A cellular automaton is a discrete model studied in computability theory, mathematics, physics, complexity science, theoretical biology and microstructure modelling. It consists of a regular grid of cells, each in one of a finite number of states, such as 'On' or 'Off'. The grid can be in any finite number of dimensions. For each cell, a set of cells called its neighbourhood (usually including the cell itself) is defined relative to the specified cell. This book presents current research from across the globe in the study of cellular automata, including using cellular automata to solve optimisation problems; modelling drug release science using cellular automata; using the cellular automata model to study the dispersion of aphids and ladybugs in a block of citric trees; and the reversibility of cellular automata.
Language: English
Pages: 308
Tags: Информатика и вычислительная техника;Искусственный интеллект;Нейронные сети;
Title Page
......Page 4
CONTENTS......Page 6
PREFACE......Page 8
ABSTRACT......Page 14
1. INTRODUCTION......Page 15
2. COMPLEX SYSTEMS......Page 18
3. OPTIMIZATION......Page 20
3.1. History......Page 21
3.2. Objective Function......Page 22
3.3. System Optimization......Page 23
4. OPTIMIZATION BY CA......Page 25
4.1.1. Simulated annealing......Page 26
4.1.2. Procedure......Page 27
4.1.3. A Sample problem solving......Page 30
4.2.1. Procedure......Page 38
4.2.2. A Sample problem solving......Page 41
5. CONCLUSION......Page 46
REFERENCES......Page 49
ABSTRACT......Page 52
1. INTRODUCTION......Page 53
2. HISTORICAL REVIEW......Page 56
3. MODELING MATRIX EROSION......Page 59
3.1. Describing the Primary State of the Matrix......Page 60
3.3. Step 2 of Polymer Erosion: Polymer Degradation......Page 62
3.4. Step 3 of Polymer Erosion: Loss of Polymer Bulk......Page 63
4. MODELING DRUG DIFFUSION......Page 64
5. EVALUATING THE PREDICTIVE VALUE OF MODELS......Page 66
REFERENCES......Page 67
ABSTRACT......Page 72
1.1. Citrus Sudden Death......Page 73
1.2. Cellular Automata......Page 74
1.3. Fuzzy Rule-Based System......Page 75
2. CELLULAR AUTOMATA MODEL......Page 76
3. SIMULATIONS WITH CELLULAR AUTOMATA MODEL......Page 77
ACKNOWLEDGMENTS......Page 81
REFERENCES......Page 82
ABSTRACT......Page 84
INTRODUCTION......Page 85
CELLULAR FORMULATION......Page 86
COMBINED CELLULAR – GENETIC FORMULATION......Page 87
LOCAL SEARCH ALGORITHM......Page 90
RESULTS AND DISCUSSION......Page 91
REFERENCES......Page 92
1. INTRODUCTION......Page 94
2. A SIMPLE CELLULAR AUTOMATON......Page 95
3. RECONFIGURABLE COMPUTING......Page 96
4.2. Processor Design......Page 97
4.3. Hardware Implementation......Page 98
5. EXPERIMENTAL RESULTS......Page 99
6. CONCLUSIONS AND FUTURE WORK......Page 102
REFERENCES......Page 103
Abstract......Page 104
2.Cellular Growth Testbed......Page 105
2.1.1. Von Neumann Neighborhood......Page 106
2.1.3. 2-Radial Neighborhood......Page 107
2.3. Net Logo Models......Page 108
3. Morphogenetic Gradients......Page 109
4. Genomes......Page 110
5.1. Chromosome structure......Page 114
5.1.1. Chromosome structure forform generation......Page 115
5.2.1. One structural gene......Page 116
6.1. 2D shapes......Page 117
6.2. 3D shapes......Page 119
6.3. Chosen neighborhoods for pattern generation......Page 120
7. Pattern Generation......Page 122
8. Discussion......Page 124
References......Page 127
Abstract......Page 132
1. Introduction......Page 133
2.1. Discrete Dynamical Models with Space......Page 135
2.1.1. Example of Discrete Model with Emergent Space-time.......Page 136
