# Fractals

What I cannot create, I do not understand.”
— Richard P. Feynman

## Introduction

Here you can find algorithms and examples of source code for drawing fractals.

Multiplatform, open source and free tools are suggested.

Make a good description of programa/algorithms. Program is as good as it's documentation.

Try to disjoin computing parameters from creating images ( in other words : "separate the calculation phase from the colouring phase" Claude Heiland-Allen) 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
3. Mathematics
2. Iterations of real numbers : 1D
3. Iterations of complex numbers :2D
1. Rational maps
1. Polynomials
1. Iterations of Chebyshev polynomials
1. Theory
2. Dynamical plane : Julia and Fatou set
1. Julia set
2. Fatou set
1. Basin of attraction of superattracting fixed point (infinity) : exterior of all Julia sets and interior of some Julia sets
2. Interior of Julia sets:
3. Parameter plane and Mandelbrot set
1. Topological model of Mandelbrot set : Lavaurs algorithm and lamination of parameter plane
2. Parts of parameter plane
1. Exterior of Mandelbrot set
2. Mandelbrot set
1. Boundary
2. Interior
3. Transformations of parameter plane
4. Algorithms
2. The Buddhabrot.
3. exponential families
4. trigonometric families
5. The Newton-Raphson fractal
4. Quaternion Fractals : 3D
5. Iterated function systems
1. Nonlinear IFS
2. Flame fractals
6. Misc.
1. Real-world fractals
2. Lyapunov fractal
3. L-Systems
4. Midpoint displacement algorithm
5. Diamond-square algorithm
6. a limit set of a Kleinian group
7. Fractal mountains
7. Links to other fractal learning resources on the web
Wikibook Development Stages
Sparse text Developing text Maturing text Developed text Comprehensive text