1.E. Iterated Function Systems

Generating fractals by iterating a collection of transformations is the Iterated Function System (IFS) method, popularized by Barnsley, based on theoretical work by Hutchinson and Dekking. We use a simple example to see how it works.

To illustrate the IFS method, we show how a specific set of IFS rules generates a Sierpinski gasket.
The gasket rules leave the gasket unchanged. The gasket is the only shape (of finite extent) left unchanged by these rules.
Now we consider the general setting for IFS.
Finally, here is a more more mathematical approach to IFS.