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Attractors in Restricted Cellular Automata

Mike Hurley
Proceedings of the American Mathematical Society
Vol. 115, No. 2 (Jun., 1992), pp. 563-571
DOI: 10.2307/2159280
Stable URL: http://www.jstor.org/stable/2159280
Page Count: 9
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Attractors in Restricted Cellular Automata
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Abstract

The goal of this note is to extend previous results about the dynamics of cellular automata to "restricted cellular automata." Roughly speaking, a cellular automaton is a rule that updates a configuration of "states" that are arranged along the integer lattice in R. In applications one often thinks of one of these states as "blank" or "quiescent," while the other "active" states evolve against a quiescent background. Often the physically relevant configurations are those with only a finite number of active states. If X0 is the set of all such states, and if a cellular automaton maps X0 to X0, then its restriction to X0 is a restricted cellular automaton. The main results show that there are rather strong constraints on the collection of attractors for any restricted cellular automaton. These constraints parallel those described in [H1] for the unrestricted case.

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