{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,21]],"date-time":"2025-09-21T18:07:37Z","timestamp":1758478057796,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>\r\n\r\n\r\nWe study cellular automata whose rules are selected uniformly at random. Our setting are two-neighbor one-dimensional rules with a large number $n$ of states. The main quantity we analyze is the asymptotic distribution, as $n \\to \\infty$, of the number of different periodic solutions with given spatial and temporal periods. The main tool we use is the Chen-Stein method for Poisson approximation, which establishes that the number of periodic solutions, with their spatial and temporal periods confined to a finite range, converges to a Poisson random variable with an explicitly given parameter. The limiting probability distribution of the smallest temporal period for a given spatial period is deduced as a corollary and relevant empirical simulations are presented.\r\n\r\n\r\n<\/jats:p>","DOI":"10.37236\/10114","type":"journal-article","created":{"date-parts":[[2021,12,17]],"date-time":"2021-12-17T01:49:10Z","timestamp":1639705750000},"source":"Crossref","is-referenced-by-count":2,"title":["Periodic Solutions of One-Dimensional Cellular Automata with Uniformly Chosen Random Rules"],"prefix":"10.37236","volume":"28","author":[{"given":"Janko","family":"Gravner","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaochen","family":"Liu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2021,12,9]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v28i4p51\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v28i4p51\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,12,17]],"date-time":"2021-12-17T01:49:10Z","timestamp":1639705750000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v28i4p51"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,12,9]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2021,10,8]]}},"URL":"https:\/\/doi.org\/10.37236\/10114","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2021,12,9]]},"article-number":"P4.51"}}