A NONLINEAR DYNAMICS PERSPECTIVE OF WOLFRAM'S NEW KIND OF SCIENCE PART VIII: MORE ISLES OF EDEN
| Autor: | Leon O. Chua, Jinwook Shin, Junbiao Guan, Valery I. Sbitnev, Kristof Karacs |
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| Rok vydání: | 2007 |
| Předmět: | |
| Zdroj: | International Journal of Bifurcation and Chaos. 17:3741-3894 |
| ISSN: | 1793-6551 0218-1274 |
| DOI: | 10.1142/s0218127407019901 |
| Popis: | This paper presents the basin tree diagrams of all hyper Bernoulli στ-shift rules for string lengths L = 3, 4, …, 8. These diagrams have revealed many global and time-asymptotic properties that we have subsequently proved to be true for all L < ∞. In particular, we have proved that local rule $\kern.5pt{\fboxsep2pt\fbox{60}}\kern.5pt\xspace$ has no Isles of Eden for all L, and that local rules $\kern.5pt{\fboxsep2pt\fbox{154}}\kern.5pt\xspace$ and $\kern.5pt{\fboxsep2pt\fbox{45}}\kern.5pt\xspace$ 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 $\kern.5pt{\fboxsep2pt\fbox{154}}\kern.5pt\xspace$, $\kern.5pt{\fboxsep2pt\fbox{45}}\kern.5pt\xspace$, $\kern.5pt{\fboxsep2pt\fbox{150}}\kern.5pt\xspace$, $\kern.5pt{\fboxsep2pt\fbox{105}}\kern.5pt\xs... |
| Databáze: | OpenAIRE |
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