A Nonlinear Dynamics Perspective of Wolfram's New Kind of Science (6) - Couverture rigide

Chua, Leon O

Couverture rigide

ISBN 10 : 9814460877 ISBN 13 : 9789814460873

Editeur : World Scientific Publishing Co Pte Ltd, 2013

Synopsis

This invaluable volume ends the quest to uncover the secret recipes for predicting the long-term evolution of a ring of identical elementary cells where the binary state of each cell during each generation of an attractor (i.e. after the transients had disappeared) is determined uniquely by the state of its left and right neighbors in the previous generation, as decreed by one of 256 truth tables. As befitting the contents aimed at school children, it was found pedagogically appealing to code each truth table by coloring each of the 8 vertices of a cubical graph in red (for binary state 1), or blue (for binary state 0), forming a toy universe of 256 Boolean cubes, each bearing a different vertex color combination.The corresponding collection of 256 distinct Boolean cubes are then segegrated logically into 6 distinct groups where members from each group share certain common dynamics which allow the long-term evolution of the color configuration of each bit string, of arbitrary length, to be predicted painlessly, via a toy-like gaming procedure, without involving any calculation. In particular, the evolution of any bit string bearing any initial color configuration which resides in any one of the possibly many distinct attractors, can be systematically predicted, by school children who are yet to learn arithmetic, via a simple recipe, for any Boolean cube belonging to group 1, 2, 3, or 4. The simple recipe for predicting the time-asymptotic behaviors of Boolean cubes belonging to groups 1, 2, and 3 has been covered in Vols. I, II, ..., V.This final volume continues the recipe for each of the 108, out of 256, local rules, dubbed the Bernoulli rules, belonging to group 4. Here, for almost half of the toy universe, surprisingly simple recipes involving only the following three pieces of information are derived in Vol. VI; namely, a positive integer τ, a positive, or negative, integer σ, and a sign parameter β > 0, or β 0 (resp. σ

A propos du livre

À propos de l?auteur

Leon Chua is a foreign member of the Academia Europea and a recipient of eight USA patents and 14 Docteur Honoris Causa. He has received numerous international awards, including the first IEEE Kirchhoff Award, the Neural Networks Pioneer Award, the Guggenheim Fellow Award, the Distinguished Professor Award at the Technische Universitat Munchen and the "Top 15 Cited Authors" 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.

Détails de l'édition

• Éditeur: World Scientific Publishing Co Pte Ltd
• Date d'édition: 2013
• Langue: anglais
• ISBN 10: 9814460877
• ISBN 13: 9789814460873
• Reliure: Relié
• Nombre de pages: 580
• Coordonnées du fabricant: non disponible
• Personne responsable: non disponible