Open main menu

Wikibooks β

Fractals

TODO

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

What I cannot create, I do not understand.
—Richard P. Feynman


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.

Contents

IntroductionEdit

ProgrammingEdit

"Just keep in mind that what is obvious for you won't be necessarily obvious for the reader."   :— (cKleinhuis )

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
TheoryEdit
AlgorithmsEdit
 Dynamical plane Julia and Fatou setEdit
 Parameter plane and Mandelbrot setEdit

The BuddhabrotEdit

exponential familiesEdit

trigonometric familiesEdit

The Newton-Raphson fractalEdit

Quaternion Fractals : 3DEdit

Other fractalsEdit

softwareEdit

LinksEdit

Wikibook Development Stages
Sparse text   Developing text   Maturing text   Developed text   Comprehensive text