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Contenido

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 ??-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.

   INDICE: Isles of Eden: Recap of Main Results from Parts I to VI; Basin Tree Diagrams of Ten Complex Bernoulli Shift Rules; Global Analysis of Local Rule 90; Global Analysis of Local Rules 150 and 105; More Iseles of Eden: The Beginning of the End; Basin Tree Diagrams of Eight Hyper Bernoulli Shift Rules; Global Analysis of Local Rule 60; Global Analysis of Local Rule 154 and 45; Dense Isles-of-Eden Property.

Detalles del artículo

• Páginas : 360
• Editorial : World Scientific
• Idioma : Inglés
• Fecha de Publicación : 11/10/2009
• ISBN: 9789812837936
• Encuadernación : Cartoné
• Nº Volúmenes : 1
• País de Publicación : Singapur