Abstract
We study the dynamics of cellular automata, and more specifically their transitivity and expansivity, when the set of configurations is endowed with a shift-invariant (pseudo-)distance. We first give an original proof of the non-transitivity of cellular automata when the set of configurations is endowed with the Besicovitch pseudo-distance. We then show that the Besicovitch pseudo-distance induces a distance on the set of shift-invariant measures and on the whole space of measures, and we prove that in these spaces also, cellular automata cannot be expansive nor transitive. © Springer-Verlag Berlin Heidelberg 2007.
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CITATION STYLE
Bienvenu, L., & Sablik, M. (2007). The dynamics of cellular automata in shift-invariant topologies. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 4588 LNCS, pp. 84–95). Springer Verlag. https://doi.org/10.1007/978-3-540-73208-2_11
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