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

ISBN-10: 0262062003

ISBN-13: 9780262062008

Edition: 1998

Authors: Gary William Flake

List price: $75.00
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Description:

This work develops in depth the idea that recurrent rules can produce rich and complicated behaviours. The author argues that it is the computational properties of interactions that account for much of what we think of as beautiful and interesting.
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Book details

List price: $75.00
Copyright year: 1998
Publisher: MIT Press
Publication date: 7/10/1998
Binding: Hardcover
Pages: 420
Size: 8.50" wide x 9.50" long x 1.50" tall
Weight: 2.794
Language: English

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
Computation
Number Systems and Infinity
Introduction to Number Properties
Counting Numbers
Rational Numbers
Irrational Numbers
Further Reading
Computability and Incomputability
Godelization
Models of Computation
Lisp and Stutter
Equivalence and Time Complexity
Universal Computation and Decision Problems
Incomputability
Number Sets Revisited
Further Reading
Postscript: Computation
Godel's Incompleteness Result
Incompleteness versus Incomputability
Discrete versus Continuous
Incomputability versus Computability
Further Reading
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
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 Henon 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 Henon Map
Further Exploration
Further Reading
Postscript: Chaos
Chaos and Randomness
Randomness and Incomputability
Incomputability and Chaos
Further Reading
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
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
Bibliography
Index