{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:29:42Z","timestamp":1760243382807,"version":"build-2065373602"},"reference-count":28,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2014,10,24]],"date-time":"2014-10-24T00:00:00Z","timestamp":1414108800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>A method is known by which any integer \\(\\, n\\geq2\\,\\)  in a metric Cantor space of right-infinite words \\(\\,\\tilde{A}_{n}^{\\,\\mathbb N}\\,\\) gives a construction of a non-injective cellular automaton \\(\\,(\\tilde{A}_{n}^{\\,\\mathbb N},\\,\\tilde{F}_{n}),\\,\\) which is chaotic in Devaney sense, has a radius \\(\\, r=1,\\,\\) continuum of fixed points and topological entropy \\(\\, log(n).\\,\\) As a generalization of this method we present for any integer \\(\\, n\\geq2,\\,\\) a construction of a cellular automaton \\(\\,(A_{n}^{\\,\\mathbb{N}},\\, F_{n}),\\,\\) which has the listed properties of \\(\\,(\\tilde{A}_{n}^{\\,\\mathbb N},\\,\\tilde{F}_{n}),\\,\\) but has no fixed points and has continuum of periodic points with the period 2. The construction is based on  properties of cellular automaton introduced here \\(\\,(B^{\\,\\mathbb N},\\, F)\\,\\) with radius \\(1\\) defined for any prime number \\(\\, p.\\,\\) We prove that \\(\\,(B^{\\,\\mathbb N},\\, F)\\,\\) is non-injective, chaotic in Devaney sense, has no fixed points, has continuum of periodic points with the period \\(2\\) and topological entropy \\(\\, log(p).\\,\\)<\/jats:p>","DOI":"10.3390\/e16115601","type":"journal-article","created":{"date-parts":[[2014,10,24]],"date-time":"2014-10-24T11:46:16Z","timestamp":1414151176000},"page":"5601-5617","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["On One-Sided, D-Chaotic CA Without Fixed Points, Having Continuum of Periodic Points With Period 2 and Topological Entropy log(p) for Any Prime p"],"prefix":"10.3390","volume":"16","author":[{"given":"Wit","family":"Forys","sequence":"first","affiliation":[{"name":"Institute of Computer Science, Jagiellonian University, \u0141ojasiewicza 6, 30-348 Krak\u00f3w, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Janusz","family":"Matyja","sequence":"additional","affiliation":[{"name":"Department of Computer Science and Econometrics, Silesian Technical University, Roosevelta 26-28, 41-800 Zabrze, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2014,10,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1007\/BF02760680","article-title":"Dynamical Properties of Expansive Cellular Automata","volume":"99","author":"Blanchard","year":"1997","journal-title":"Isr. 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