The Computational Beauty of Nature: Computer Explorations of Fractals, Chaos, Complex Systems, and Adaptation / Edition 1

The Computational Beauty of Nature: Computer Explorations of Fractals, Chaos, Complex Systems, and Adaptation / Edition 1

by Gary William Flake
     
 

ISBN-10: 0262062003

ISBN-13: 9780262062008

Pub. Date: 07/10/1998

Publisher: MIT Press

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

Overview

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.

Product Details

ISBN-13:
9780262062008
Publisher:
MIT Press
Publication date:
07/10/1998
Series:
Bradford Book Series
Edition description:
First Edition
Pages:
515
Product dimensions:
8.33(w) x 9.27(h) x 1.38(d)

Table of Contents

Prefacexiii
How to Read This Bookxiv
Dealing with Difficult Subjectsxv
Personal Motivationxvi
Acknowledgmentsxvi
1Introduction1
1.1Simplicity and Complexity2
1.2The Convergence of the Sciences5
1.3The Silicon Laboratory6
IComputation9
2Number Systems and Infinity11
2.1Introduction to Number Properties12
2.2Counting Numbers14
2.3Rational Numbers15
2.4Irrational Numbers16
2.5Further Reading22
3Computability and Incomputability23
3.1Godelization25
3.2Models of Computation26
3.3Lisp and Stutter30
3.4Equivalence and Time Complexity36
3.5Universal Computation and Decision Problems40
3.6Incomputability42
3.7Number Sets Revisited45
3.8Further Reading48
4Postscript: Computation51
4.1Godel's Incompleteness Result52
4.2Incompleteness versus Incomputability53
4.3Discrete versus Continuous55
4.4Incomputability versus Computability56
4.5Further Reading57
IIFractals59
5Self-Similarity and Fractal Geometry61
5.1The Cantor Set62
5.2The Koch Curve65
5.3The Peano Curve66
5.4Fractional Dimensions67
5.5Random Fractals in Nature and Brownian Motion71
5.6Further Exploration75
5.7Further Reading76
6L-Systems and Fractal Growth77
6.1Production Systems78
6.2Turtle Graphics80
6.3Further Exploration81
6.4Further Reading92
7Affine Transformation Fractals93
7.1A Review of Linear Algebra94
7.2Composing Affine Linear Operations96
7.3The Multiple Reduction Copy Machine Algorithm98
7.4Iterated Functional Systems103
7.5Further Exploration105
7.6Further Reading106
8The Mandelbrot Set and Julia Sets111
8.1Iterative Dynamical Systems112
8.2Complex Numbers112
8.3The Mandelbrot Set114
8.4The M-Set and Computability118
8.5The M-Set as the Master Julia Set120
8.6Other Mysteries of the M-Set125
8.7Further Exploration125
8.8Further Reading127
9Postscript: Fractals129
9.1Algorithmic Regularity as Simplicity130
9.2Stochastic Irregularity as Simplicity132
9.3Effective Complexity134
9.4Further Reading136
IIIChaos137
10Nonlinear Dynamics in Simple Maps139
10.1The Logistic Map141
10.2Stability and Instability144
10.3Bifurcations and Universality148
10.4Prediction, Layered Pastry, and Information Loss150
10.5The Shadowing Lemma153
10.6Characteristics of Chaos154
10.7Further Exploration156
10.8Further Reading158
11Strange Attractors159
11.1The Henon Attractor160
11.2A Brief Introduction to Calculus165
11.3The Lorenz Attractor168
11.4The Mackey-Glass System173
11.5Further Exploration176
11.6Further Reading180
12Producer-Consumer Dynamics181
12.1Producer-Consumer Interactions182
12.2Predator-Prey Systems183
12.3Generalized Lotka-Volterra Systems186
12.4Individual-Based Ecology187
12.5Unifying Themes197
12.6Further Exploration198
12.7Further Reading201
13Controlling Chaos203
13.1Taylor Expansions204
13.2Vector Calculus205
13.3Inner and Outer Vector Product207
13.4Eigenvectors, Eigenvalues, and Basis209
13.5OGY Control211
13.6Controlling the Henon Map215
13.7Further Exploration218
13.8Further Reading219
14Postscript: Chaos221
14.1Chaos and Randomness222
14.2Randomness and Incomputability224
14.3Incomputability and Chaos226
14.4Further Reading227
IVComplex Systems229
15Cellular Automata231
15.1One-Dimensional CA232
15.2Wolfram's CA Classification236
15.3Langton's Lambda Parameter242
15.4Conway's Game of Life245
15.5Natural CA-like Phenomena251
15.6Further Exploration255
15.7Further Reading258
16Autonomous Agents and Self-Organization261
16.1Termites262
16.2Virtual Ants264
16.3Flocks, Herds, and Schools270
16.4Unifying Themes275
16.5Further Exploration276
16.6Further Reading278
17Competition and Cooperation281
17.1Game Theory and Zero-Sum Games282
17.2Nonzero-Sum Games and Dilemmas288
17.3Iterated Prisoner's Dilemma293
17.4Stable Strategies and Other Considerations295
17.5Ecological and Spatial Worlds297
17.6Final Thoughts303
17.7Further Exploration303
17.8Further Reading304
18Natural and Analog Computation307
18.1Artificial Neural Networks309
18.2Associative Memory and Hebbian Learning312
18.3Recalling Letters316
18.4Hopfield Networks and Cost Optimization318
18.5Unifying Themes324
18.6Further Exploration325
18.7Further Reading326
19Postscript: Complex Systems327
19.1Phase Transitions in Networks328
19.2Phase Transitions in Computation332
19.3Phase Transitions and Criticality334
19.4Further Reading336
VAdaptation337
20Genetics and Evolution339
20.1Biological Adaptation340
20.2Heredity as Motivation for Simulated Evolution342
20.3Details of a Genetic Algorithm343
20.4A Sampling of GA Encodings348
20.5Schemata and Implicit Parallelism353
20.6Other Evolutionary Inspirations355
20.7Unifying Themes356
20.8Further Exploration358
20.9Further Reading360
21Classifier Systems361
21.1Feedback and Control363
21.2Production, Expert, and Classifier Systems364
21.3The Zeroth Level Classifier System370
21.4Experiments with ZCS373
21.5Further Exploration379
21.6Further Reading380
22Neural Networks and Learning383
22.1Pattern Classification and the Perceptron385
22.2Linear Inseparability390
22.3Multilayer Perceptrons392
22.4Backpropagation393
22.5Function Approximation398
22.6Internal Representations404
22.7Other Applications409
22.8Unifying Themes410
22.9Further Exploration411
22.10Further Reading413
23Postscript: Adaptation415
23.1Models and Search Methods416
23.2Search Methods and Environments419
23.3Environments and Models422
23.4Adaptation and Computation423
23.5Further Reading424
Epilogue425
24Duality and Dichotomy427
24.1Web of Connections428
24.2Interfaces to Hierarchies429
24.3Limitations on Knowledge431
Source Code Notes435
Glossary443
Bibliography469
Index483

Customer Reviews

Average Review:

Write a Review

and post it to your social network

     

Most Helpful Customer Reviews

See all customer reviews >