Edge of chaos

For the computer game, see Independence War 2: Edge of Chaos.

The phrase edge of chaos was coined by mathematician Doyne Farmer to describe the transition phenomenon discovered by computer scientist Christopher Langton. The phrase originally refers to an area in the range of a variable, λ (lambda), which was varied while examining the behavior of a cellular automaton (CA). As λ varied, the behavior of the CA went through a phase transition of behaviors. Langton found a small area conducive to produce CAs capable of universal computation. 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.

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

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

References

Christopher G. Langton (1990). "Computation at the edge of chaos" (PDF). Physica D. 42. doi:10.1016/0167-2789(90)90064-V.
J. P. Crutchfield and K. Young (1990). "Computation at the Onset of Chaos". In W. Zurek. Entropy, Complexity, and the Physics of Information (PDF). SFI Studies in the Sciences of Complexity, VIII. Reading, Massachusetts: Addison-Wesley. pp. 223–269.
Melanie Mitchell, Peter T. Hraber, and James P. Crutchfield. Revisiting the edge of chaos: Evolving cellular automata to perform computations. Complex Systems, 7:89–130, 1993.
Melanie Mitchell, James P. Crutchfield and Peter T. Hraber. Dynamics, Computation, and the "Edge of Chaos": A Re-Examination
Origins of Order: Self-Organization and Selection in Evolution by Stuart Kauffman
Mora, Thierry; Bialek, William. "Are biological systems poised at criticality?". arXiv:1012.2242.

External links

"The Edge of Chaos" – a criticism of the idea's prevalence.
"Google Scholar Search"

Chaos theory

Chaos theory	Anosov diffeomorphism Bifurcation theory Butterfly effect Chaos theory in organizational development Complexity Control of chaos Dynamical system Edge of chaos Fractal Predictability Quantum chaos Santa Fe Institute Synchronization of chaos Unintended consequences

Chaotic maps (list)	Arnold tongue Arnold's cat map Baker's map Complex quadratic map Complex squaring map Coupled map lattice Double pendulum Double scroll attractor Duffing equation Duffing map Dyadic transformation Dynamical billiards outer Exponential map Gauss map Gingerbreadman map Hénon map Horseshoe map Ikeda map Interval exchange map Kaplan–Yorke map Logistic map Lorenz system Multiscroll attractor Rabinovich–Fabrikant equations Rössler attractor Standard map Swinging Atwood's machine Tent map Tinkerbell map Van der Pol oscillator Zaslavskii map

Chaos systems	Bouncing ball dynamics Chua's circuit Economic bubble Tilt-A-Whirl

Chaos theorists	Michael Berry Leon O. Chua Mitchell Feigenbaum Martin Gutzwiller Brosl Hasslacher Michel Hénon Edward Norton Lorenz Aleksandr Lyapunov Benoît Mandelbrot Henri Poincaré Otto Rössler David Ruelle Oleksandr Mykolaiovych Sharkovsky Floris Takens James A. Yorke

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