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

作者：Chua Leon O^*; Pazienza Giovanni E

来源：International Journal of Bifurcation and Chaos, 2010, 20(8): 2253-2425.

DOI：10.1142/S0218127410027155

• Cellular automata
• nonlinear dynamics
• Bernoulli sigma(tau)-shift rules
• group 4 rules
• omega-limit orbits
• attractors
• Isles of Eden
• basin-tree diagrams
• superstring
• robust omega-limit orbits
• non-robust omega-limit orbits
• classification of local rules
• rotation groups

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 sigma(tau)-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.-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".

• 出版日期2010-8