Fractals

Introduction

Here you can find algorithms and examples of source code for drawing fractals. Multiplatform, open source and free tools are suggested. Try to disjoin computing parameters from creating images ( it can slow the program but makes it easier to understand the algorithm ). If it is possible make one-file programs.

Contents

1. Introduction
   1. Introductory Examples
   2. Computer graphic techniques
      1. Computer graphic techniques - 2D
         1. graphic files
      2. Computer graphic techniques - 3D
      3. 4D
   3. Mathematics
      1. Newton method
      2. Period detection
      3. Group theory
         1. Binary adding group
2. Real-world fractals
3. Lyapunov fractal
4. Iterations of real numbers : 1D
5. Iterations in the complex plane :2D
   1. Iterations of complex quadratic polynomials
      1. Theory
         1. Definitions
         2. Iterations of complex quadratic polynomials : forward and backward ( inverse )
      2. Dynamical plane : Julia and Fatou set
         1. Julia set
         2. Fatou set
            1. Basin of attraction of superattracting fixed point (infinity) - exterior of Julia set
               1. Escape time
               2. Boettcher coordinate
               3. Orbit portraits and lamination of Julia sets
            2. Basin of attraction of attracting peroiodic/fixed point - Koenigs coordinate
            3. Local dynamics near indifferent fixed point/cycle
               1. Local dynamics near rationally indifferent fixed point/cycle ( parabolic ). Leau-Fatou flower theorem
               2. Local dynamics near irrationally indifferent fixed point/cycle ( elliptic ) - Siegel disc
      3. Parameter plane and Mandelbrot set
         1. Topological model of Mandelbrot set : Lavaurs algorithm
   2. Other rational maps
   3. Multibrot sets ( monic polynomials )
   4. The Buddhabrot.
   5. Iterations of Chebyshev polynomials
   6. exponential families
   7. trigonometric families
   8. The Newton-Raphson fractal
6. Quaternion Fractals : 3D
7. Iterated function systems
   1. Nonlinear IFS
   2. Flame fractals
8. Misc.
   1. L-Systems
   2. Midpoint displacement algorithm
   3. Diamond-square algorithm
   4. Apollonian fractals
9. Applications
   1. Fractal mountains
10. Links to other fractal learning resources on the web