Fran%C3%A7ois_Jacob" title="François Jacob">François Jacob</a> and <a href="/wiki/Jacques_Monod" title="Jacques Monod">Jacques Monod</a> developed their first model of gene regulation, Goodwin proposed the first model of a genetic oscillator, showing that regulatory interactions among genes allowed periodic fluctuations to occur. Shortly after this model became published, he also formulated a general theory of complex <a href="/wiki/Gene_regulatory_networks" class="mw-redirect" title="Gene regulatory networks">gene regulatory networks</a> using <a href="/wiki/Statistical_mechanics" title="Statistical mechanics">statistical mechanics</a>. In its simplest form, Goodwin's oscillator involves a single gene that represses itself. Goodwin equations were originally formulated in terms of conservative (Hamiltonian) systems, thus not taking into account dissipative effects that are required in a realistic approach to regulatory phenomena in biology. Many versions have been developed since then. The simplest (but realistic) formulation considers three variables, X, Y and Z indicating the concentrations of <a href="/wiki/RNA" title="RNA">RNA</a>, <a href="/wiki/Protein" title="Protein">protein</a> and end product which generates the negative <a href="/wiki/Feedback" title="Feedback">feedback</a> loop. The equations are </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {dX}{dt}}={k_{1} \over K_{1}+Z^{n}}-k_{2}X}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mi>X</mi> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mrow> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>+</mo> <msup> <mi>Z</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>−</mo> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mi>X</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {dX}{dt}}={k_{1} \over K_{1}+Z^{n}}-k_{2}X}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c80267762fa40c6eefd0e2ce934a2fffc5a8092d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:23.847ex; height:5.676ex;" alt="{\displaystyle {\frac {dX}{dt}}={k_{1} \over K_{1}+Z^{n}}-k_{2}X}"></span></dd></dl> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {dY}{dt}}=k_{3}X-k_{4}Y}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mi>Y</mi> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mi>X</mi> <mo>−</mo> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msub> <mi>Y</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {dY}{dt}}=k_{3}X-k_{4}Y}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5e2676cefbe611940626e0bf024f272a25252aad" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:18.048ex; height:5.509ex;" alt="{\displaystyle {\frac {dY}{dt}}=k_{3}X-k_{4}Y}"></span></dd></dl> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {dZ}{dt}}=k_{5}Y-k_{6}Z}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mi>Z</mi> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> </msub> <mi>Y</mi> <mo>−</mo> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> </msub> <mi>Z</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {dZ}{dt}}=k_{5}Y-k_{6}Z}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f0e39ddb1d8b9d90dc8f68b72177ef38f4a201f3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:17.656ex; height:5.509ex;" alt="{\displaystyle {\frac {dZ}{dt}}=k_{5}Y-k_{6}Z}"></span></dd></dl> <p>and closed oscillations can occur for n>8 and behave <a href="/wiki/Limit_cycles" class="mw-redirect" title="Limit cycles">limit cycles</a>: after a perturbation of the system's state, it returns to its previous attractor. A simple modification of this model, adding other terms introducing additional steps in the transcription machinery allows to find oscillations for smaller n values. Goodwin's model and its extensions have been widely used over the years as the basic skeleton for other models of oscillatory behavior, including <a href="/wiki/Circadian_rhythm" title="Circadian rhythm">circadian clocks</a>, <a href="/wiki/Cell_division" title="Cell division">cell division</a> or physiological control systems. </p> <div class="mw-heading mw-heading2"><h2 id="Developmental_biology">Developmental biology</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Brian_Goodwin&action=edit&section=3" title="Edit section: Developmental biology"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In the field of <a href="/wiki/Developmental_biology" title="Developmental biology">developmental biology</a>, Goodwin explored <a href="/wiki/Self-organization" title="Self-organization">self-organization</a> in <a href="/wiki/Pattern_formation" title="Pattern formation">pattern formation</a>, using case studies from single-cell (as <i><a href="/wiki/Acetabularia" title="Acetabularia">Acetabularia</a></i>) to multicellular organisms, including early development in <i><a href="/wiki/Drosophila" title="Drosophila">Drosophila</a></i>. He proposed that <a href="/wiki/Morphogenetic_field" title="Morphogenetic field">morphogenetic fields</a>, defined in terms of spatial distributions of chemical signals (morphogenes), could pattern and shape the embryo. In this way, geometry and development were linked through a mathematical formalism. Along with his colleague Lynn Trainor, Goodwin developed a