Attractors in Restricted Cellular Automata

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 Xq to Xq , then its restriction to Xq 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 [HI] for the unrestricted case.

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