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The Computational Beauty of Nature : Computer Explorations of Fractals, Chaos, Complex Systems, and Adaptation - Gary William Flake

The Computational Beauty of Nature

Computer Explorations of Fractals, Chaos, Complex Systems, and Adaptation

Paperback Published: 27th January 2000
ISBN: 9780262561273
Number Of Pages: 520
For Ages: 18+ years old

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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.

Industry Reviews

"This book is a delight." Barak Pearlmutter , University of New Mexico "This delightful book illustrates beautifully the paradigm shift inphysics from writing equations and solving them to computer modelingand experimentation." Greg Chaitin , author of The Limits of Mathematics

Prefacep. xiii
How to Read This Bookp. xiv
Dealing with Difficult Subjectsp. xv
Personal Motivationp. xvi
Acknowledgmentsp. xvi
Introductionp. 1
Simplicity and Complexityp. 2
The Convergence of the Sciencesp. 5
The Silicon Laboratoryp. 6
Computationp. 9
Number Systems and Infinityp. 11
Introduction to Number Propertiesp. 12
Counting Numbersp. 14
Rational Numbersp. 15
Irrational Numbersp. 16
Further Readingp. 22
Computability and Incomputabilityp. 23
Godelizationp. 25
Models of Computationp. 26
Lisp and Stutterp. 30
Equivalence and Time Complexityp. 36
Universal Computation and Decision Problemsp. 40
Incomputabilityp. 42
Number Sets Revisitedp. 45
Further Readingp. 48
Postscript: Computationp. 51
Godel's Incompleteness Resultp. 52
Incompleteness versus Incomputabilityp. 53
Discrete versus Continuousp. 55
Incomputability versus Computabilityp. 56
Further Readingp. 57
Fractalsp. 59
Self-Similarity and Fractal Geometryp. 61
The Cantor Setp. 62
The Koch Curvep. 65
The Peano Curvep. 66
Fractional Dimensionsp. 67
Random Fractals in Nature and Brownian Motionp. 71
Further Explorationp. 75
Further Readingp. 76
L-Systems and Fractal Growthp. 77
Production Systemsp. 78
Turtle Graphicsp. 80
Further Explorationp. 81
Further Readingp. 92
Affine Transformation Fractalsp. 93
A Review of Linear Algebrap. 94
Composing Affine Linear Operationsp. 96
The Multiple Reduction Copy Machine Algorithmp. 98
Iterated Functional Systemsp. 103
Further Explorationp. 105
Further Readingp. 106
The Mandelbrot Set and Julia Setsp. 111
Iterative Dynamical Systemsp. 112
Complex Numbersp. 112
The Mandelbrot Setp. 114
The M-Set and Computabilityp. 118
The M-Set as the Master Julia Setp. 120
Other Mysteries of the M-Setp. 125
Further Explorationp. 125
Further Readingp. 127
Postscript: Fractalsp. 129
Algorithmic Regularity as Simplicityp. 130
Stochastic Irregularity as Simplicityp. 132
Effective Complexityp. 134
Further Readingp. 136
Chaosp. 137
Nonlinear Dynamics in Simple Mapsp. 139
The Logistic Mapp. 141
Stability and Instabilityp. 144
Bifurcations and Universalityp. 148
Prediction, Layered Pastry, and Information Lossp. 150
The Shadowing Lemmap. 153
Characteristics of Chaosp. 154
Further Explorationp. 156
Further Readingp. 158
Strange Attractorsp. 159
The Henon Attractorp. 160
A Brief Introduction to Calculusp. 165
The Lorenz Attractorp. 168
The Mackey-Glass Systemp. 173
Further Explorationp. 176
Further Readingp. 180
Producer-Consumer Dynamicsp. 181
Producer-Consumer Interactionsp. 182
Predator-Prey Systemsp. 183