set of mathematical equations describing the changes of both physical boundaries in the organism and chemical gradients. </p><p>By considering the mechanochemical behaviour of the cortical cytoplasm (or cytogel) of plant cells, a viscoelastic material mainly composed of actin microfilaments and reinforced by a microtubules network, Goodwin & Trainor (1985) showed how to couple calcium and the mechanical properties of the cytoplasm. The cytogel is treated as a continuous viscoelastic medium in which calcium ions can diffuse and interact with the cytoskeleton. The model consists in two non-linear partial differential equations which describe the evolution of the mechanical strain field and of the calcium distribution in the cytogel. </p><p>It has been shown (Trainor & Goodwin, 1986) that, in a range of parameter values, instabilities may occur and develop in this system, leading to intracellular patterns of strain and calcium concentration. The equations read, in their general form: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \rho {\partial ^{2}\xi \over \partial t^{2}}={\partial \over \partial x}\left(P_{1}(\chi ){\partial \xi \over \partial x}\right)+{\partial \over \partial x}\left(P_{2}(\chi ){\partial ^{2}\xi \over \partial x\partial t}\right)-P_{3}(\chi )-F_{0}{\partial \chi \over \partial x}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>ξ</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi mathvariant="normal">∂</mi> <mrow> <mi mathvariant="normal">∂</mi> <mi>x</mi> </mrow> </mfrac> </mrow> <mrow> <mo>(</mo> <mrow> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi>χ</mi> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>ξ</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>x</mi> </mrow> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi mathvariant="normal">∂</mi> <mrow> <mi mathvariant="normal">∂</mi> <mi>x</mi> </mrow> </mfrac> </mrow> <mrow> <mo>(</mo> <mrow> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi>χ</mi> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>ξ</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>x</mi> <mi mathvariant="normal">∂</mi> <mi>t</mi> </mrow> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> <mo>−</mo> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi>χ</mi> <mo stretchy="false">)</mo> <mo>−</mo> <msub> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>χ</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>x</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho {\partial ^{2}\xi \over \partial t^{2}}={\partial \over \partial x}\left(P_{1}(\chi ){\partial \xi \over \partial x}\right)+{\partial \over \partial x}\left(P_{2}(\chi ){\partial ^{2}\xi \over \partial x\partial t}\right)-P_{3}(\chi )-F_{0}{\partial \chi \over \partial x}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6d4b7d9bdfade0de0aa9ee9a02d54e841b3f871a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:64.386ex; height:6.343ex;" alt="{\displaystyle \rho {\partial ^{2}\xi \over \partial t^{2}}={\partial \over \partial x}\left(P_{1}(\chi ){\partial \xi \over \partial x}\right)+{\partial \over \partial x}\left(P_{2}(\chi ){\partial ^{2}\xi \over \partial x\partial t}\right)-P_{3}(\chi )-F_{0}{\partial \chi \over \partial x}}"></span></dd></dl> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\partial \chi \over \partial t}=\left(a_{0}+a{\partial \xi \over \partial x}\right)(K-\chi )-k_{1}(\beta +\chi )\chi ^{n}+D{\partial ^{2}\xi \over \partial x^{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>χ</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow> <mo>(</mo> <mrow> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>+</mo> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>ξ</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>x</mi> </mrow> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> <mo stretchy="false">(</mo> <mi>K</mi> <mo>−</mo> <mi>χ</mi> <mo stretchy="false">)</mo> <mo>−</mo> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi>β</mi> <mo>+</mo> <mi>χ</mi> <mo stretchy="false">)</mo> <msup> <mi>χ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> <mo>+</mo> <mi>D</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi mathvariant="normal">∂</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>ξ</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\partial \chi \over \partial t}=\left(a_{0}+a{\partial \xi \over \partial x}\right)(K-\chi )-k_{1}(\beta +\chi )\chi ^{n}+D{\partial ^{2}\xi \over \partial x^{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/04e7822f8d0765e570bd2dd8efb0aba23cf85240" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:53.044ex; height:6.343ex;" alt="{\displaystyle {\partial \chi \over \partial t}=\left(a_{0}+a{\partial \xi \over \partial x}\right)(K-\chi )-k_{1}(\beta +\chi )\chi ^{n}+D{\partial ^{2}\xi \over \partial x^{2}}}"></span></dd></dl> <p>These equations describe the spatiotemporal dynamics of the displacement from the reference state and the calcium concentration, respectively. Here x and t are the space and time coordinates, respectively. These equations can be applied to many different scenarios and the different functions P(x) introduce the specific mechanical properties of