Edge of chaos

"The truly creative changes and the big shifts occur right at the edge of chaos."[1]

— Dr. Robert Bilder, Professor at the UCLA Semel Institute for Neuroscience and Human Behavior

The edge of chaos is a transition space between order and disorder that is hypothesized to exist within a wide variety of systems. This transition zone is a region of bounded instability that engenders a constant dynamic interplay between order and disorder.[2]

Even though the idea of the edge of chaos is an abstract one, it has many applications in such fields as ecology,[3] business management,[4] psychology,[5] political science, and other domains of the social sciences. Physicists have shown that adaptation to the edge of chaos occurs in almost all systems with feedback.[6]


The phrase edge of chaos was coined in the late 1980s by chaos theory physicist Norman Packard.[7][8] 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.[7] 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.[9][10][11] 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.[10][9][12] 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.[13]

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.[14][15] The generality and significance of the idea, however, has since been called into question by Melanie Mitchell and others.[16] 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]

Stuart Kauffman has studied mathematical models of evolving systems in which the rate of evolution is maximized near the edge of chaos.[17]


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.[18] 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 (CAS) seem to intuitively evolve toward a regime near the boundary between chaos and order.[19] Physics has shown that edge of chaos is the optimal settings for control of a system.[20] It is also an optional setting that can influence the ability of a physical system to perform primitive functions for computation.[21] In CAS, coevolution generally occurs near the edge of chaos, and a balance should be maintained between flexibility and stability to avoid structural failure.[22][23][24][25] As a response to coping with turbulent environments, CAS bring out flexibility, creativity,[26] agility, anti-fragility and innovation near the edge of chaos, provided these systems are sufficiently decentralized and non-hierarchical.[24][23][22]

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.[27][28] Another example of this phenomenon is the self-organized criticality in avalanche and earthquake models.[29]

The simplest model for chaotic dynamics is the logistic map. Self-adjusting logistic map dynamics exhibit adaptation to the edge of chaos.[30] Theoretical analysis allowed prediction of the location of the narrow parameter regime near the boundary to which the system evolves.[31]

