The Chaos Cookbook - 1st Edition - ISBN: 9780750603041, 9781483104201

The Chaos Cookbook

1st Edition

A Practical Programming Guide

Authors: Joe Pritchard
eBook ISBN: 9781483104201
Imprint: Butterworth-Heinemann
Published Date: 13th January 1992
Page Count: 376
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Description

The Chaos Cookbook: A Practical Programming Guide discusses the use of chaos in computer programming. The book is comprised of 11 chapters that tackle various topics relevant to chaos and programming. Chapter 1 reviews the concept of chaos, and Chapter 2 discusses the iterative functions. Chapters 3 and 4 cover differential and Lorenz equations. Chapter 5 talks about strange attractors, while Chapter 6 deals with the fractal link. The book also discusses the Mandelbrot set, and then covers the Julia sets. The other fractal systems and the cellular automata are also explained. The last chapter discusses practical chaos. The book will be of great use to professionals, students, and hobbyist programmers who have an interest with the chaos systems.

Table of Contents


Preface

Introduction

The Computer

Graphics

Memory

Processing Power

Disc Drives

Interfaces

Programming Languages

Numerical Resolution

Numerical Accuracy

Numerical Overflow

Types of Computer

Processing of Screen Images

Saving Video Memory

Getting a Hard Copy

Data Export

Language Versions Used in this Book

1 What is Chaos

2 Iterative Functions

The Square Root Function

The Square Function

The Function 2x(x - 1)

The Logistic Equation

Other Functions

Plotting the Attractor

Iterating Two-dimensional Functions

BBC BASIC Listings

Turbo Pascal Listings

3 Differential Equations

Analysis

Graphical Solution

A Predator-Prey Model

Nomenclature of Phase Diagrams

The Runge-Kutta Method

Dependence on Starting Conditions

Stability

Forced Non-linear Oscillators

More Complicated Systems

BBC BASIC Listings

Turbo Pascal Listings

4 The Lorenz Equations

First Investigations

Feedback — The Common Factor

The Butterfly Effect

Further Analysis of the Equations

Phase Portraits of the Lorenz Equations

The strange Attractor

BBC BASIC Listings

Turbo Pascal Listings

5 Strange Attractors

The Hénon Attractor

Fractal Dimensions and Strange Attractors

Other Hénon Attractors

Strange Attractors from Differential Equations

Other Strange Attractors

Strange Attractors from Real Data

How Can Strange Attractors be Found

BBC Basic Listings

Turbo Pascal Listings

6 The Fractal Link

The Koch Curve

Recursion

Turtle Graphics

Fractal Brownian Motion

Cantor Set

Peano

Dragon and C Curves

Sierpinski Carpet

Drawing with the L-Language

Fractals in the Real World

Fluid Flow

Catalysts and Enzymes

BBC Basic Listings

Turbo Pascal Listings

7 The Mandelbrot Set

Complex Numbers

The Mandelbrot Set

Nomenclature

Interesting Areas

Color Selection and Aesthetics

Time-Saving Steps

Calculation Types

Different Starting z Values

Mandelbroids

Three-Dimensional Representations

Periodicity in the Mandelbrot Set

BBC BASIC Listings

Turbo Pascal Listings

8 Julia sets

Trajectories for the Julia Set

Plotting the Julia Set

Iteration Number

The Value of C

Periodicity and Link to the Mandelbrot Set

Newton's Method

Quaternions

Inverted Julia Sets

Some Final Comments

BBC BASIC Listings

Turbo Pascal Listings

9 Other Fractal Systems

Fractal Landscapes

Mid-point Displacement

Fault Line Modeling

Fractal Plants and Trees

Iterated Function Systems

The Collage Theorem

BBC BASIC Listings

Turbo Pascal Listings

10 Cellular Automata

Dimensions in Automata

One-Dimensional Cellular Automata

The Rule Set

Non-totalistic Rule Sets

Mutation

Noise

Thermodynamics, Reversibility and Entropy

Simple Two-dimensional Automata

Selection in Two-Dimensional Systems

Cell Eat Cell

Time Dependent Rules

The Game of Life

Dynamic Structures

Suggestions for Further Experiments

Applications of Cellular Automata

Modeling

Pattern Design

BBC BASIC Listings

Turbo Pascal Listings

11 Practical Chaos

The Stock Market

Weather

The Dripping Tap

A Chaotic Pendulum

A Driven Pendulum

Electronic Chaos

Driven LCR Network

Plotting Phase Portraits with an Oscilloscope

Driven Oscillator

Analogue Computers

Appendix

Bibliography

Periodicals

Other Reading

Software

Index

Details

No. of pages:
376
Language:
English
Copyright:
© Butterworth-Heinemann 1992
Published:
Imprint:
Butterworth-Heinemann
eBook ISBN:
9781483104201

About the Author

Joe Pritchard