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]
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
mathematicianDoyne 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 scientistChristopher 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
physicistJames 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
socialsystems 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]
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]
^Complexity Labs.
"Edge of Chaos". Complexity Labs. Archived from
the original on May 15, 2017. Retrieved August 24, 2016.
^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.
^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.
^
ab"Edge of Chaos". systemsinnovation.io. 2016. Archived from
the original on 12 November 2020. Retrieved 12 November 2020.
J. P. Crutchfield and K. Young (1990).
"Computation at the Onset of Chaos"(PDF). In W. Zurek (ed.). Entropy, Complexity, and the Physics of Information. SFI Studies in the Sciences of Complexity, VIII. Reading, Massachusetts:
Addison-Wesley. pp. 223–269.