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.

Preface	p. xiii
How to Read This Book	p. xiv
Dealing with Difficult Subjects	p. xv
Personal Motivation	p. xvi
Acknowledgments	p. xvi
Introduction	p. 1
Simplicity and Complexity	p. 2
The Convergence of the Sciences	p. 5
The Silicon Laboratory	p. 6
Computation	p. 9
Number Systems and Infinity	p. 11
Introduction to Number Properties	p. 12
Counting Numbers	p. 14
Rational Numbers	p. 15
Irrational Numbers	p. 16
Further Reading	p. 22
Computability and Incomputability	p. 23
Godelization	p. 25
Models of Computation	p. 26
Lisp and Stutter	p. 30
Equivalence and Time Complexity	p. 36
Universal Computation and Decision Problems	p. 40
Incomputability	p. 42
Number Sets Revisited	p. 45
Further Reading	p. 48
Postscript: Computation	p. 51
Godel's Incompleteness Result	p. 52
Incompleteness versus Incomputability	p. 53
Discrete versus Continuous	p. 55
Incomputability versus Computability	p. 56
Further Reading	p. 57
Fractals	p. 59
Self-Similarity and Fractal Geometry	p. 61
The Cantor Set	p. 62
The Koch Curve	p. 65
The Peano Curve	p. 66
Fractional Dimensions	p. 67
Random Fractals in Nature and Brownian Motion	p. 71
Further Exploration	p. 75
Further Reading	p. 76
L-Systems and Fractal Growth	p. 77
Production Systems	p. 78
Turtle Graphics	p. 80
Further Exploration	p. 81
Further Reading	p. 92
Affine Transformation Fractals	p. 93
A Review of Linear Algebra	p. 94
Composing Affine Linear Operations	p. 96
The Multiple Reduction Copy Machine Algorithm	p. 98
Iterated Functional Systems	p. 103
Further Exploration	p. 105
Further Reading	p. 106
The Mandelbrot Set and Julia Sets	p. 111
Iterative Dynamical Systems	p. 112
Complex Numbers	p. 112
The Mandelbrot Set	p. 114
The M-Set and Computability	p. 118
The M-Set as the Master Julia Set	p. 120
Other Mysteries of the M-Set	p. 125
Further Exploration	p. 125
Further Reading	p. 127
Postscript: Fractals	p. 129
Algorithmic Regularity as Simplicity	p. 130
Stochastic Irregularity as Simplicity	p. 132
Effective Complexity	p. 134
Further Reading	p. 136
Chaos	p. 137
Nonlinear Dynamics in Simple Maps	p. 139
The Logistic Map	p. 141
Stability and Instability	p. 144
Bifurcations and Universality	p. 148
Prediction, Layered Pastry, and Information Loss	p. 150
The Shadowing Lemma	p. 153
Characteristics of Chaos	p. 154
Further Exploration	p. 156
Further Reading	p. 158
Strange Attractors	p. 159
The Henon Attractor	p. 160
A Brief Introduction to Calculus	p. 165
The Lorenz Attractor	p. 168
The Mackey-Glass System	p. 173
Further Exploration	p. 176
Further Reading	p. 180
Producer-Consumer Dynamics	p. 181
Producer-Consumer Interactions	p. 182
Predator-Prey Systems	p. 183
Generalized Lotka-Volterra Systems	p. 186
Individual-Based Ecology	p. 187
Unifying Themes	p. 197
Further Exploration	p. 198
Further Reading	p. 201
Controlling Chaos	p. 203
Taylor Expansions	p. 204
Vector Calculus	p. 205
Inner and Outer Vector Product	p. 207
Eigenvectors, Eigenvalues, and Basis	p. 209
OGY Control	p. 211
Controlling the Henon Map	p. 215
Further Exploration	p. 218
Further Reading	p. 219
Postscript: Chaos	p. 221
Chaos and Randomness	p. 222
Randomness and Incomputability	p. 224
Incomputability and Chaos	p. 226
Further Reading	p. 227
Complex Systems	p. 229
Cellular Automata	p. 231
One-Dimensional CA	p. 232
Wolfram's CA Classification	p. 236
Langton's Lambda Parameter	p. 242
Conway's Game of Life	p. 245
Natural CA-like Phenomena	p. 251
Further Exploration	p. 255
Further Reading	p. 258
Autonomous Agents and Self-Organization	p. 261
Termites	p. 262
Virtual Ants	p. 264
Flocks, Herds, and Schools	p. 270
Unifying Themes	p. 275
Further Exploration	p. 276
Further Reading	p. 278
Competition and Cooperation	p. 281
Game Theory and Zero-Sum Games	p. 282
Nonzero-Sum Games and Dilemmas	p. 288
Iterated Prisoner's Dilemma	p. 293
Stable Strategies and Other Considerations	p. 295
Ecological and Spatial Worlds	p. 297
Final Thoughts	p. 303
Further Exploration	p. 303
Further Reading	p. 304
Natural and Analog Computation	p. 307
Artificial Neural Networks	p. 309
Associative Memory and Hebbian Learning	p. 312
Recalling Letters	p. 316
Hopfield Networks and Cost Optimization	p. 318
Unifying Themes	p. 324
Further Exploration	p. 325
Further Reading	p. 326
Postscript: Complex Systems	p. 327
Phase Transitions in Networks	p. 328
Phase Transitions in Computation	p. 332
Phase Transitions and Criticality	p. 334
Further Reading	p. 336
Adaptation	p. 337
Genetics and Evolution	p. 339
Biological Adaptation	p. 340
Heredity as Motivation for Simulated Evolution	p. 342
Details of a Genetic Algorithm	p. 343
A Sampling of GA Encodings	p. 348
Schemata and Implicit Parallelism	p. 353
Other Evolutionary Inspirations	p. 355
Unifying Themes	p. 356
Further Exploration	p. 358
Further Reading	p. 360
Classifier Systems	p. 361
Feedback and Control	p. 363
Production, Expert, and Classifier Systems	p. 364
The Zeroth Level Classifier System	p. 370
Experiments with ZCS	p. 373
Further Exploration	p. 379
Further Reading	p. 380
Neural Networks and Learning	p. 383
Pattern Classification and the Perceptron	p. 385
Linear Inseparability	p. 390
Multilayer Perceptrons	p. 392
Backpropagation	p. 393
Function Approximation	p. 398
Internal Representations	p. 404
Other Applications	p. 409
Unifying Themes	p. 410
Further Exploration	p. 411
Further Reading	p. 413
Postscript: Adaptation	p. 415
Models and Search Methods	p. 416
Search Methods and Environments	p. 419
Environments and Models	p. 422
Adaptation and Computation	p. 423
Further Reading	p. 424
Epilogue	p. 425
Duality and Dichotomy	p. 427
Web of Connections	p. 428
Interfaces to Hierarchies	p. 429
Limitations on Knowledge	p. 431
Source Code Notes	p. 435
Glossary	p. 443
Bibliography	p. 469
Index	p. 483
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The Computational Beauty of Nature Computer Explorations of Fractals, Chaos, Complex Systems, and Adaptation

9780262561273

0262561271

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