Fractals

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

Introduction[edit]

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 disjoin 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.

Contents[edit]

  1. Introduction
    1. Introductory Examples
    2. Computer graphic techniques
      1. 2D
        1. graphic files
        2. plane
        3. color
        4. optimisation
      2. 3D
      3. 4D
    3. Mathematics
      1. Numbers
      2. Numerical analysis of dynamical systems : numerical methods
        1. Newton method
      3. Period
      4. Group theory
        1. Binary adding group
        2. Basilica group
        3. Kleinian group
  2. Iterations of real numbers : 1D
  3. Iterations of complex numbers :2D
    1. Rational maps
      1. Polynomials
        1. Iterations of Chebyshev polynomials
        2. Complex quadratic polynomials
          1. Theory
            1. 0% developed  as of  2010.08.01Definitions
            2. Iterations : forward and backward ( inverse )
          2. 25% developed  as of  2010.08.01Dynamical plane : Julia and Fatou set
            1. Julia set
              1. Cremer Julia sets
            2. Fatou set
              1. Basin of attraction of superattracting fixed point (infinity) : exterior of all Julia sets and interior of some Julia sets
                1. Escape time
                2. 0% developed  as of  2010.08.01 Boettcher coordinate
                3. 0% developed  as of  2010.08.01Orbit portraits and lamination of dynamical plane
              2. Interior of Julia sets:
                1. 0% developed  as of  2010.08.01 Basin of attraction of attracting periodic/fixed point - Koenigs coordinate
                2. 0% developed  as of  2010.08.01 Local dynamics near indifferent fixed point/cycle
                  1. 0% developed  as of  2010.08.01 Local dynamics near rationally indifferent fixed point/cycle ( parabolic ). Leau-Fatou flower theorem
                    1. Fatou_coordinate
                    2. Repelling and attracting directions
                    3. Rays landing on the parabolic fixed point
                  2. 0% developed  as of  2010.08.01 Local dynamics near irrationally indifferent fixed point/cycle ( elliptic ) - Siegel disc
          3. 25% developed  as of  2010.08.01Parameter plane and Mandelbrot set
            1. Topological model of Mandelbrot set : Lavaurs algorithm and lamination of parameter plane
            2. Parts of parameter plane
              1. Exterior of Mandelbrot set
              2. Mandelbrot set
                1. Boundary
                2. Interior
            3. Transformations of parameter plane
            4. Algorithms
              1. DEM/M
              2. atom domains
    2. The Buddhabrot.
    3. exponential families
    4. trigonometric families
    5. The Newton-Raphson fractal
  4. Quaternion Fractals : 3D
  5. Iterated function systems
    1. Nonlinear IFS
    2. Flame fractals
  6. Misc.
    1. Real-world fractals
    2. Lyapunov fractal
    3. L-Systems
    4. Midpoint displacement algorithm
    5. Diamond-square algorithm
    6. a limit set of a Kleinian group
      1. 25% developed  as of  2010.08.01 Apollonian fractals
    7. 0% developed  as of  2010.08.01Fractal mountains
  7. Links to other fractal learning resources on the web
    1. Programs
      1. mightymandel by Claude Heiland-Allen
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