the medium. These equations can generate a rich variety of static and dynamic patterns, from complex geometrical motifs to oscillations and chaos (Briere 1994)<sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Template:Harvard_citation_documentation#Wikilink_to_citation_does_not_work" title="Template:Harvard citation documentation"><span title="Template:Harvard citation documentation#Wikilink to citation does not work (November 2020)">citation not found</span></a></i>]</sup>. </p> <div class="mw-heading mw-heading2"><h2 id="Structuralism">Structuralism</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Brian_Goodwin&action=edit&section=4" title="Edit section: Structuralism"><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/Structuralism" title="Structuralism">Structuralism</a></div> <p>He was also a strong advocate of the view that genes cannot fully explain the <a href="/wiki/Complexity" title="Complexity">complexity</a> of biological systems. In that sense, he became one of the strongest defenders of the systems view against <a href="/wiki/Reductionism" title="Reductionism">reductionism</a>. He suggested that nonlinear phenomena and the fundamental laws defining their behavior were essential to understand biology and its evolutionary paths. His position within evolutionary biology can be defined as a <a href="/wiki/Structuralism_(biology)" title="Structuralism (biology)">structuralist</a> one. To Goodwin, many <a href="/wiki/Patterns_in_nature" title="Patterns in nature">patterns in nature</a> are a byproduct of constraints imposed by complexity. The limited repertoire of motifs observed in the spatial organization of plants and animals (at some scales) would be, in Goodwin's opinion, a fingerprint of the role played by such constraints. The role of <a href="/wiki/Natural_selection" title="Natural selection">natural selection</a> would be secondary. </p><p>These opinions were highly controversial, and they brought Goodwin into conflict with many prominent Darwinian evolutionists, whereas some physicists found some of his views natural. Physicist <a href="/wiki/Murray_Gell-Mann" title="Murray Gell-Mann">Murray Gell-Mann</a> for example acknowledged that "when biological evolution — based on largely random variation in genetic material and on natural selection — operates on the structure of actual organisms, it does so subject to the laws of physical science, which place crucial limitations on how living things can be constructed." <a href="/wiki/Richard_Dawkins" title="Richard Dawkins">Richard Dawkins</a>, the former professor for public understanding of science at Oxford University and a well known Darwinian evolutionist, conceded: "I don't think there's much good evidence to support [his thesis], but it's important that somebody like Brian Goodwin is saying that kind of thing, because it provides the other extreme, and the truth probably lies somewhere between." Dawkins also agreed that "It's a genuinely interesting possibility that the underlying laws of morphology allow only a certain limited range of shapes.". For his part, Goodwin did not reject basic Darwinism, only its excesses. </p> <div class="mw-heading mw-heading2"><h2 id="Reception">Reception</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Brian_Goodwin&action=edit&section=5" title="Edit section: Reception"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Biologist <a href="/wiki/Gert_Korthof" title="Gert Korthof">Gert Korthof</a> has praised the research of Goodwin commenting he tried to "improve Darwinism in a scientific way."<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> <a href="/wiki/David_B._Wake" title="David B. Wake">David B. Wake</a> has also positively reviewed Goodwin's research describing him as a "thoughtful scientist, one of the great dissenters from the orthodoxies of modern evolutionary, genetic and developmental biology".<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> </p><p>Goodwin had argued that <a href="/wiki/Natural_selection" title="Natural selection">natural selection</a> was "too weak [a] force" to explain evolution and only operated as a filter mechanism. He claimed that modern evolutionary biology failed to provide an explanation for the theory of biological form and had ignored the importance of <a href="/wiki/Morphogenesis" title="Morphogenesis">morphogenesis</a> in evolution. He claimed to provide a new evolutionary theory to replace neo-Darwinism. In a critical review, biologist Catherine S. C. Price noted that although he had succeeded in providing an alternative to mutation as the only source of variation, he failed to provide an alternative to natural selection as a mechanism of adaptation.<sup id="cite_ref-Price_1995_9-0" class="reference"><a href="#cite_note-Price_1995-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> Price claimed Goodwin's "discussion of evolution is biased, insufficiently developed and poorly informed", and that he misrepresented Darwinism, used <a href="/wiki/Straw_man" title="Straw man">straw man</a> arguments and ignored research from <a href="/wiki/Population_genetics" title="Population genetics">population genetics</a>.