We study the set of strictly temporally periodic points in surjective cellular automata, i.e., the set of those configurations which are temporally periodic for a given automaton but are not spatially periodic. This set turns out to be residual for equicontinuous surjective cellular automata, 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 temporally periodic points can be either dense or empty. The latter happens if and only if the cellular automaton is topologically transitive
Dennunzio, A., Lena, P., Margara, L. (2012). Strictly Temporally Periodic Points in Cellular Automata. Intervento presentato a: International Workshop on Cellular Automata and Discrete Complex Systems and 3rd International Symposium Journees Automates Cellulaires, AUTOJAC 2012 19 September 2012 through 21 September, La Marana, Corsica [10.4204/EPTCS.90.18].
Strictly Temporally Periodic Points in Cellular Automata
Dennunzio, A;
2012
Abstract
We study the set of strictly temporally periodic points in surjective cellular automata, i.e., the set of those configurations which are temporally periodic for a given automaton but are not spatially periodic. This set turns out to be residual for equicontinuous surjective cellular automata, 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 temporally 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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