“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 )
Here you can find algorithms and examples of source code for drawing fractals and some techiques related with it like :
- making images
- numerical and symbolic computations
Multiplatform, open source and free tools are suggested.
Make a good description of programs/algorithms :
- both formal ( strict definition ) and informal description
- code in various programming languages.
The 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, or prcedures which can be used in other programs.
- 1 Introduction
- 2 Programming
- 3 Mathematics
- 4 Fractals made by the iterations
- 4.1 Iterations of real numbers : 1D
- 4.2 Iterations of complex numbers :2D
- 4.3 Quaternion Fractals : 3D
- 5 Other fractals
- 6 Links to other fractal learning resources on the web
- 7 Fractal programs
“It can be argued that the mathematics behind these images is even prettier than the pictures themselves.” Robert L. Devaney
Fractals made by the iterationsEdit
Iterations of complex numbers :2DEdit
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
- Local dynamics near rationally indifferent fixed point/cycle ( parabolic ). Leau-Fatou flower theorem
- Local dynamics near irrationally indifferent fixed point/cycle ( elliptic ) - Siegel disc
- Parameter plane and Mandelbrot set
- Topological model of Mandelbrot set : Lavaurs algorithm and lamination of parameter plane
- Transformations of parameter plane
- Parts of parameter plane