2.1.2. Space Symmetries in More Detail.......Page 139
2.1.3. Unification of Space and Internal Symmetries.......Page 140
3. Structural Analysis of Discrete Relations......Page 142
3.1.1. Relations......Page 143
3.1.2. Compatibility of Systems of Relations......Page 144
3.1.4. On Representation of Relations in Computer......Page 145
3.2.1. J. Conway’s Game of Life......Page 146
3.2.2. Elementary Cellular Automata......Page 149
4. Soliton-like Structures in Deterministic Dynamics......Page 153
5.1. Statistical Mechanics......Page 157
5.2.1. Lattice Models.......Page 158
5.3. Phase Transitions......Page 159
6.1. Discrete Gauge Principle......Page 161
6.2. Quantum Behavior and Gauge Connection......Page 164
6.2.1. Illustrative Example Inspired by Free Particle.......Page 165
6.2.2. Local Quantum Models on Regular Graphs......Page 167
6.3. General Discussion of Quantization in Finite Systems......Page 168
6.3.1. Permutations and Linear Representations......Page 169
6.3.2. Interpretation of Quantum Description in Finite Background......Page 171
Acknowledgments......Page 174
References......Page 175
1. Introduction......Page 178
2. Quivers......Page 181
2.1. De Bruijn Quiver......Page 182
2.2. Adjacency Matrices......Page 187
3. Cellular Automata......Page 190
3.1. Wolfram Cellular Automaton......Page 192
3.2. Correspondence to de Bruijn Quiver......Page 193
3.3. Global Transition of Configuration Algebra......Page 198
3.4. Transition Matrices......Page 199
4.1. Periodic Reductions of WCA......Page 201
4.2. Reversibility of n-WCA......Page 204
4.3. Necessary Conditions for Reversibility of n-WCA......Page 205
5.1. Equivalence Classes of Rules......Page 207
5.2. Reversibility of Rule 154......Page 212
5.3. Complete List of Reversible Rules......Page 215
6.Conclusion......Page 218
REFERENCES......Page 219
1. Introduction......Page 224
2.1. Set of Cellular Automata......Page 225
2.3. Isotropy......Page 226
2.4. Number of Automata......Page 227
2.5. Quiescent State......Page 228
2.6.2. Glider......Page 230
2.7.Glider Gun......Page 231
3.2. AND Gate......Page 233
3.3. NOT Gate......Page 234
4.1. Evolutionary Algorithm......Page 236
4.2.1. Orthogonal Gliders......Page 238
4.2.2. Diagonal Gliders......Page 239
5. Universality......Page 240
5.2.1. Evolutionary Algorithm......Page 243
5.2.2. The Eater of the R Automaton: an Experimental Result......Page 247
5.3. NAND Gate......Page 248
5.3.1. Collisions......Page 249
5.3.2. New Pattern......Page 251
5.3.3. Assembling Patterns into a NOT Gate......Page 252
5.5. Simulation of the Game of Life......Page 253
5.5.3. Simulation of the Game of Life in R......Page 255
6.Conclusion......Page 256
References......Page 257
1. Introduction......Page 262
3 .Encryption System......Page 263
3.1.1. Unidirectional coupling......Page 265
3.2. The Basic Unit Cipher......Page 266
4. Pseudo Random Sequences Generator......Page 268
4.1. Modified Generator......Page 270
4.2. Performance Analysis......Page 271
4.3. Multifractal Properties of the Matrix HN......Page 275
5.2. Wavelet Transform......Page 277
5.3. Compression Scheme......Page 279
6. Numerical Implementation......Page 281
7.Conclusion......Page 282
References......Page 284
Introduction......Page 286
1. Definitions......Page 287
2.1. Factor Subshifts......Page 288
2.2. Generators......Page 289
2.3. Column Factors......Page 290
3. Traces of Cellular Automata......Page 291
4. Equicontinuity......Page 294
5. Expansivity......Page 297
6. Entropy......Page 298
References......Page 300
INDEX......Page 302
