Nonlinear Dynamics Perspective of Wolfram's New Kind of Science

• Main Author: O, CHUA LEON
• Format: eBook
• Language: English
• Published: World Scientific Publishing 11.08.2009
• Series: World Scientific Series on Nonlinear Science: Seri
• ISBN: 9812837930; 9789812837936
• DOI: 10.1142/7835#t=toc

Volume III continues the author's quest for developing a pedagogical, self-contained, yet rigorous analytical theory of 1-D cellular automata via a nonlinear dynamics perspective. Using carefully conceived and illuminating color graphics, the global dynamical behaviors of the 50 (out of 256) local rules that have not yet been covered in Volumes I and II are exposed via their stunningly revealing basin tree diagrams. The Bernoulli στ-shift dynamics discovered in Volume II is generalized to hold for all 50 (or 18 globally equivalent) local rules via complex and hyper Bernoulli wave dynamics. Explicit global state transition formulas derived for rules 60, 90, 105, and 150 reveal a new scale-free phenomenon. The most surprising new result unveiled in this volume is the "Isle of Eden" found hidden in most (almost 90%) of the 256 local rules. Readers are challenged to hunt for long-period, isolated Isles of Eden. These are rare gems waiting to be discovered.Sample Chapter(s)Chapter 1: An Ode to Joy (5,734 KB)Contents: Isles of Eden:Recap of Main Results from Parts I to VIBasin Tree Diagrams of Ten Complex Bernoulli Shift RulesGlobal Analysis of Local Rule 90Global Analysis of Local Rules 150 and 105More Iseles of Eden:The Beginning of the EndBasin Tree Diagrams of Eight Hyper Bernoulli Shift RulesGlobal Analysis of Local Rule 60Global Analysis of Local Rule 154 and 45Dense Isles-of-Eden PropertyReadership: Graduate students, researchers and academics interested in nonlinear dynamics, computer science and complexity theory.