<sup id="cite_ref-Price_1995_9-1" class="reference"><a href="#cite_note-Price_1995-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p><p>The evolutionary biologist <a href="/wiki/G%C3%BCnter_P._Wagner" title="Günter P. Wagner">Günter P. Wagner</a> described Goodwin's structuralism as "a <a href="/wiki/Pseudoscience" title="Pseudoscience">fringe</a> movement in evolutionary biology".<sup id="cite_ref-Wagner2014_10-0" class="reference"><a href="#cite_note-Wagner2014-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Publications">Publications</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Brian_Goodwin&action=edit&section=6" title="Edit section: Publications"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <dl><dt>Books</dt></dl> <ul><li>1963. <i>Temporal Organization in Cells</i> Academic Press, London 1963, <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><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/1376206161" title="Special:BookSources/1376206161">1376206161</a></li> <li>1989. <i>Theoretical Biology: Epigenetic and Evolutionary Order for Complex Systems</i> with Peter Saunders, Edinburgh University Press, 1989, <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/0-85224-600-5" title="Special:BookSources/0-85224-600-5">0-85224-600-5</a></li> <li>1994. <i>Mechanical Engineering of the Cytoskeleton in Developmental Biology (International Review of Cytology)</i>, with Kwang W. Jeon and Richard J. Gordon, Academic Press, London 1994, <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/0-12-364553-0" title="Special:BookSources/0-12-364553-0">0-12-364553-0</a></li> <li>1996. <i>Form and Transformation: Generative and Relational Principles in Biology</i>, Cambridge Univ Press, 1996.</li> <li>1997. <i>How the Leopard Changed its Spots: The Evolution of Complexity</i>, Scribner, 1994, <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/0-02-544710-6" title="Special:BookSources/0-02-544710-6">0-02-544710-6</a> (German: <i>Der Leopard, der seine Flecken verliert</i>, Piper, München 1997, <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/3-492-03873-5" title="Special:BookSources/3-492-03873-5">3-492-03873-5</a>)</li> <li>2001. <i>Signs of Life: How Complexity Pervades Biology</i>, with Ricard V. Solé, Basic Books, 2001, <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/0-465-01927-7" title="Special:BookSources/0-465-01927-7">0-465-01927-7</a></li> <li>2007. <i>Nature's Due: Healing Our Fragmented Culture</i>, Floris Books, 2007, <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/0-86315-596-0" title="Special:BookSources/0-86315-596-0">0-86315-596-0</a></li></ul> <dl><dt>Selected Scientific papers</dt></dl> <ul><li>Goodwin, BC 1965, "Oscillatory behaviour in enzymatic control processes", Adv. Enz. Reg. 3: 425-428.</li> <li>Goodwin BC 1978, "A cognitive view of biological process." J Soc Biol Structures 1:117-125</li> <li>Gordon, DM, Goodwin, BC and Trainor LEH 1992, "A parallel distributed model of the behaviour of ant colonies", J. Theor. Biol. 156, 293-307.</li> <li>1997, "Temporal organization and disorganization in organisms". in: <i>Chronobiology International</i> 14 (5): 531-536 1997</li> <li>Goodwin BC, 1978 "A cognitive view of biological process", J. Soc. Biol. Struct. 1, 117-125.</li> <li>2000, "The life of form. Emergent patterns of morphological transformation". in: <i>Comptes rendud de la Academie des Science III</i> 323 (1): 15-21 JAN 2000</li> <li>Goodwin BC (2000). The life of form. Emergent patterns of morphological transformation. Comptes rendus de l'academie des sciencies III - Sciences de la vie-life sciences 323 (1): 15-21</li> <li>Goodwin BC. (1997) Temporal organization and disorganization in organisms. Chronobiology international 14 (5): 531-536</li> <li>Solé, R., O. Miramontes y Goodwin BC. (1993) "Order and chaos in ant societies". J. Theor. Biol. 161: 343</li> <li>Miramontes, O., R. Solé y BC Goodwin (1993), Collective Behaviour of Random-Activated Mobile Cellular Automata. Physica D 63: 145-160</li> <li>Jaeger, J. and Goodwin BC 2001, "A cellular oscillator model for periodic pattern formation" J. Theor. Biol. 213, 71-181.</li> <li>2002, "In the Shadow of Culture". in: "The Next Fifty Years: Science in the First Half of the Twenty-First Century" Edited by John Brockman, Vintage Books, MAY 2002, <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/0-375-71342-5" title="Special:BookSources/0-375-71342-5">0-375-71342-5</a></li> <li>Goodwin B 2005, "Meaning in evolution" J. Biol. Phys. Chem. 5, 51–56.</li></ul> <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=Brian_Goodwin&action=edit&section=7" 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"> <div class="mw-references-wrap"><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">Dickinson, W. Joseph. (1998). <i>Form and Transformation: Generative and Relational Principles in Biology. by Gerry Webster; Brian Goodwin</i>. <i><a href="/wiki/The_Quarterly_Review_of_Biology" title="The Quarterly Review of Biology">The Quarterly Review of Biology</a></i>. Vol. 73, No. 1. pp. 62-63.