The Computational Beauty of Nature: Computer Explorations of Fractals, Chaos, Complex Systems, and AdaptationGary William Flake develops in depth the simple idea that recurrent rules can produce rich and complicated behaviors. "Simulation," writes Gary Flake in his preface, "becomes a form of experimentation in a universe of theories. The primary purpose of this book is to celebrate this fact."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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Great chapters on fractals, chaos theory and swarm intelligence.
Really interesting.....as the explanations are carefully driving from basic science to the real applications
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 
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