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Strictly Temporally Periodic Points in Cellular Automata · arXivDesk

1208.2770Aug 14, 2012In Proceedings AUTOMATA&JAC 2012, arXiv:1208.2498

Strictly Temporally Periodic Points in Cellular Automata

Alberto Dennunzio, Pietro Di Lena, Luciano Margara

Formal Languages and Automata Theory Computational Complexity Discrete Mathematics Cellular Automata and Lattice Gases

Abstract

We study the set of strictly periodic points in surjective cellular automata, i.e., the set of those configurations which are temporally periodic for a given automaton but they not spatially periodic. This set turns out to be dense for almost equicontinuous surjective cellular automata while it is empty for the positively expansive ones. In the class of additive cellular automata, the set of strictly periodic points can be either dense or empty. The latter happens if and only if the cellular automaton is topologically transitive.

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The paper addresses: Strictly Temporally Periodic Points in Cellular Automata.
We study the set of strictly periodic points in surjective cellular automata, i.e., the set of those configurations which are temporally periodic for a given automaton but they not spatially periodic.