Chaos and Fractals

In the fall of 1999 I read Chaos and Fractals by Peitgen, Jürgens, and Saupe. This book introduces the reader to the mathematical field of chaos theory.

At the end of each chapter is an example program, written in BASIC (which was an appropriate choice in 1992 when the book was published). The sample programs are short, each less than one page in size. In order to try these programs, and to understand them better, I translated each one to Java to run in a web browser applet.

Chapter 1 - iteration: Demonstrates graphical iteration.
Chapter 2 - sierpinski: Creates a representation of the Sierpinski gasket, a figure that surfaces again and again in chaos theory.
Chapter 3 - koch: Creates a representation of the Koch curve.
Chapter 4 - staircase: Creates the "Devil's Staircase", which is related to the Cantor set.
Chapter 5 - mrcm: Implements a Multiple Reduction Copy Machine.
Chapter 6 - fern: Implements the Chaos Game for the classic fern fractal figure.
Chapter 7 - lsystems: Implements an L-system.
Chapter 8 - automata: Implements a cellular automaton.
Chapter 9 - brownian: Creates a "Brownian Skyline" using random midpoint displacement.
Chapter 10 - timeseries: Shows the error inherent in computer computations of the quadratic iterator.
Chapter 11 - feigenbaum: Creates the Feigenbaum final state diagram for the quadratic iterator.
Chapter 12 - rossler: Creates the Rössler attractor.
Chapter 13 - julia: Creates a Julia set.
Chapter 14 - mandelbrot: Creates the Mandelbrot set.