Editing Edge of chaos (section)

== History ==
The phrase ''edge of chaos'' was coined in the late 1980s by [[chaos theory]] physicist [[Norman Packard]].<ref name=EOC-T-30>{{cite book|last=A. Bass|first=Thomas|title = The Predictors : How a Band of Maverick Physicists Used Chaos Theory to Trade Their Way to a Fortune on Wall Street|url =https://books.google.com/books?id=MQ-xGC7BdS0C&pg=PA138|publisher = Henry Holt and Company |year =1999|isbn =9780805057560 |page =[https://books.google.com/books?id=MQ-xGC7BdS0C&pg=PA138 138] |access-date=12 November 2020}}</ref><ref name=EOC-T-20>{{cite web|last=H. Packard|first=Norman|title = Adaptation Toward the Edge of Chaos|url =https://books.google.com/books?id=8prgtgAACAAJ|publisher = University of Illinois at Urbana-Champaign, Center for Complex Systems Research |year =1988|access-date=12 November 2020}}</ref> In the next decade, Packard and mathematician [[Doyne Farmer]] co-authored many papers on understanding how self-organization and order emerges at the edge of chaos.<ref name=EOC-T-30/> One of the original catalysts that led to the idea of the edge of chaos were the experiments with [[cellular automata]] done by [[computer scientist]] [[Christopher Langton]] where a transition phenomenon was discovered.<ref name=EOC-T-19>{{cite web|title = Edge of Chaos|url = https://www.systemsinnovation.io/post/edge-of-chaos-1|publisher = systemsinnovation.io|year = 2016|access-date = 12 November 2020|archive-date = 12 November 2020|archive-url = https://web.archive.org/web/20201112200758/https://www.systemsinnovation.io/post/edge-of-chaos-1|url-status = usurped}}</ref><ref name=EOC-T-18>{{cite book|last=A. Bass|first=Thomas|title = The Predictors : How a Band of Maverick Physicists Used Chaos Theory to Trade Their Way to a Fortune on Wall Street|url =https://books.google.com/books?id=MQ-xGC7BdS0C&pg=PA139|publisher = Henry Holt and Company |year =1999|isbn =9780805057560 |page =[https://books.google.com/books?id=MQ-xGC7BdS0C&pg=PA139 139] |access-date=12 November 2020}}</ref><ref name=EOC-T-16>{{cite book|last=Shaw|first=Patricia|title = Changing Conversations in Organizations : A Complexity Approach to Change|url =https://books.google.com/books?id=vKVuXyNb2CoC&pg=PA67|publisher =Routledge |year =2002|isbn =9780415249140|page =[https://books.google.com/books?id=vKVuXyNb2CoC&pg=PA67 67] |access-date=12 November 2020}}</ref> The phrase refers to an area in the range of a [[Variable (programming)|variable]], λ (lambda), which was varied while examining the behaviour of a [[cellular automaton]] (CA). As λ varied, the behaviour of the CA went through a [[phase transition]] of behaviours. Langton found a small area conducive to produce CAs capable of [[universal computation]].<ref name=EOC-T-18/><ref name=EOC-T-19/><ref name=EOC-T-17>{{cite journal|last1=Langton|first1=Christopher.|title=Studying artificial life with cellular automata|journal=Physica D|date=1986|volume=22|issue=1–3|pages=120–149|doi=10.1016/0167-2789(86)90237-X|bibcode=1986PhyD...22..120L |hdl=2027.42/26022|hdl-access=free}}</ref> At around the same time physicist [[James P. Crutchfield]] and others used the phrase ''onset of chaos'' to describe more or less the same concept.<ref name=EOC-T-28>{{cite web|last2=Young|first2=Karl|last1=P. Crutchfleld|first1=James|title=Computation at the Onset of Chaos|url=http://csc.ucdavis.edu/~cmg/papers/CompOnset.pdf|year=1990|access-date=11 November 2020}}</ref>

In the sciences in general, the phrase has come to refer to a metaphor that some physical, biological, economic and social  systems operate in a region between order and either complete [[randomness]] or [[chaos theory|chaos]], where the [[complexity]] is maximal.<ref name=EOC-T-32>{{cite book|last=Shulman |first=Helene|title = Living at the Edge of Chaos, Complex Systems in Culture and Psyche|url = https://books.google.com/books?id=lpnWBIMCGCUC&pg=PA115|publisher = Daimon |year =1997|isbn =9783856305611 |page=[https://books.google.com/books?id=lpnWBIMCGCUC&pg=PA115 115] |access-date=11 November 2020}}</ref><ref name=EOC-T-33>{{cite book|title =Complexity Thinking in Physical Education : Reframing Curriculum, Pedagogy, and Research; edited by Alan Ovens, Joy Butler, Tim Hopper|url=https://books.google.com/books?id=0FPAlqreX-cC&pg=PA212|publisher = Routledge |year =2013|isbn=9780415507219 |page=[https://books.google.com/books?id=0FPAlqreX-cC&pg=PA212 212] |access-date=11 November 2020}}</ref> 
The generality and significance of the idea, however, has since been called into question by [[Melanie Mitchell]] and others.<ref name=EOC-T-29>{{cite web|last1=Mitchell|first1=Melanie|last2=T. Hraber|first2=Peter|last3=P. Crutchfleld|first3=James|title=Revisiting the Edge of Chaos: Evolving Cellular Automata to Perform Computations|url= https://content.wolfram.com/uploads/sites/13/2018/02/07-2-1.pdf|year=1993|access-date=11 November 2020}}</ref> The phrase has also been borrowed by the business community and is sometimes used inappropriately and in contexts that are far from the original scope of the meaning of the term.{{citation needed|date=November 2020}} 

[[Stuart Kauffman]] has studied [[mathematical model]]s of evolving systems in which the rate of evolution is maximized near the edge of chaos.<ref name=EOC-T-31>{{cite book|last=Gros |first=Claudius|title = Complex and Adaptive Dynamical Systems A Primer|url = https://books.google.com/books?id=PyFpDYaJZ8MC&pg=PA97  |publisher = Springer Berlin Heidelberg |year =2008|isbn =9783540718741 |page =[https://books.google.com/books?id=PyFpDYaJZ8MC&pg=PA97 97], [https://books.google.com/books?id=PyFpDYaJZ8MC&pg=PA98 98] |access-date=11 November 2020}}</ref>