One dimensional cellular automata are analyzed via their generalized permutivity. Invariant subalphabets provide a systematic way of identifying periodic and aperiodic tilings as well as stationary distributions invariant under the cellular automaton iteration. In the case of several invariant subalphabets a hierarchy of interaction phenomena arise. In particular the interaction of subalphabets can generate random walks as well as their degenerate forms. A comprehensive scheme emerges that uni es the analysis of topological defects in cellular automata. The probabilistic details of the random walks involved are treated in the companion paper 4].
Topological defects or phase boundaries discerned in a number of one-dimensional cellular automata appear to perform random walks as well as simpler motions. We analyze their properties rigorously using probabilistic methods. This results in a complete classi cation in the partially permutive case. The paper complements 1] where the general framework of tilings and subpermutivity was introduced and non-probabilistic properties were analyzed.
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