A nonlinear dynamics perspective of Wolfram's New kind of science Volume 1 / Leon O. Chua.

Format:

Book

Author/Creator:

Chua, Leon O., 1936-

Series:

World Scientific series on nonlinear science. Monographs and treatises ; Series A, v. 57.

World Scientific series on nonlinear science, Series A, Monographs and treatises ; v. 57

Language:

English

Subjects (All):

Cellular automata.

Computational complexity.

Dynamics.

Nonlinear theories.

Wolfram, Stephen, 1959- New kind of science.

Wolfram, Stephen.

Physical Description:

1 online resource (397 p.)

Place of Publication:

Hackensack, N.J. : World Scientific, c2006.

Language Note:

English

Summary:

This novel book introduces cellular automata from a rigorous nonlinear dynamics perspective. It supplies the missing link between nonlinear differential and difference equations to discrete symbolic analysis. A surprisingly useful interpretations of cellular automata in terms of neural networks is also given. The book provides a scientifically sound and original analysis, and classifications of the empirical results presented in Wolfram's monumental "New Kind of Science."

Contents:

PREFACE; CONTENTS; PROLOGUE; Chapter 1 THRESHOLD OF COMPLEXITY; 1. Introduction; 2. Cellular Automata is a Special Case of CNN; 3. Every Local Rule is a Cube with Eight Colored Vertices; 4. Every Local Rule is a Code for Attractors of a Dynamical System; 4.1. Dynamical System for Rule 110; 4.2 .There are Eight Attractors for Each Local Rule; 5. Every Local Rule has a Unique Complexity Index; 5.1. Geometrical Interpretation of Projection o and Discriminant w(o); 5.2. Geometrical Interpretation of Transition Points of Discriminant Function w(o); 5.3. Geometrical Structure of Local Rules

4.2. Partitioning 256 local rules into 16 gene families4.3. Each gene family has 16 gene siblings; 5. The Double-Helix Torus; 5.1. Algorithm for generating all 16 local rules belonging to each gene family; 5.2. ""8/24"" Distribution pattern in gene siblings; 5.3. Coding local rules on a double helix; 6. Explaining and Predicting Pattern Features; 6.1. Gallery of gene family patterns; 6.2. Predicting the background; Chapter 3 PREDICTING THE UNPREDICTABLE; 1. Introduction; 2. Local versus Global Equivalence; 3. Predicting the Unpredictable

4.5. Combining transformations from the Vierergruppe V and the rotation group R4.6. Laterally symmetric interaction group for local equivalence classes; 4.7. Mapping parameter vectors between rule 110 and its locally-equivalent rules; 5. Concluding Remarks; REFERENCES; INDEX

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

ISBN:

9789812772138

9812772138