{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,3]],"date-time":"2022-04-03T15:25:25Z","timestamp":1648999525022},"reference-count":16,"publisher":"World Scientific Pub Co Pte Lt","issue":"07","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2010,7]]},"abstract":" More than one third of the 88 globally-independent Cellular Automata rules exhibit robust simple Bernoulli-shift dynamics. Among them we find rule [Formula: see text], which we proved to be chaotic in the previous episodes of our chronicle, and rule [Formula: see text], the famous global majority rule. Therefore, we cannot overstate the importance of the Bernoulli \u03c3\u03c4<\/jats:sub>-shift rules which we will present in two parts of our continuing odyssey on the Nonlinear Dynamics Perspective of Cellular Automata. This paper covers the first 15 of the 30 Bernoulli \u03c3\u03c4<\/jats:sub>-shift rules. In this paper, after recalling the main concepts of Bernoulli rules \u2014 such as the role of the three Bernoulli parameters \u03c3, \u03c4 and \u03b2 \u2014 we will display the basin tree diagrams of these rules together with a convenient summary of the results extracted from them. Then, we will show that the superstring [Formula: see text] is an excellent testing signal to find the robust behavior of a given rule. Finally, we will conclude this paper with a discussion about the difference between robust and nonrobust \u03c9-limit orbits of the Bernoulli \u03c3\u03c4<\/jats:sub>-shift rules. <\/jats:p>","DOI":"10.1142\/s0218127410026903","type":"journal-article","created":{"date-parts":[[2010,8,4]],"date-time":"2010-08-04T09:55:35Z","timestamp":1280915735000},"page":"1859-2003","source":"Crossref","is-referenced-by-count":7,"title":["A NONLINEAR DYNAMICS PERSPECTIVE OF WOLFRAM'S NEW KIND OF SCIENCE. PART XIII: BERNOULLI \u03c3\u03c4<\/sub>-SHIFT RULES"],"prefix":"10.1142","volume":"20","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"}]},{"given":"GIOVANNI E.","family":"PAZIENZA","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering and Computer Sciences, University of California at Berkeley, Berkeley, CA 94720, USA"},{"name":"Cellular Sensory and Wave Computing Laboratory, Computer and Automation Research Institute \u2014 MTA-SZTAKI and Pazmany University, Budapest, Hungary"}]}],"member":"219","published-online":{"date-parts":[[2012,5,2]]},"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","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127406015544"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127407019068"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127407019901"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127408021853"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127409023822"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127409023974"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127409025365"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1887\/0750305088"},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1109\/TCS.1983.1085409"},{"key":"rf15","volume-title":"Nonlinear Problems in Random Theory","author":"Wiener N.","year":"1958"},{"key":"rf16","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\/S0218127410026903","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T20:49:31Z","timestamp":1565124571000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127410026903"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,7]]},"references-count":16,"journal-issue":{"issue":"07","published-online":{"date-parts":[[2012,5,2]]},"published-print":{"date-parts":[[2010,7]]}},"alternative-id":["10.1142\/S0218127410026903"],"URL":"https:\/\/doi.org\/10.1142\/s0218127410026903","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,7]]}}}