The Chaos Cookbook

PrefaceIntroduction 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 Book1 What is Chaos2 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 Listings3 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 Listings4 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 Listings5 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 Listings6 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 Listings7 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 Listings8 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 Listings9 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 Listings10 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 Listings11 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 ComputersAppendixBibliography Periodicals Other Reading SoftwareIndex