</span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="https://www.theguardian.com/theguardian/2009/aug/09/brian-goodwin-obituary">Brian Goodwin obituary - <i>The Guardian</i>, 9 August 2009</a></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGoodwin1961" class="citation thesis cs1">Goodwin, Brian C. (1961). <a rel="nofollow" class="external text" href="https://era.ed.ac.uk/handle/1842/12041"><i>Studies in the general theory of development and evolution</i></a> (Thesis). University of Edinburgh.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adissertation&rft.title=Studies+in+the+general+theory+of+development+and+evolution&rft.inst=University+of+Edinburgh&rft.date=1961&rft.aulast=Goodwin&rft.aufirst=Brian+C.&rft_id=https%3A%2F%2Fera.ed.ac.uk%2Fhandle%2F1842%2F12041&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABrian+Goodwin" class="Z3988"></span></span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://www.anthropress.org/author.html?au=2084">Brian Goodwin</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20110904035038/http://www.anthropress.org/author.html?au=2084">Archived</a> 4 September 2011 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>, SteinerBooks</span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="https://www.independent.co.uk/news/obituaries/brian-goodwin-hugely-influential-and-insightful-biologist-philosopher-and-writer-1765240.html">Brian Goodwin Obituary - <i>The Independent</i>, 31 July 2009</a>.</span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://www.schumachercollege.org.uk/news/professor-brian-goodwin">Professor Brian Goodwin</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20090913102117/http://www.schumachercollege.org.uk/news/professor-brian-goodwin">Archived</a> 13 September 2009 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>, Schumacher College</span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://wasdarwinwrong.com/kortho23.htm">"How the Leopard Changed Its Spots"</a>. Retrieved 2014-04-25.</span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text"><a href="/wiki/David_B._Wake" title="David B. Wake">Wake, David B</a>. (1996). <i>How the Leopard Changed Its Spots: The Evolution of Complexity by Brian Goodwin</i>. <i><a href="/wiki/American_Scientist" title="American Scientist">American Scientist</a></i>. Vol. 84, No. 3. pp. 300-301.</span> </li> <li id="cite_note-Price_1995-9"><span class="mw-cite-backlink">^ <a href="#cite_ref-Price_1995_9-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Price_1995_9-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text">Price, Catherine S. C. (1995). <i>Structurally Unsound</i>. <i><a href="/wiki/Evolution_(journal)" title="Evolution (journal)">Evolution</a></i>. Vol. 49, No. 6. pp. 1298-1302.</span> </li> <li id="cite_note-Wagner2014-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-Wagner2014_10-0">^</a></b></span> <span class="reference-text"><a href="/wiki/G%C3%BCnter_P._Wagner" title="Günter P. Wagner">Wagner, Günter P.</a>, <i>Homology, Genes, and Evolutionary Innovation</i>. Princeton University Press. 2014. Chapter 1: The Intellectual Challenge of Morphological Evolution: A Case for Variational Structuralism. Page 7</span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Brian_Goodwin&action=edit&section=8" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="http://www.edge.org/3rd_culture/goodwin/goodwin_p1.html">A New Science of Qualities: a Talk With Brian Goodwin</a></li> <li><a rel="nofollow" class="external text" href="http://ngin.tripod.com/article8.htm">An interview with Professor Brian Goodwin</a></li></ul> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist 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href="http://data.bibliotheken.nl/id/thes/p070151490">Netherlands</a></span></li><li><span class="uid"><span class="rt-commentedText tooltip tooltip-dotted" title="Goodwin, B. C. (Brian Carey)"><a rel="nofollow" class="external text" href="https://kopkatalogs.lv/F?func=direct&local_base=lnc10&doc_number=000141235&P_CON_LNG=ENG">Latvia</a></span></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="http://olduli.nli.org.il/F/?func=find-b&local_base=NLX10&find_code=UID&request=987007446977105171">Israel</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://cantic.bnc.cat/registre/981058515741106706">Catalonia</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://opac.kbr.be/LIBRARY/doc/AUTHORITY/14334048">Belgium</a></span></li></ul></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Academics</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://ci.nii.ac.jp/author/DA02959162?l=en">CiNii</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://zbmath.org/authors/?q=ai:goodwin.brian-c">zbMATH</a></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="https://mathscinet.ams.org/mathscinet/MRAuthorID/75340">MathSciNet</a></span></li></ul></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">People</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://www.deutsche-digitale-bibliothek.de/person/gnd/172101654">DDB</a></span></li></ul></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://www.idref.fr/03158408X">IdRef</a></span></li></ul></div></td></tr></tbody></table></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; 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