edge of chaos

The phrase edge of chaos was coined in the late 1980s by chaos theory physicist Norman Packard.{{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}}{{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}} 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. 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.{{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}}{{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}}{{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}} The phrase refers to an area in the range of a 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.{{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}} 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.{{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}}

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, where the complexity is maximal.{{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}}{{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}}

The generality and significance of the idea, however, has since been called into question by Melanie Mitchell and others.{{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}} 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 models of evolving systems in which the rate of evolution is maximized near the edge of chaos.{{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}}

Adaptation plays a vital role for all living organisms and systems. All of them are constantly changing their inner properties to better fit in the current environment.{{cite book|last1=Strogatz|first1=Steven|title=Nonlinear dynamics and Chaos|date=1994|publisher=Westview Press}} The most important instruments for the adaptation are the self-adjusting parameters inherent for many natural systems. The prominent feature of systems with self-adjusting parameters is an ability to avoid chaos. The name for this phenomenon is "Adaptation to the edge of chaos".

Adaptation to the edge of chaos refers to the idea that many complex adaptive systems (CASs) seem to intuitively evolve toward a regime near the boundary between chaos and order.{{cite book|last1=Kauffman|first1=S.A.|title=The Origins of Order Self-Organization and Selection in Evolution|url=https://archive.org/details/originsoforderse0000kauf|url-access=registration|date=1993|publisher=Oxford University Press|location=New York|isbn=9780195079517}} Physics has shown that edge of chaos is the optimal settings for control of a system.{{cite journal|last1=Pierre|first1=D.|last2=et.|first2=al.|title=A theory for adaptation and competition applied to logistic map dynamics|journal=Physica D|date=1994|volume=75|issue=1–3|pages=343–360|bibcode=1994PhyD...75..343P|doi=10.1016/0167-2789(94)90292-5}} It is also an optional setting that can influence the ability of a physical system to perform primitive functions for computation.{{cite journal|last1=Langton|first1=C.A.|title=Computation at the edge of chaos|journal=Physica D|date=1990|volume=42|issue=1–3|pages=12|doi=10.1016/0167-2789(90)90064-v|bibcode=1990PhyD...42...12L|osti=7264125 |url=https://zenodo.org/record/1258375}} In CAS, coevolution generally occurs near the edge of chaos, and a balance should be maintained between flexibility and stability to avoid structural failure.{{cite web |url=http://www.faculty.umb.edu/david_levy/complex00.pdf|title=Applications and Limitations of Complexity Theory in Organization Theory and Strategy |publisher=umb.edu|last=L. Levy|first=David |access-date=23 August 2020}}{{cite web |url=http://www.strategy-business.com/article/15099?gko=d48d4|title=Between Chaos and Order: What Complexity Theory Can Teach Business|publisher=strategy-business.com|last=Berreby|first=David|date=1 April 1996|access-date=23 August 2020}}{{cite web |url=https://forestbioproducts.umaine.edu/wp-content/uploads/sites/202/2010/10/Porter.Coev-Proofs.pdf|title=Coevolution as a research framework for organizations and the natural environment|publisher=University of Maine|last=B. Porter|first=Terry|access-date=23 August 2020}}{{cite web |url=https://grantome.com/grant/NSF/DBI-9201536|title=Coevolution in Complex Adaptive Systems|publisher=Santa Fe Institute|last=Kauffman|first=Stuart |date=15 January 1992|access-date=24 August 2020}} As a response to coping with turbulent environments, CAS bring out flexibility, creativity,{{cite web |url=https://www.researchgate.net/publication/328890717|title=The Order-Chaos Dynamic of Creativity|publisher=University of New Brunswick|last=A Lambert|first=Philip|date=June 2018|access-date=24 August 2020}} agility, anti-fragility, and innovation near the edge of chaos, provided these systems are sufficiently decentralized and non-hierarchical.

