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

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

Copyright © Gary William Flake, 1998-2002. All Rights Reserved. Last modified: 30 Nov 2002