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| Acknowledgments Preface Foreword Chapter 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 Book Chapter 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 CA Chapter 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 Approach Chapter 5 Analytic Approach Chapter 6 Cellular Automata and Language Theory Chapter 7 Probabilistic CA Chapter 8 Generalized Models Chapter 9 CA Models of Fluid Dynamics Chapter 10 Neural Networks Chapter 11 Artifical-Life Chapter 12 Is Nature, Underneath it All, a CA? Appendix A CA Research Tools Appendix B Complex Systems Theory Resources Bibliography Index |
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