The Chaos Cookbook
A Practical Programming Guide
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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
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
Product details
- No. of pages: 376
- Language: English
- Copyright: © Butterworth-Heinemann 1992
- Published: January 13, 1992
- Imprint: Butterworth-Heinemann
- eBook ISBN: 9781483104201