# Fractals

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

**"Just keep in mind that what is obvious for you won't be necessarily obvious for the reader."**

- — (cKleinhuis )

## Introduction[edit]

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 programs/algorithms. A program is as good as it's documentation.

Try to separate 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[edit]

- Introduction
- Introductory Examples
- Programming
- Formula parser
**Computer graphic techniques**

**Mathematics**- Numbers
- Numerical methods
- Symbolic methods
- Geometry

- Iterations of
**real numbers : 1D** - Iterations of
**complex numbers :2D**- Rational maps
- Polynomials
- Iterations of Chebyshev polynomials
- Complex quadratic polynomials
- Theory
**Dynamical plane**Julia and Fatou set**Julia set**- Fatou set
- Basin of attraction of superattracting fixed point (infinity) :
**exterior of all Julia sets**and interior of some Julia sets **Interior of Julia sets**:- Basin of attraction of
**attracting**periodic/fixed point - Koenigs coordinate - Local dynamics near indifferent fixed point/cycle

- Basin of attraction of

- Basin of attraction of superattracting fixed point (infinity) :

**Parameter plane**and**Mandelbrot set**- Topological model of Mandelbrot set : Lavaurs algorithm and lamination of parameter plane
- Parts of parameter plane
- Exterior of Mandelbrot set
- Mandelbrot set

- Transformations of parameter plane
- Algorithms

- Polynomials
- The Buddhabrot.
- exponential families
- trigonometric families
- The Newton-Raphson fractal

- Rational maps
**Quaternion Fractals : 3D**- Iterated function systems
- Nonlinear IFS
- Flame fractals

- Misc.
- Real-world fractals
- Lyapunov fractal
- L-Systems
- Midpoint displacement algorithm
- Diamond-square algorithm
- a limit set of a Kleinian group
- Fractal mountains

- Links to other fractal learning resources on the web
- Programs
- fractint
- Spider by Yuval Fisher
- Fragmentarium - GLSL
- Kalles Fraktaler
- Mandel - software for real and complex dynamics by Wolf Jung
- Mandel Machine
- gnofract
- Programs by Claude Heiland-Allen
- Xaos
- Shadertoy - GLSL

- Programs