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 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]

                     "separate the calculation phase from the colouring phase" Claude Heiland-Allen


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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