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, 1998-2005. All Rights Reserved.