Strictly Temporally Periodic Points in Cellular Automata
نویسندگان
چکیده
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.
منابع مشابه
Periodic Points for onto Cellular Automata
Let φ be a one-dimensional surjective cellular automaton map. We prove that if φ is a closing map, then the configurations which are both spatially and temporally periodic are dense. (If φ is not a closing map, then we do not know whether the temporally periodic configurations must be dense.) The results are special cases of results for shifts of finite type, and the proofs use symbolic dynamic...
متن کاملCellular Automata and Models of Computation
Preface This issue contains seven papers presented during the " Third Symposium on Cellular Automata– Journées Automates Cellulaires " (JAC 2012), held in La Marana, Corsica (France) in the period Septem-ber 19th–21th, 2012. The scope of the symposium is centered on Cellular Automata (CA), tilings and related models of computation. Topics of interest include (but are not limited to) algorithmic...
متن کاملJointly Periodic Points in Cellular Automata: Computer Explorations and Conjectures
We develop a rather elaborate computer program to investigate the jointly periodic points of one-dimensional cellular automata. The experimental results and mathematical context lead to questions, conjectures and a
متن کاملPeriodic Points and Entropies for Cellular Automata
For the class of permutive cellular automata the number of periodic points and the topological and metrical entropies are calculated.
متن کاملDensity of periodic points, invariant measures and almost equicontinuous points of Cellular Automata
Revisiting the notion of μ-almost equicontinuous cellular automata introduced by R. Gilman, we show that the sequence of image measures of a shift ergodic measure μ by iterations of such automata converges in Cesaro mean to an invariant measure μc. If the initial measure μ is a Bernouilli measure, we prove that the Cesaro mean limit measure μc is shift mixing. Therefore we also show that for an...
متن کامل