Edge of chaos
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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.
- 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. 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 1. Retrieved 28 September 2013.