Long-range correlations in chaotic cellular automata

Abstract One-dimensional cellular automata of class 3 are studied as models for spatially extended, chaotic systems. Their irreversible dynamics can generate weak, but long-range spatial correlations. The one labelled 22 by Wolfram is treated in an exemplary way. Its stationary state is approximated by a Markov chain. The regular grammar underlying the Markov chain is chosen with care, so that it includes a maximum amount of information on the stationary state. The approximation can be performed without simulating the dynamics of the cellular automaton 22 and reproduces its long-range correlations qualitatively. Their origin is explained intuitively and they are argued to be a frequent feature of cellular automata with more complicated rules.

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