细胞的自控：离散的宇宙CELLULAR AUTOMATA: A DISCRETE UNIVERSE

2002-12  

Aspen Publishers  

Ilachinski,Andrew  

808  

CELLULAR AUTOMATAA Discrete Universeby Andrew Ilachinski (Center for Naval Analyses, USA) Cellular automata are a class of spatially and temporally discrete mathematical systems characterized by local interaction and synchronous dynamical evolution. Introduced by the mathematician John von Neumann in the 1950s as simple models of biological self-reproduction, they are prototypical models for complex systems and processes consisting of a large number of simple, homogeneous, locally interacting components. Cellular automata have been the focus of great attention over the years because of their ability to generate a rich spectrum of very complex patterns of behavior out of sets of relatively simple underlying rules. Moreover, they appear to capture many essential features of complex self-organizing cooperative behavior observed in real systems. This book provides a summary of the basic properties of cellular automata, and explores in depth many important cellular-automata-related research areas, including artificial life, chaos, emergence, fractals, nonlinear dynamics, and self-organization. It also presents a broad review of the speculative proposition that cellular automata may eventually prove to be theoretical harbingers of a fundamentally new information-based, discrete physics. Designed to be accessible at the junior/senior undergraduate level and above, the book will be of interest to all students, researchers, and professionals wanting to learn about order, chaos, and the emergence of complexity. It contains an extensive bibliography and provides a listing of cellular automata resources available on the World Wide Web.

AcknowledgmentsPrefaceForewordChapter 1 Introduction: Preliminary Musings　1.1 Complex Systems 　1.1.1 Short History　1.2 Cellular Automata　　1.2.1 CA & Computation　　1.2.2 Why Study CA?　　　1.2.2.1 CA as Powerful Computation Engines　　　1.2.2.2 CA as Discrete Dynamical System Simulators　　　1.2.2.3 CA as Conceptual Vehicles for Exploring Pattern Formation　　　1.2.2.4 CA as Original Models of Fundamental Physics　　1.2.3 Example #1: One-dimensionM CA　　1.2.4 Example #2: Conway's Life　　1.2.5 Example #3: Belousov-Zhabotinski Reaction　　1.2.6 Example #4: Lattice Gases　　1.2.7 Example #5: Collective Behavior in Higher Dimensions　　1.2.8 Other Variants　1.3 Outline of BookChapter 2 Formalism　2.1 Mathematical Preliminaries　　2.1.1 Set Theory　　2.1.2 Information Theory　　2.1.3 Graph Theory 2.1.4 Groups, Rings and Fields　　2.1.5 Abstract Automata　2.2 Dynamical Rules: Notation and Definitions　　2.2.1 One-dimensional CA　　2.2.2 Two-dimensional CAChapter 3 Phenomenological Studies of Generic CA　3.1 One-dimensional Systems　　3.1.1 Space-Time Patterns　　3.1.2 Behavioral Classes　　　 3.1.2.1 Difference Patterns　　　 3.1.2.2 Blocking Transformations　　 3.1.3 General Properties of Elementary CA　　　 3.1.3.1 Local Properties　　　 3.1.3.2 Global Properties　　 3.1.4 A Small Sampling of Rules　　　 3.1.4.1 The k=2, r=l rule R22: Just How Complex Is It? 　　　 3.1.4.2 The k=2, r=l rule R30: Just How Random Is It? 　　　 3.1.4.3 Critical-Like Behavior　　　 3.1.4.4 Particle-Like Behavior　　　 3.1.4.5 Reversible Rules　3.2 Parameterizing the Space of CA Rules　　 3.2.1 Langton's λ Parameter　　 3.2.2 Qualitative Overview of Behavior as a Function of A　　 3.2.3 Quantitative Overview of Behavior as a Function of A　　　 3.2.3.1 Difference Pattern Spreading Rates　　　 3.2.3.2 Entropy　　 3.2.4 Mutual Information　　 3.2.5 Discussion　　　 3.2.5.1 Large Af Limit　　　 3.2.5.2 Large k Limit　　　 3.2.5.3 Complexity Resides in the Transition Region? 　3.3 Dependence on Lattice Topology　　 3.3.1 Natural Topology　　 3.3.2 Transitional Lattice Construction　　 3.3.3 [2 : 2 : 2] Dynamical Profiles　　 3.3.4 [3 : 3 : 3] Dynamical Profiles　　 3.3.5 Dynamical Profiles for Range Dependent Rules　　 3.3.6 Discussion　3.4 Two-dimensional Systems　　 3.4.1 Simple Seeds　　 3.4.2 Random Seeds　　 3.4.3 Voting Rules　……Chapter 4 Dynamical Systems Theory ApproachChapter 5 Analytic ApproachChapter 6 Cellular Automata and Language TheoryChapter 7 Probabilistic CAChapter 8 Generalized ModelsChapter 9 CA Models of Fluid DynamicsChapter 10 Neural NetworksChapter 11 Artifical-LifeChapter 12 Is Nature, Underneath it All, a CA?Appendix A CA Research ToolsAppendix B Complex Systems Theory ResourcesBibliographyIndex

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