A nonlinear dynamics perspective of Wolfram's new kind of science. Part VIII: More Isles of Eden

作者：Chua Leon O; Karacs Chua Kristof^*; Sbitnev Valery I; Guan Junbiao; Shin Jinwook

来源：International Journal of Bifurcation and Chaos, 2007, 17(11): 3741-3894.

DOI：10.1142/S0218127407019901

• cellular automata
• nonlinear dynamics
• attractors
• Isles of Eden
• Bernoulli shift
• shift maps
• basin tree diagram
• Bernoulli velocity
• Bernoulli return time
• complex Bernoulli shifts
• hyper Bernoulli shifts
• Binomial series
• scale-free phenomena
• Rule 45
• Rule 60
• Rule 90
• Rule 105
• Rule 150
• Rule 154

This paper presents the basin tree diagrams of all hyper Bernoulli sigma(tau)-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 < infinity. In particular, we have proved that local rule 60 has no Isles of Eden for all L, and that local rules [154] and [45] 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 [154], [45], [150], [105], as well as all invariant local rules, such as rules [170], [240], [15] and [85], subject to no constraints.

• 出版日期2007-11
• 单位上海大学