Generalized Lotka-Volterra Systemsp. 186
Individual-Based Ecologyp. 187
Unifying Themesp. 197
Further Explorationp. 198
Further Readingp. 201
Controlling Chaosp. 203
Taylor Expansionsp. 204
Vector Calculusp. 205
Inner and Outer Vector Productp. 207
Eigenvectors, Eigenvalues, and Basisp. 209
OGY Controlp. 211
Controlling the Henon Mapp. 215
Further Explorationp. 218
Further Readingp. 219
Postscript: Chaosp. 221
Chaos and Randomnessp. 222
Randomness and Incomputabilityp. 224
Incomputability and Chaosp. 226
Further Readingp. 227
Complex Systemsp. 229
Cellular Automatap. 231
One-Dimensional CAp. 232
Wolfram's CA Classificationp. 236
Langton's Lambda Parameterp. 242
Conway's Game of Lifep. 245
Natural CA-like Phenomenap. 251
Further Explorationp. 255
Further Readingp. 258
Autonomous Agents and Self-Organizationp. 261
Termitesp. 262
Virtual Antsp. 264
Flocks, Herds, and Schoolsp. 270
Unifying Themesp. 275
Further Explorationp. 276
Further Readingp. 278
Competition and Cooperationp. 281
Game Theory and Zero-Sum Gamesp. 282
Nonzero-Sum Games and Dilemmasp. 288
Iterated Prisoner's Dilemmap. 293
Stable Strategies and Other Considerationsp. 295
Ecological and Spatial Worldsp. 297
Final Thoughtsp. 303
Further Explorationp. 303
Further Readingp. 304
Natural and Analog Computationp. 307
Artificial Neural Networksp. 309
Associative Memory and Hebbian Learningp. 312
Recalling Lettersp. 316
Hopfield Networks and Cost Optimizationp. 318
Unifying Themesp. 324
Further Explorationp. 325
Further Readingp. 326
Postscript: Complex Systemsp. 327
Phase Transitions in Networksp. 328
Phase Transitions in Computationp. 332
Phase Transitions and Criticalityp. 334
Further Readingp. 336
Adaptationp. 337
Genetics and Evolutionp. 339
Biological Adaptationp. 340
Heredity as Motivation for Simulated Evolutionp. 342
Details of a Genetic Algorithmp. 343
A Sampling of GA Encodingsp. 348
Schemata and Implicit Parallelismp. 353
Other Evolutionary Inspirationsp. 355
Unifying Themesp. 356
Further Explorationp. 358
Further Readingp. 360
Classifier Systemsp. 361
Feedback and Controlp. 363
Production, Expert, and Classifier Systemsp. 364
The Zeroth Level Classifier Systemp. 370
Experiments with ZCSp. 373
Further Explorationp. 379
Further Readingp. 380
Neural Networks and Learningp. 383
Pattern Classification and the Perceptronp. 385
Linear Inseparabilityp. 390
Multilayer Perceptronsp. 392
Backpropagationp. 393
Function Approximationp. 398
Internal Representationsp. 404
Other Applicationsp. 409
Unifying Themesp. 410
Further Explorationp. 411
Further Readingp. 413
Postscript: Adaptationp. 415
Models and Search Methodsp. 416
Search Methods and Environmentsp. 419
Environments and Modelsp. 422
Adaptation and Computationp. 423
Further Readingp. 424
Epiloguep. 425
Duality and Dichotomyp. 427
Web of Connectionsp. 428
Interfaces to Hierarchiesp. 429
Limitations on Knowledgep. 431
Source Code Notesp. 435
Glossaryp. 443
Bibliographyp. 469
Indexp. 483
Table of Contents provided by Syndetics. All Rights Reserved.

ISBN: 9780262561273
ISBN-10: 0262561271
Series: The Computational Beauty of Nature
Audience: Professional
For Ages: 18+ years old
Format: Paperback
Language: English
Number Of Pages: 520
Published: 27th January 2000
Publisher: MIT Press Ltd
Country of Publication: US
Dimensions (cm): 22.8 x 20.4  x 2.3
Weight (kg): 0.92