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Preface | |
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How to Read This Book | |
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Dealing with Difficult Subjects | |
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Personal Motivation | |
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Acknowledgments | |
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Introduction | |
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Simplicity and Complexity | |
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The Convergence of the Sciences | |
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The Silicon Laboratory | |
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Computation | |
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Number Systems and Infinity | |
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Introduction to Number Properties | |
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Counting Numbers | |
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Rational Numbers | |
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Irrational Numbers | |
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Further Reading | |
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Computability and Incomputability | |
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Godelization | |
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Models of Computation | |
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Lisp and Stutter | |
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Equivalence and Time Complexity | |
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Universal Computation and Decision Problems | |
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Incomputability | |
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Number Sets Revisited | |
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Further Reading | |
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Postscript: Computation | |
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Godel's Incompleteness Result | |
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Incompleteness versus Incomputability | |
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Discrete versus Continuous | |
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Incomputability versus Computability | |
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Further Reading | |
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Fractals | |
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Self-Similarity and Fractal Geometry | |
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The Cantor Set | |
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The Koch Curve | |
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The Peano Curve | |
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Fractional Dimensions | |
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Random Fractals in Nature and Brownian Motion | |
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Further Exploration | |
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Further Reading | |
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L-Systems and Fractal Growth | |
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Production Systems | |
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Turtle Graphics | |
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Further Exploration | |
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Further Reading | |
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Affine Transformation Fractals | |
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A Review of Linear Algebra | |
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Composing Affine Linear Operations | |
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The Multiple Reduction Copy Machine Algorithm | |
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Iterated Functional Systems | |
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Further Exploration | |
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Further Reading | |
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The Mandelbrot Set and Julia Sets | |
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Iterative Dynamical Systems | |
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Complex Numbers | |
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The Mandelbrot Set | |
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The M-Set and Computability | |
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The M-Set as the Master Julia Set | |
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Other Mysteries of the M-Set | |
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Further Exploration | |
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Further Reading | |
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Postscript: Fractals | |
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Algorithmic Regularity as Simplicity | |
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Stochastic Irregularity as Simplicity | |
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Effective Complexity | |
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Further Reading | |
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Chaos | |
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Nonlinear Dynamics in Simple Maps | |
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The Logistic Map | |
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Stability and Instability | |
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Bifurcations and Universality | |
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Prediction, Layered Pastry, and Information Loss | |
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The Shadowing Lemma | |
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Characteristics of Chaos | |
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Further Exploration | |
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Further Reading | |
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Strange Attractors | |
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The Henon Attractor | |
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A Brief Introduction to Calculus | |
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The Lorenz Attractor | |
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The Mackey-Glass System | |
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Further Exploration | |
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Further Reading | |
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Producer-Consumer Dynamics | |
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Producer-Consumer Interactions | |
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Predator-Prey Systems | |
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Generalized Lotka-Volterra Systems | |
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Individual-Based Ecology | |
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Unifying Themes | |
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Further Exploration | |
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Further Reading | |
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Controlling Chaos | |
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Taylor Expansions | |
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Vector Calculus | |
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Inner and Outer Vector Product | |
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Eigenvectors, Eigenvalues, and Basis | |
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OGY Control | |
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Controlling the Henon Map | |
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Further Exploration | |
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Further Reading | |
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Postscript: Chaos | |
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Chaos and Randomness | |
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Randomness and Incomputability | |
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Incomputability and Chaos | |
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Further Reading | |
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Complex Systems | |
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Cellular Automata | |
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One-Dimensional CA | |
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Wolfram's CA Classification | |
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Langton's Lambda Parameter | |
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Conway's Game of Life | |
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Natural CA-like Phenomena | |
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Further Exploration | |
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Further Reading | |
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Autonomous Agents and Self-Organization | |
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Termites | |
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Virtual Ants | |
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Flocks, Herds, and Schools | |
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Unifying Themes | |
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Further Exploration | |
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Further Reading | |
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Competition and Cooperation | |
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Game Theory and Zero-Sum Games | |
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Nonzero-Sum Games and Dilemmas | |
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Iterated Prisoner's Dilemma | |
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Stable Strategies and Other Considerations | |
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Ecological and Spatial Worlds | |
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Final Thoughts | |
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Further Exploration | |
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Further Reading | |
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Natural and Analog Computation | |
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Artificial Neural Networks | |
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Associative Memory and Hebbian Learning | |
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Recalling Letters | |
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Hopfield Networks and Cost Optimization | |
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Unifying Themes | |
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Further Exploration | |
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Further Reading | |
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Postscript: Complex Systems | |
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Phase Transitions in Networks | |
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Phase Transitions in Computation | |
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Phase Transitions and Criticality | |
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Further Reading | |
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Adaptation | |
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Genetics and Evolution | |
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Biological Adaptation | |
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Heredity as Motivation for Simulated Evolution | |
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Details of a Genetic Algorithm | |
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A Sampling of GA Encodings | |
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Schemata and Implicit Parallelism | |
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Other Evolutionary Inspirations | |
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Unifying Themes | |
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Further Exploration | |
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Further Reading | |
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Classifier Systems | |
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Feedback and Control | |
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Production, Expert, and Classifier Systems | |
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The Zeroth Level Classifier System | |
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Experiments with ZCS | |
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Further Exploration | |
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Further Reading | |
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Neural Networks and Learning | |
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Pattern Classification and the Perceptron | |
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Linear Inseparability | |
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Multilayer Perceptrons | |
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Backpropagation | |
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Function Approximation | |
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Internal Representations | |
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Other Applications | |
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Unifying Themes | |
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Further Exploration | |
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Further Reading | |
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Postscript: Adaptation | |
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Models and Search Methods | |
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Search Methods and Environments | |
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Environments and Models | |
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Adaptation and Computation | |
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Further Reading | |
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Epilogue | |
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Duality and Dichotomy | |
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Web of Connections | |
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Interfaces to Hierarchies | |
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Limitations on Knowledge | |
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Source Code Notes | |
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Glossary | |
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Bibliography | |
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Index | |