The Computational Beauty of Nature: Computer Explorations of Fractals, Chaos, Complex Systems, and Adaptations

Gary William Flake

MIT Press, 1998 - Computers - 493 pages

Honorable Mention, 1998, category of Computer Science, Professional/Scholarly Publishing Annual Awards Competition presented by the Association of American Publishers, Inc.

In this book Gary William Flake develops in depth the simple idea that recurrent rules can produce rich and complicated behaviors. Distinguishing "agents" (e.g., molecules, cells, animals, and species) from their interactions (e.g., chemical reactions, immune system responses, sexual reproduction, and evolution), Flake argues that it is the computational properties of interactions that account for much of what we think of as "beautiful" and "interesting." From this basic thesis, Flake explores what he considers to be today's four most interesting computational topics: fractals, chaos, complex systems, and adaptation.

Each of the book's parts can be read independently, enabling even the casual reader to understand and work with the basic equations and programs. Yet the parts are bound together by the theme of the computer as a laboratory and a metaphor for understanding the universe. The inspired reader will experiment further with the ideas presented to create fractal landscapes, chaotic systems, artificial life forms, genetic algorithms, and artificial neural networks.

What people are saying

Review: The Computational Beauty of Nature: Computer Explorations of Fractals, Chaos, Complex Systems, and Adaptation

User Review  - Amar Pai - Goodreads

I was somewhat disappointed by this book. Maybe 15 years ago the ideas presented here were radical and surprising, but now they're old hat. Much of the material is stuff that will be familiar to ...

Review: The Computational Beauty of Nature: Computer Explorations of Fractals, Chaos, Complex Systems, and Adaptation

User Review  - Thomas - Goodreads

Very interesting book. The subjects are well selected and complementary to each other. Even if it is more about computing than nature, it is interesting to see the connections that are made between some natural phenomena and math/CS theories.

