A method to identify the invariant subsets of bi‐infinite configurations of cellular automata that propagate rigidly with a constant velocity ν is described. Causal traveling configurations, propagating at speeds not greater than the automaton range, |ν|≤r, are considered. The sets of traveling configurations are presented by finite automata and its topological entropy is calculated. When the invariant subset of traveling configurations has nonzero topological entropy, the dynamics is dominated by the interaction of domains, composed of traveling patterns of finite size. The sets of traveling patterns and domains are presented by finite automata. End‐resolving CA are shown to always have sets of traveling configurations that are spatially periodic with zero entropy, except possibly for traveling configurations at top speed. The elementary CA are examined exhaustively along these lines.

Topics
Entropy, Theoretical computer science
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© 1996 American Institute of Physics.
1996
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