Abstract
When properly viewed, the transition rule of a cellular automaton becomes a mapF from a set
to itself. The set
may be made a probability space. Sufficient conditions are given to ensure thatF be measure-preserving and ergodic. Some geometric consequences of ergodicity are noted.
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Willson, S.J. On the ergodic theory of cellular automata. Math. Systems Theory 9, 132–141 (1975). https://doi.org/10.1007/BF01704016
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DOI: https://doi.org/10.1007/BF01704016