Because of the importance of adaptation in many natural systems, adaptation to the edge of the chaos takes a prominent position in many scientific researches. Physicists demonstrated that adaptation to state at the boundary of chaos and order occurs in population of cellular automata rules which optimize the performance evolving with a genetic algorithm.{{cite journal|last1=Packard|first1=N.H.|title=Adaptation toward the edge of chaos|journal=Dynamic Patterns in Complex Systems|date=1988|pages=293–301}}{{cite journal|last1=Mitchell|first1=M.|last2=Hraber|first2=P.|last3=Crutchfield|first3=J.|title=Revisiting the edge of chaos: Evolving cellular automata to perform computations|journal=Complex Systems|date=1993|volume=7|issue=2|pages=89–130|arxiv=adap-org/9303003|bibcode=1993adap.org..3003M}} Another example of this phenomenon is the self-organized criticality in avalanche and earthquake models.{{cite journal|last1=Bak|first1=P.|last2=Tang|first2=C.|last3=Wiesenfeld|first3=K.|title=Self-organized criticality|journal=Physical Review A|date=1988|volume=38|issue=1|pages=364–374|doi=10.1103/PhysRevA.38.364|bibcode=1988PhRvA..38..364B|pmid=9900174}}

The simplest model for chaotic dynamics is the logistic map. Self-adjusting logistic map dynamics exhibit adaptation to the edge of chaos.{{cite journal|last1=Melby|first1=P.|last2=et.|first2=al.|title=Adaptation to the edge of chaos in the self-adjusting logistic map.|journal=Phys. Rev. Lett.|date=2000|doi=10.1103/PhysRevLett.84.5991|arxiv=nlin/0007006|bibcode=2000PhRvL..84.5991M|volume=84|issue=26|pages=5991–5993|pmid=10991106}} Theoretical analysis allowed prediction of the location of the narrow parameter regime near the boundary to which the system evolves.{{cite journal|last1=Baym|first1=M.|last2=et.|first2=al.|title=Conserved quantities and adaptation to the edge of chaos|journal=Physical Review E|date=2006|volume=73|issue=5|pages=056210|doi=10.1103/PhysRevE.73.056210|pmid=16803029 |bibcode=2006PhRvE..73e6210B}}

• Chaos theory
• Complexity theory and organizations
• Self-organized criticality

{{Reflist}}

• {{cite journal |author=Christopher G. Langton |title=Computation at the edge of chaos |journal=Physica D |volume=42 |pages=12 |year=1990 |issue=1–3 |url=http://shinyverse.org/al4ai/papers/Langton.EdgeOfChaos.pdf |archive-url=https://web.archive.org/web/20221223200151/http://shinyverse.org/al4ai/papers/Langton.EdgeOfChaos.pdf |archive-date=2022-12-23 |doi=10.1016/0167-2789(90)90064-V |bibcode=1990PhyD...42...12L |osti=7264125}}
• {{cite book|author=J. P. Crutchfield and K. Young|chapter=Computation at the Onset of Chaos|title=Entropy, Complexity, and the Physics of Information|editor=W. Zurek|series=SFI Studies in the Sciences of Complexity, VIII|publisher=Addison-Wesley|location=Reading, Massachusetts|year=1990|pages=223–269|chapter-url=http://csc.ucdavis.edu/~cmg/papers/CompOnset.pdf}}
• {{cite journal | last1 = Mitchell | first1 = Melanie | last2 = Hraber | first2 = Peter T. | last3 = Crutchfield | first3 = James P. | year = 1993 | title = Revisiting the edge of chaos: Evolving cellular automata to perform computations | url = http://web.cecs.pdx.edu/~mm/rev-edge.pdf | journal = Complex Systems | volume = 7 | pages = 89–130 | arxiv = adap-org/9303003 | bibcode = 1993adap.org..3003M | access-date = 2007-05-04 | archive-date = 2010-06-08 | archive-url = https://web.archive.org/web/20100608020036/http://web.cecs.pdx.edu/~mm/rev-edge.pdf | url-status = dead }}
• Melanie Mitchell, James P. Crutchfield and Peter T. Hraber. [http://web.cecs.pdx.edu/~mm/dyn-comp-edge.pdf Dynamics, Computation, and the "Edge of Chaos": A Re-Examination] {{Webarchive|url=https://web.archive.org/web/20100608012919/http://web.cecs.pdx.edu/~mm/dyn-comp-edge.pdf |date=8 June 2010 }}
• Origins of Order: Self-Organization and Selection in Evolution by Stuart Kauffman
• {{Cite journal|last1=Mora |first1=Thierry |last2=Bialek |first2=William |year= 2010|title=Are biological systems poised at criticality? |journal=Journal of Statistical Physics |volume=144 |issue=2 |pages=268–302 |arxiv= 1012.2242|doi=10.1007/s10955-011-0229-4 |bibcode=2011JSP...144..268M }}

• [http://bactra.org/notebooks/edge-of-chaos.html "The Edge of Chaos"] – a criticism of the idea's prevalence.

{{Chaos theory}}

Category:Chaos theory

Category:Self-organization