Fractal Explorer
GUI-based program for exploring and studying the most common form of fractals, chaotic systems and fractional dimension systems. An overview of the features with a small introductory text is available at
http://ltcmail.ethz.ch/cavin/fractals.html
The usage is straightforward. Type "fractal_explorer", and the main window will be opened and the Mandelbrot Set will be drawn. All features are available via menus and buttons. Information is given on the bottom-left corner of the figure, while tips and information will appear on the left side of the figure when user input is required/possible. For most functions, dialogs will allow introducing user-defined parameters or equations for the calculation. Most dialog contains a button labeled "Cool Params" or "Examples" - this will propose a set of parameters leading to a chaotic behavior (as it is sometimes difficult to find a good parameter set); when only one typical set of parameter is customarily used, it will be given by default the first time the function is called.
The features include:
- Logistic Equation [1]
- Real 2D Attractors:
- Henon Attractor [1]
- Pickover System [1]
- Arbitrary Quadratic Map [1]
- Real 3D Attractors:
- Lorenz Attractor [2]
- Roessler Attractor [2]
- Limited Quadratic Map [2]
- Complex Maps:
- Mandelbrot Set [1,5]
- Julia Sets [1,3,5]
- Arbitrary Polynomial Newton-Raphson
Attraction Basins [1,5]
- Barnsley's Tree [1,5]
- Arbitrary Mandelbrot and Julia-based
Sets [1,5]
- Quaternions:
- Mandelbrot and Julia Sets [2]
- String Systems:
- Lindemayer Systems Single Rule
- Lindenmayer Systems Multiple-Rules
- Plant-like systems:
- Barbsley's Fern [4,6]
- Fractal Trees
- 3D Systems
- 3D-Multiple-Rules Lindenmayer
Systems [2]
- Menger Sponge [2,4]
- FOlded Plans:
- Mesh grids [2]
- Fractals Clouds
- Fractal Landscapes [2]
Notes:
[1] Interactive Zooming
[2] Interactive 3-D View
[3] Julia explorer with on-the-fly previews
[4] Limited to built-in parameters
[5] Include the function Make-It-3D?
[6] Equations taken from Brian Mearns's "Fractal Fern"
For more information, see http://ltcmail.ethz.ch/cavin/fractals.html#SOFT |