A Nonlinear Dynamics Perspective of Wolfram's New Kind of Science: v. 4 (World Scientific Series on Nonlinear Science Series A 76)
By: Leon O. Chua (editor)Hardback
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Volume IV continues the author's odyssey on l-D cellular automata as chronicled in Volumes I, II and III, by uncovering a novel quasi-ergodicity phenomenon involving orbits meandering among omega-limit orbits of complex (group 5) and hyper (group 6) Bernoulli rules. This discovery is embellished with analytical formulas characterizing the fractal properties of characteristic functions, as well as explicit formulas for generating colorful and pedagogically revealing isomorphic basin tree diagrams. Many new results were derived and proved by uncovering subtle symmetries endowed by various subsets of the 256 Boolean cubes. For the first time, rigorous analyses were used to identify 67, out off 256, local rules whose asymptotic behaviors consist of robust period-l orbits. The highlight of this continuing odyssey is the discovery of an isolated period-3240 Isle of Eden hidden among the dense omega-limit orbits of Wolfram's remarkable "random number generating" rule 30. This is the largest gem known to-date and readers are challenged to uncover even larger ones.
Leon Chua is a foreign member of the Academia Europea and a recipient of eight USA patents and 12 docteur honoris causa. He has received numerous international awards, including the first IEEE Kirchhoff Award, the Neural Networks Pioneer Award, and the Top 15 Cited AuthorsA" Award based on the ISI Citation Index in Engineering from 1991 to 2001. When not immersed in science, he relaxes by searching for Wagner's leitmotifs, musing over Kandinsky's chaos, and contemplating Wittgenstein's inner thoughts.
Quasi-Ergodicity; Period-1 Rules.
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- ID: 9789814317306
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