{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,10]],"date-time":"2026-03-10T13:16:37Z","timestamp":1773148597924,"version":"3.50.1"},"reference-count":5,"publisher":"World Scientific Pub Co Pte Lt","issue":"11","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2007,11]]},"abstract":"<jats:p> This paper presents the basin tree diagrams of all hyper Bernoulli \u03c3<jats:sub>\u03c4<\/jats:sub>-shift rules for string lengths L = 3, 4, \u2026, 8. These diagrams have revealed many global and time-asymptotic properties that we have subsequently proved to be true for all L &lt; \u221e. In particular, we have proved that local rule [Formula: see text] has no Isles of Eden for all L, and that local rules [Formula: see text] and [Formula: see text] are inhabited by a dense set (continuum) of Isles of Eden if, and only if, L is an odd integer. A novel and powerful graph-theoretic tool, called Isles-of-Eden digraph, has been developed and can be used to test the existence of dense Isles of Eden of any local rule which satisfies certain constraints, such as rules [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], as well as all invariant local rules, such as rules [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text], subject to no constraints. <\/jats:p>","DOI":"10.1142\/s0218127407019901","type":"journal-article","created":{"date-parts":[[2008,2,14]],"date-time":"2008-02-14T11:26:37Z","timestamp":1202988397000},"page":"3741-3894","source":"Crossref","is-referenced-by-count":25,"title":["A NONLINEAR DYNAMICS PERSPECTIVE OF WOLFRAM'S NEW KIND OF SCIENCE PART VIII: MORE ISLES OF EDEN"],"prefix":"10.1142","volume":"17","author":[{"given":"LEON O.","family":"CHUA","sequence":"first","affiliation":[{"name":"Department of Electrical Engineering and Computer Sciences, University of California at Berkeley, Berkeley, CA 94720, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"KRISTOF","family":"KARACS","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering and Computer Sciences, University of California at Berkeley, Berkeley, CA 94720, USA"},{"name":"Faculty of Information Technology, Peter Pazmany Catholic University, Prater 50-A Budapest, 1083, Hungary"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"VALERY I.","family":"SBITNEV","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering and Computer Sciences, University of California at Berkeley, Berkeley, CA 94720, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"JUNBIAO","family":"GUAN","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering and Computer Sciences, University of California at Berkeley, Berkeley, CA 94720, USA"},{"name":"Department of Mathematics, Shanghai University, Shanghai 200436, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"JINWOOK","family":"SHIN","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering and Computer Sciences, University of California at Berkeley, Berkeley, CA 94720, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127403008041"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127404011764"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127405012995"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127405014775"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127407019068"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127407019901","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T14:58:52Z","timestamp":1565189932000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127407019901"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,11]]},"references-count":5,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2007,11]]}},"alternative-id":["10.1142\/S0218127407019901"],"URL":"https:\/\/doi.org\/10.1142\/s0218127407019901","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2007,11]]}}}