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

Front Cover
MIT Press, 1998 - Computers - 493 pages
6 Reviews
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.
 

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LibraryThing Review

User Review  - mobill76 - LibraryThing

I feel a strange draw towards two poles. I love the highly technial man-made achievements and I love the completely unspoiled "nature of nature". This book sythesizes the two extremes beautifully. As ... Read full review

User Review - Flag as inappropriate

Great chapters on fractals, chaos theory and swarm intelligence.

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
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

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
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
Copyright

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Page xiii - The scientist does not study nature because it is useful; he studies it because he delights in it, and he delights in it because it is beautiful.
Page 1 - I aim at, because the point of philosophy is to start with something so simple as not to seem worth stating, and to end with something so paradoxical that no one will believe it.

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About the author (1998)

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

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