Fractals

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
  • equations
  • images ( if it is possible put comment into image: EXIF, ... )
  • pseudocode
  • 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.

Contents

IntroductionEdit

ProgrammingEdit

MathematicsEdit

       “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 real numbers : 1DEdit

Iterations of complex numbers :2DEdit

Rational mapsEdit

PolynomialsEdit
Chebyshev polynomialsEdit
Complex quadratic polynomialsEdit

The BuddhabrotEdit

exponential familiesEdit

trigonometric familiesEdit

The Newton-Raphson fractalEdit

Quaternion Fractals : 3DEdit

Other fractalsEdit

Links to other fractal learning resources on the webEdit

Fractal programsEdit

Wikibook Development Stages
Sparse text 0% Developing text 25% Maturing text 50% Developed text 75% Comprehensive text 100%