See also


  1. ^ Schwartz, Katrina (6 May 2014). "On the Edge of Chaos: Where Creativity Flourishes". KQED. Archived from the original on 23 April 2022. Retrieved 2 June 2022.
  2. ^ Complexity Labs. "Edge of Chaos". Complexity Labs. Archived from the original on May 15, 2017. Retrieved August 24, 2016.
  3. ^ Ranjit Kumar Upadhyay (2009). "Dynamics of an ecological model living on the edge of chaos". Applied Mathematics and Computation. 210 (2): 455–464. doi:10.1016/j.amc.2009.01.006.
  4. ^ Deragon, Jay. "Managing On The Edge Of Chaos". Relationship Economy.
  5. ^ Lawler, E.; Thye, S.; Yoon, J. (2015). Order on the Edge of Chaos Social Psychology and the Problem of Social Order. Cambridge University Press. ISBN 9781107433977.
  6. ^ Wotherspoon, T.; et., al. (2009). "Adaptation to the edge of chaos with random-wavelet feedback". J. Phys. Chem. A. 113 (1): 19–22. Bibcode:2009JPCA..113...19W. doi:10.1021/jp804420g. PMID 19072712.
  7. ^ a b A. Bass, Thomas (1999). The Predictors : How a Band of Maverick Physicists Used Chaos Theory to Trade Their Way to a Fortune on Wall Street. Henry Holt and Company. p. 138. ISBN 9780805057560. Retrieved 12 November 2020.
  8. ^ H. Packard, Norman (1988). "Adaptation Toward the Edge of Chaos". University of Illinois at Urbana-Champaign, Center for Complex Systems Research. Retrieved 12 November 2020.
  9. ^ a b "Edge of Chaos". systemsinnovation.io. 2016. Archived from the original on 12 November 2020. Retrieved 12 November 2020.
  10. ^ a b A. Bass, Thomas (1999). The Predictors : How a Band of Maverick Physicists Used Chaos Theory to Trade Their Way to a Fortune on Wall Street. Henry Holt and Company. p. 139. ISBN 9780805057560. Retrieved 12 November 2020.
  11. ^ Shaw, Patricia (2002). Changing Conversations in Organizations : A Complexity Approach to Change. Routledge. p. 67. ISBN 9780415249140. Retrieved 12 November 2020.
  12. ^ Langton, Christopher. (1986). "Studying artificial life with cellular automata". Physica D. 22 (1–3): 120–149. doi:10.1016/0167-2789(86)90237-X. hdl:2027.42/26022.
  13. ^ P. Crutchfleld, James; Young, Karl (1990). "Computation at the Onset of Chaos" (PDF). Retrieved 11 November 2020.
  14. ^ Shulman, Helene (1997). Living at the Edge of Chaos, Complex Systems in Culture and Psyche. Daimon. p. 115. ISBN 9783856305611. Retrieved 11 November 2020.
  15. ^ Complexity Thinking in Physical Education : Reframing Curriculum, Pedagogy, and Research; edited by Alan Ovens, Joy Butler, Tim Hopper. Routledge. 2013. p. 212. ISBN 9780415507219. Retrieved 11 November 2020.
  16. ^ Mitchell, Melanie; T. Hraber, Peter; P. Crutchfleld, James (1993). "Revisiting the Edge of Chaos: Evolving Cellular Automata to Perform Computations" (PDF). Retrieved 11 November 2020.
  17. ^ Gros, Claudius (2008). Complex and Adaptive Dynamical Systems A Primer. Springer Berlin Heidelberg. p. 97, 98. ISBN 9783540718741. Retrieved 11 November 2020.
  18. ^ Strogatz, Steven (1994). Nonlinear dynamics and Chaos. Westview Press.
  19. ^ Kauffman, S.A. (1993). The Origins of Order Self-Organization and Selection in Evolution. New York: Oxford University Press. ISBN 9780195079517.
  20. ^ Pierre, D.; et., al. (1994). "A theory for adaptation and competition applied to logistic map dynamics". Physica D. 75 (1–3): 343–360. Bibcode:1994PhyD...75..343P. doi:10.1016/0167-2789(94)90292-5.
  21. ^ Langton, C.A. (1990). "Computation at the edge of chaos". Physica D. 42 (1–3): 12. Bibcode:1990PhyD...42...12L. doi:10.1016/0167-2789(90)90064-v.
  22. ^ a b L. Levy, David. "Applications and Limitations of Complexity Theory in Organization Theory and Strategy" (PDF). umb.edu. Retrieved 23 August 2020.
  23. ^ a b Berreby, David (1 April 1996). "Between Chaos and Order: What Complexity Theory Can Teach Business". strategy-business.com. Retrieved 23 August 2020.
  24. ^ a b B. Porter, Terry. "Coevolution as a research framework for organizations and the natural environment" (PDF). University of Maine. Retrieved 23 August 2020.
  25. ^ Kauffman, Stuart (15 January 1992). "Coevolution in Complex Adaptive Systems". Santa Fe Institute. Retrieved 24 August 2020.
  26. ^ A Lambert, Philip (June 2018). "The Order-Chaos Dynamic of Creativity". University of New Brunswick. Retrieved 24 August 2020.
  27. ^ Packard, N.H. (1988). "Adaptation toward the edge of chaos". Dynamic Patterns in Complex Systems: 293–301.
  28. ^ Mitchell, M.; Hraber, P.; Crutchfield, J. (1993). "Revisiting the edge of chaos: Evolving cellular automata to perform computations". Complex Systems. 7 (2): 89–130. arXiv:adap-org/9303003. Bibcode:1993adap.org..3003M.
  29. ^ Bak, P.; Tang, C.; Wiesenfeld, K. (1988). "Self-organized criticality". Physical Review A. 38 (1): 364–374. Bibcode:1988PhRvA..38..364B. doi:10.1103/PhysRevA.38.364. PMID 9900174.
  30. ^ Melby, P.; et., al. (2000). "Adaptation to the edge of chaos in the self-adjusting logistic map". Phys. Rev. Lett. 84 (26): 5991–5993. arXiv:nlin/0007006. Bibcode:2000PhRvL..84.5991M. doi:10.1103/PhysRevLett.84.5991. PMID 10991106.
  31. ^ Baym, M.; et., al. (2006). "Conserved quantities and adaptation to the edge of chaos". Physical Review E. 73 (5): 056210. Bibcode:2006PhRvE..73e6210B. doi:10.1103/PhysRevE.73.056210. PMID 16803029.