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A NONLINEAR DYNAMICS PERSPECTIVE OF WOLFRAM'S NEW KIND OF SCIENCE PART XIV:: MORE BERNOULLI στ-SHIFT RULES.

Authors :
CHUA, LEON O.
PAZIENZA, GIOVANNI E.
Source :
International Journal of Bifurcation & Chaos in Applied Sciences & Engineering. Aug2010, Vol. 20 Issue 8, p2253-2425. 173p.
Publication Year :
2010

Abstract

Over the past eight years, we have studied one of the simplest, yet extremely interesting, dynamical systems; namely, the one-dimensional binary Cellular Automata. The most remarkable results have been presented in a series of papers which is concluded by the present article. The final stop of our odyssey is devoted to the analysis of the second half of the 30 Bernoulli στ-shift rules, which constitute the largest among the six groups in which we classified the 256 local rules. For all these 15 rules, we present the basin-tree diagrams obtained by using each bit string with L ≤ 8 as initial state, a summary of the characteristics of their ω-limit orbits, and the space-time patterns generated from the superstring. Also, in the last section we summarize the main results we obtained by means of our "nonlinear dynamics perspective". [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
02181274
Volume :
20
Issue :
8
Database :
Academic Search Index
Journal :
International Journal of Bifurcation & Chaos in Applied Sciences & Engineering
Publication Type :
Academic Journal
Accession number :
55204071
Full Text :
https://doi.org/10.1142/S0218127410027155