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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 )
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.
- Introductory Examples
- Iterations of real numbers : 1D
- Iterations of complex numbers :2D
- Rational maps
- Iterations of Chebyshev polynomials
- Complex quadratic polynomials
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
- Parts of parameter plane
- Exterior of Mandelbrot set
- Mandelbrot set
- Transformations of parameter plane
- The Buddhabrot.
- exponential families
- trigonometric families
- The Newton-Raphson fractal
- Rational maps
- Quaternion Fractals : 3D
- Iterated function systems
- Nonlinear IFS
- Flame fractals
- Links to other fractal learning resources on the web