Fractals

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TODO

Editor's note
This book is still under development. Please help us

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.

Introduction[edit]

Programming[edit]

Mathematics[edit]

       “It can be argued that the mathematics behind these images is even prettier than the pictures themselves.” Robert L. Devaney

Fractals made by the iterations[edit]

Iterations of real numbers : 1D[edit]

Iterations of complex numbers :2D[edit]

Rational maps[edit]

Polynomials[edit]
Chebyshev polynomials[edit]
Complex quadratic polynomials[edit]

The Buddhabrot[edit]

exponential families[edit]

trigonometric families[edit]

The Newton-Raphson fractal[edit]

Quaternion Fractals : 3D[edit]

Other fractals[edit]


Fractal programs[edit]

Links to other fractal learning resources on the web[edit]

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