Iterated Function Systems with GSF
GSF, or Generalized Sierpinski Fractals, is a program created by Professor Dan Ashlock
The Sierpinski Triangle
The Sierpinski triangle is a simple fractal that can be generated with this iterated function system software.
The algorithm for the triangle is:
- Choose three points (the triangle's vertices).
- Create a moving point P.
- Start P on one of the vertices.
- Repeat
- Pick one of the three vertices at random,
- Move P half way to the selected vertex,
- Plot P.
- Until the triangle fills in
This example borrowed with permission from Dr. Ashlock's webpage.
The generalization of this algorithm is:
- Choose your fixed points. In the first example, the points form a square.
- When you have more than three points, you will need to choose which points you want "connected" to which other points. The placement of the points and the connectivity you give to them determines what the output will be.
- Then the moving point creates the fractal. It starts at one of the fixed points and then iteratively moves halfway towards one of the points connected to the starting point.
Example Fractals
