{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,10]],"date-time":"2026-03-10T13:16:32Z","timestamp":1773148592879,"version":"3.50.1"},"reference-count":12,"publisher":"World Scientific Pub Co Pte Lt","issue":"12","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2007,12]]},"abstract":"<jats:p> We establish the relation between the extended (i.e. I = \u221e) one-dimensional binary Cellular Automata (1D CA) and the bi-infinite symbolic sequences in symbolic dynamics. That is, the 256 local rules of 1D CA correspond to 256 local rule mappings in the symbolic space. By employing the two homeomorphisms T<jats:sup>\u2020<\/jats:sup> and [Formula: see text] from [Chua et al., 2004] for finite I, we classify these 256 local rule mappings into the same 88 equivalence classes identified in [Chua et al., 2004] and [Chua, 2006]. Different mappings in the same equivalence class are mutually topologically conjugate. <\/jats:p>","DOI":"10.1142\/s0218127407019925","type":"journal-article","created":{"date-parts":[[2008,3,11]],"date-time":"2008-03-11T14:35:40Z","timestamp":1205246140000},"page":"4245-4259","source":"Crossref","is-referenced-by-count":27,"title":["EXTENDING CHUA'S GLOBAL EQUIVALENCE THEOREM ON WOLFRAM'S NEW KIND OF SCIENCE"],"prefix":"10.1142","volume":"17","author":[{"given":"JUNBIAO","family":"GUAN","sequence":"first","affiliation":[{"name":"Department of Mathematics, Shanghai University, Shanghai 200444, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"SHAOWEI","family":"SHEN","sequence":"additional","affiliation":[{"name":"College of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou, Zhejiang 310000, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"CHANGBING","family":"TANG","sequence":"additional","affiliation":[{"name":"Department of Basic Courses, Zhejiang Shuren University, Hangzhou, Zhejiang 310015, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"FANGYUE","family":"CHEN","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang 321004, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127402006333"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127403008041"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127404011764"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127405012995"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127405014775"},{"key":"rf6","volume-title":"A Nonlinear Dynamics Perspective of Wolfram's New Kind of Science","volume":"1","author":"Chua L. O.","year":"2006"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127406015544"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-58822-8"},{"key":"rf9","volume-title":"Theory of Self-Reproducing Automata","author":"Neumann J. V.","year":"1966"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-4067-7"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1016\/0167-2789(84)90245-8"},{"key":"rf12","volume-title":"A New Kind of Science","author":"Wolfram S.","year":"2002"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127407019925","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T23:59:33Z","timestamp":1565135973000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127407019925"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,12]]},"references-count":12,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2007,12]]}},"alternative-id":["10.1142\/S0218127407019925"],"URL":"https:\/\/doi.org\/10.1142\/s0218127407019925","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2007,12]]}}}