# Iterated Function Systems

*Iterated Function System* (IFS) is a collection of contracting operators that act on subsets of vector spaces. And, as such, they have a fixed point which also a subset of the underlying space. The fixed points of the IFS can be obtain by iterative processes with a random selection of operators from the IFS and can, therefore, be defined algorithmically. Very complex sets may, therefore, be defined with very few parameters (that specify the operators in the IFS.)

The applet below is a tool for forming IFSs with affine transforms. There are several built-in examples that could be modified and the new system can also be defined.

What if applet does not run? |

### About Fractals

- Dot Patterns, Pascal Triangle and Lucas Theorem
- Sierpinski Gasket Via Chaos Game
- The Chaos Game: Address Space vs IFS
- Sierpinski Gasket By Common Trema Removal
- Sierpinski Gasket By Trema Removal
- Sierpinski's Gasket and Dihedral Symmetry
- Iterated Function Systems
- Variations on the Theme of (Triangular) Tremas
- Variations on the Theme of (Rectangular) Tremas
- Sierpinski Gasket and Tower of Hanoi
- Fractal Curves and Dimension
- Color Cycling on the Mandelbrot Set
- Iterations and the Mandelbrot Set
- Mandelbrot and Julia sets
- Emergence of Chaos
- Logistic Model
- Weird curves bound normal areas
- Exercise with Square Spiral

|Activities| |Contact| |Front page| |Contents| |Geometry|

Copyright © 1996-2018 Alexander Bogomolny

67254765