The Chaos Cookbook

The Chaos Cookbook

A Practical Programming Guide

1st Edition - January 13, 1992

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  • Author: Joe Pritchard
  • eBook ISBN: 9781483104201

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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


    The Computer



    Processing Power

    Disc Drives


    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


    Graphical Solution

    A Predator-Prey Model

    Nomenclature of Phase Diagrams

    The Runge-Kutta Method

    Dependence on Starting Conditions


    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


    Turtle Graphics

    Fractal Brownian Motion

    Cantor Set


    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


    Interesting Areas

    Color Selection and Aesthetics

    Time-Saving Steps

    Calculation Types

    Different Starting z Values


    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


    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



    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


    Pattern Design

    BBC BASIC Listings

    Turbo Pascal Listings

    11 Practical Chaos

    The Stock Market


    The Dripping Tap

    A Chaotic Pendulum

    A Driven Pendulum

    Electronic Chaos

    Driven LCR Network

    Plotting Phase Portraits with an Oscilloscope

    Driven Oscillator

    Analogue Computers




    Other Reading



Product details

  • No. of pages: 376
  • Language: English
  • Copyright: © Butterworth-Heinemann 1992
  • Published: January 13, 1992
  • Imprint: Butterworth-Heinemann
  • eBook ISBN: 9781483104201

About the Author

Joe Pritchard

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