A nonlinear dynamics perspective of Wolfram's new kind of science. Volume VI / Leon O. Chua, University of California at Berkeley, USA.

Format:

Book

Author/Creator:

Chua, Leon O., 1936- author.

Series:

World Scientific series on nonlinear science. Monographs and treatises ; Series A, v. 85.

Nonlinear dynamics perspective of Wolfram's new kind of science ; v. 6

World Scientific series on nonlinear science. Series A ; v. 85

Language:

English

Subjects (All):

Wolfram, Stephen, 1959-.

Wolfram, Stephen.

Cellular automata.

Computational complexity.

Dynamics.

Nonlinear theories.

Physical Description:

1 online resource (x, 568 pages) : illustrations (chiefly color)

Place of Publication:

Singapore ; Hackensack, N.J. : World Scientific, 2013.

New Jersey : World Scientific, [2013]

Language Note:

English

Summary:

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

Contents:

Dedication; Preface; CONTENTS; Volume VI; Chapter 1. Bernoulli στ -Shift Rules; 1. Introduction; 1.1. Brief notes on Bernoulli στ -shift rules; 2. Basin Tree Diagrams, Omega-Limit Orbits and Space-Time Patterns; 2.1. Basin tree diagrams and portraits of the ω-limit orbits; 2.2. Space-time patterns of Bernoulli rules using the super string as initial string; 3. Robust and Nonrobust ω-Limit Orbits of Rules from Group 4; 3.1. Robust ω-limit orbits of rules from Group 4; 3.2. Nonrobust ω-limit orbits of rules from Group 4; 4. Concluding Remarks; Chapter 2. More Bernoulli στ -Shift Rules

1. Introduction2. Bernoulli στ -Shift Rules; 2.1. General aspects of the Bernoulli στ -shift rules; 2.2. Basin-tree diagrams and portraits of their ω-limit orbits; 2.3. Space-time patterns of Bernoulli rules using the superstring as initial state; 3. Robust and Nonrobust ω-Limit Orbits of Rules from Group 4; 3.1. Robust ω-limit orbits of rules from Group 4; 3.2. Non-robust ω-limit orbits of rules from Group 4; 3.3. Rules with multiple robust ω-limit orbits; 4. Summary of Elementary 1D Cellular Automata; 4.1. Boolean cubes, complexity index, and threshold of complexity

4.2. Globally and quasi-globally equivalent rules4.3. Rotations and symmetries; 4.4. Classification of the local rules; 4.5. Fractality and quasi-ergodicity; 4.6. Isles of Eden and Omega-limit orbits; 5. Concluding Remarks; Chapter 3. Remembrance of Things Past; Vignettes from Volume I; Vignettes from Volume II; Vignettes from Volume III; Vignettes from Volume IV; Vignettes from Volume V; Vignettes from Volume VI; Vignettes of Metaphors from Biology, Cosmology, Physics, etc.; Vignettes of 256 Boolean Cubes; References; Appendices

Appendix I: Correspondence between Chapters from Edited Book and Papers from IJBC JournalAppendix II: Useful and Generic Tables and Figures; Appendix III: Pages where 16 Exquisite Elementary CA Rules are Cited, Discussed, or Characterized; Appendix IV: Contents of Volumes I-VI; Index

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

ISBN:

9789814460880

9814460885

OCLC:

857066296