Nonlinear Sciences – Adaptation and Self-Organizing Systems
Scientific paper
1993-04-02
Stat. and Comp. 1, 1991, Chapman and Hall, London
Nonlinear Sciences
Adaptation and Self-Organizing Systems
33 pages. This paper appears with permission of Chapman and Hall, London. arXiv admin note, 17Jun2003: original PCL file and P
Scientific paper
Each cell of a two-dimensional lattice is painted one of k colors, arranged in a "color wheel." The colors advance (0 to k-1 mod k) either automatically or by contact with at least a threshold number of successor colors in a prescribed local neighborhood. Discrete-time parallel systems of this sort in which color 0 updates by contact and the rest update automatically are called Greenberg-Hastings (GH) rules. A system in which all colors update by contact is called a cyclic cellular automaton (CCA). Started from appropriate initial conditions these models generate periodic traveling waves. Started from random configurations the same rules exhibit complex self-organization, typically characterized by nucleation of locally periodic "ram's horns" or spirals. Corresponding random processes give rise to a variety of "forest fire" equilibria that display large-scale stochastic wave fronts. This article describes a framework, theoretically based, but relying on extensive interactive computer graphics experimentation, for investigation of the complex dynamics shared by excitable media in a broad spectrum of scientific contexts. By focusing on simple mathematical prototypes we obtain a better understanding of the basic organizational principles underlying spatially-distributed oscillating systems.
Fisch Robert
Gravner Janko
Griffeath David
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