Contents

• Computation: 9
• Number Systems and Infinity: 11
• 21 Introduction to Number Properties: 12
• 22 Counting Numbers: 14
• 23 Rational Numbers: 15
• 24 Irrational Numbers: 16
• 25 Further Reading: 22
• Computability and Incomputability: 23
• 31 Godelization: 25
• 32 Models of Computation: 26
• 33 Lisp and Stutter: 30
• 34 Equivalence and Time Complexity: 36
• 35 Universal Computation and Decision Problems: 40
• 36 Incomputability: 42
• 37 Number Sets Revisited: 45
• 38 Further Reading: 48
• Postscript Computation: 51
• 41 Godels Incompleteness Result: 52
• 42 Incompleteness versus Incomputability: 53
• 43 Discrete versus Continuous: 55
• 44 Incomputability versus Computability: 56
• 45 Further Reading: 57
• Fractals: 59
• SelfSimilarity and Fractal Geometry: 61
• 51 The Cantor Set: 62
• 52 The Koch Curve: 65
• 53 The Peano Curve: 66
• 54 Fractional Dimensions: 67
• 55 Random Fractals in Nature and Brownian Motion: 71
• 56 Further Exploration: 75
• 57 Further Reading: 76
• LSystems and Fractal Growth: 77
• 61 Production Systems: 78
• 62 Turtle Graphics: 80
• 63 Further Exploration: 81
• 64 Further Reading: 92
• Affine Transformation Fractals: 93
• 71 A Review of Linear Algebra: 94
• 72 Composing Affine Linear Operations: 96
• 73 The Multiple Reduction Copy Machine Algorithm: 98
• 74 Iterated Functional Systems: 103
• 75 Further Exploration: 105
• 76 Further Reading: 106
• The Mandelbrot Set and Julia Sets: 111
• 81 Iterative Dynamical Systems: 112
• 83 The Mandelbrot Set: 114
• 84 The MSet and Computability: 118
• 85 The MSet as the Master Julia Set: 120
• 86 Other Mysteries of the MSet: 125
• 88 Further Reading: 127
• Postscript Fractals: 129
• 91 Algorithmic Regularity as Simplicity: 130
• 92 Stochastic Irregularity as Simplicity: 132
• 93 Effective Complexity: 134
• 94 Further Reading: 136
• Chaos: 137
• Nonlinear Dynamics in Simple Maps: 139
• 101 The Logistic Map: 141
• 102 Stability and Instability: 144
• 103 Bifurcations and Universality: 148
• 104 Prediction Layered Pastry and Information Loss: 150
• 105 The Shadowing Lemma: 153
• 106 Characteristics of Chaos: 154
• 107 Further Exploration: 156
• 108 Further Reading: 158
• Strange Attractors: 159
• 111 The Henon Attractor: 160
• 112 A Brief Introduction to Calculus: 165
• 113 The Lorenz Attractor: 168
• 114 The MackeyGlass System: 173
• 115 Further Exploration: 176
• 116 Further Reading: 180
• ProducerConsumer Dynamics: 181
• 121 ProducerConsumer Interactions: 182
• 122 PredatorPrey Systems: 183
• 123 Generalized LotkaVolterra Systems: 186
• 124 IndividualBased Ecology: 187
• 125 Unifying Themes: 197
• 126 Further Exploration: 198
• 127 Further Reading: 201
• Controlling Chaos: 203
• 131 Taylor Expansions: 204
• 132 Vector Calculus: 205
• 133 Inner and Outer Vector Product: 207
• 134 Eigenvectors Eigenvalues and Basis: 209
• 135 OGY Control: 211
• 136 Controlling the Henon Map: 215
• 137 Further Exploration: 218
• 138 Further Reading: 219
• Postscript Chaos: 221
• 141 Chaos and Randomness: 222
• 142 Randomness and Incomputability: 224
• 143 Incomputability and Chaos: 226
• 144 Further Reading: 227
• Complex Systems: 229
• Cellular Automata: 231
• 151 OneDimensional CA: 232
• 152 Wolframs CA Classification: 236
• 153 Langtons Lambda Parameter: 242
• 154 Conways Game of Life: 245
• 155 Natural CAlike Phenomena: 251
• 156 Further Exploration: 255
• 157 Further Reading: 258
• Autonomous Agents and SelfOrganization: 261
• 161 Termites: 262
• 162 Virtual Ants: 264
• 163 Flocks Herds and Schools: 270
• 164 Unifying Themes: 275
• 165 Further Exploration: 276
• 166 Further Reading: 278
• Competition and Cooperation: 281
• 171 Game Theory and ZeroSum Games: 282
• 172 NonzeroSum Games and Dilemmas: 288
• 173 Iterated Prisoners Dilemma: 293
• 174 Stable Strategies and Other Considerations: 295
• 175 Ecological and Spatial Worlds: 297
• 176 Final Thoughts: 303
• 178 Further Reading: 304
• Natural and Analog Computation: 307
• 181 Artificial Neural Networks: 309
• 182 Associative Memory and Hebbian Learning: 312
• 183 Recalling Letters: 316
• 184 Hopfield Networks and Cost Optimization: 318
• 185 Unifying Themes: 324
• 186 Further Exploration: 325
• 187 Further Reading: 326
• Postscript Complex Systems: 327
• 191 Phase Transitions in Networks: 328
• 192 Phase Transitions in Computation: 332
• 193 Phase Transitions and Criticality: 334
• 194 Further Reading: 336
• Adaptation: 337
• Genetics and Evolution: 339
• 201 Biological Adaptation: 340
• 202 Heredity as Motivation for Simulated Evolution: 342
• 203 Details of a Genetic Algorithm: 343
• 204 A Sampling of GA Encodings: 348
• 205 Schemata and Implicit Parallelism: 353
• 206 Other Evolutionary Inspirations: 355
• 207 Unifying Themes: 356
• 208 Further Exploration: 358
• 209 Further Reading: 360
• Classifier Systems: 361
• 211 Feedback and Control: 363
• 212 Production Expert and Classifier Systems: 364
• 213 The Zeroth Level Classifier System: 370
• 214 Experiments with ZCS: 373
• 215 Further Exploration: 379
• 216 Further Reading: 380
• Neural Networks and Learning: 383
• 221 Pattern Classification and the Perceptron: 385
• 222 Linear Inseparability: 390
• 223 Multilayer Perceptrons: 392
• 224 Backpropagation: 393
• 225 Function Approximation: 398
• 226 Internal Representations: 404
• 227 Other Applications: 409
• 228 Unifying Themes: 410
• 229 Further Exploration: 411
• 2210 Further Reading: 413
• Postscript Adaptation: 415
• 231 Models and Search Methods: 416
• 232 Search Methods and Environments: 419
• 233 Environments and Models: 422
• 234 Adaptation and Computation: 423
• 235 Further Reading: 424
• Epilogue: 425
• Duality and Dichotomy: 427
• 241 Web of Connections: 428
• 242 Interfaces to Hierarchies: 429
• 243 Limitations on Knowledge: 431
• Source Code Notes: 435
• Glossary: 443
• Bibliography: 469
• Index: 483

About the author

Flake is a research scientist in the Adaptive Information and Signal Professing Department of Siemens Corporate Research, Princeton, New Jersey.

Bibliographic information

• Title: The Computational Beauty of Nature: Computer Explorations of Fractals, Chaos, Complex Systems, and Adaptations; Bradford Books
• Author: Gary William Flake
• Edition: illustrated, reprint
• Publisher: MIT Press, 1998
• ISBN: 0262561271, 9780262561273
• Length: 493 pages
• Subjects: Computers / Computer Science; Computers / Computer Simulation; Computers / Programming / General