A Nonlinear Dynamics Perspective of Wolfram's New Kind of Science Part VII: ISLES of Eden
نویسندگان
چکیده
This paper continues our quest to develop a rigorous analytical theory of 1-D cellular automata via a nonlinear dynamics perspective. The 18 yet uncharacterized local rules are henceforth partitioned into ten complex Bernoulli στ -shift rules and eight hyper Bernoulli στ -shift rules, the latter including such famous rules 30 and 110 . All exhibit a bizarre composite wave dynamics with arbitrarily large Bernoulli velocity σ and Bernoulli return time τ as the length L → ∞. Basin tree diagrams of all ten complex Bernoulli στ -shift rules are exhibited for lengths L = 3, 4, . . . , 8. Superficial as it may seem, these basin tree diagrams suggest general qualitative properties which have since been proved to be true in general. Two such properties form the main results of this paper; namely,
منابع مشابه
A Nonlinear Dynamics Perspective of Wolfram's New Kind of Science Part VIII: More ISLES of Eden
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 60 has no Isles of Eden for all L, and that local rules 154 and 45 are inhabited by a dense set (...
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ورودعنوان ژورنال:
- I. J. Bifurcation and Chaos
دوره 17 شماره
صفحات -
تاریخ انتشار 2007