{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,1]],"date-time":"2022-04-01T23:08:52Z","timestamp":1648854532425},"reference-count":18,"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":[[2009,12]]},"abstract":" This 12th part of our Nonlinear Dynamics Perspective of Cellular Automata concludes a series of three articles devoted to CA local rules having robust periodic \u03c9-limit orbits. Here, we consider only the two rules, [Formula: see text] and [Formula: see text], constituting the third of the six groups in which we classified the 1D binary Cellular Automata. Among the numerous theoretical results contained in this article, we emphasize the complete characterization of the \u03c9-limit orbits, both robust and nonrobust, of these two rules and the proof that period-3 and period-6 \u03c9-limit orbits are dense for [Formula: see text] and [Formula: see text], respectively. Furthermore, we will also introduce the fundamental concepts of perfect period-T orbitsets and riddled basins, and see how they emerge in rule [Formula: see text]. <\/jats:p> As stated in the title, we also focus on permutive rules, which have been introduced in a previous installment of our series but never thoroughly studied. Indeed, we will review some of the well-known properties of such rules, like the surjectivity, examining their implications for finite and bi-infinite Cellular Automata. <\/jats:p> Finally, we propose a new list of the 88 globally-independent local rules, which is slightly different from the one we have used so far but has the great advantage of being selected via a rigorous methodology and not an arbitrary choice. For the sake of completeness, we display in the appendix the basin tree diagrams and the portraits of the \u03c9-limit orbits of the rules from this refined table which have not yet been reported in our previous articles. <\/jats:p>","DOI":"10.1142\/s0218127409025365","type":"journal-article","created":{"date-parts":[[2010,3,25]],"date-time":"2010-03-25T07:49:37Z","timestamp":1269503377000},"page":"3887-4038","source":"Crossref","is-referenced-by-count":6,"title":["A NONLINEAR DYNAMICS PERSPECTIVE OF WOLFRAM'S NEW KIND OF SCIENCE PART XII: PERIOD-3, PERIOD-6, AND PERMUTIVE RULES"],"prefix":"10.1142","volume":"19","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, MTA-SZTAKI, Budapest, Hungary"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127492000446"},{"key":"rf2","volume-title":"Dynamical Systems","author":"Birkhoff G. 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