Fractals
From Wikibooks, open books for an open world
|
|
|
|
|
A reader requests that this book be expanded to include more material. You can help by adding new material (learn how) or ask for assistance in the reading room. |
|
|
A reader requests that the formatting and layout of this book be improved. Good formatting makes a book easier to read and more interesting for readers. See Editing Wikitext for ideas, and WB:FB for examples of good books. Please continue to edit this book and improve formatting, even after this message has been removed. See the discussion page for current progress. |
[edit] Introduction
Here you can find algorithms and examples of source code for drawing fractals. Multiplatform, open source and free tools are suggested. Try to disjoin 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.
[edit] Contents
- Introduction
- Introductory Examples
- Computer graphic techniques
- Mathematics
- Real-world fractals
- Lyapunov fractal
- Iterations of real numbers : 1D
- Iterations in the complex plane :2D
- Iterations of complex quadratic polynomials
- Theory
- Dynamical plane : Julia and Fatou set
- Julia set
- Fatou set
- Basin of attraction of superattracting fixed point (infinity) - exterior of Julia set
- Basin of attraction of attracting peroiodic/fixed point - Koenigs coordinate
- Local dynamics near indifferent fixed point/cycle
- Parameter plane and Mandelbrot set
- Other rational maps
- Multibrot sets ( monic polynomials )
- The Buddhabrot.
- Iterations of Chebyshev polynomials
- exponential families
- trigonometric families
- The Newton-Raphson fractal
- Iterations of complex quadratic polynomials
- Quaternion Fractals : 3D
- Iterated function systems
- Nonlinear IFS
- Flame fractals
- Misc.
- Applications
- Fractal mountains
- Links to other fractal learning resources on the web