IfsCompose is a plug-in for the GIMP that allows the creation of Iterated Function System fractals by interactive manipulation the component transforms. Although v0.6 is fairly full featured, it is still lacking some essentials. Most importantly, it is not yet possible to save fractals in unrendered form for future modification. The rendering code could also use some more work.
The most recent source code comes with the GIMP and will be compiled and installed be default when you compile the GIMP.
Here is a screen shot of IfsCompose in action.
I've written a small tutorial about using IfsCompose.
For a brief introduction to IFS's see Foley and van Dam, et al,. Computer Graphics, Principles and Practice, 2nd Ed., (Addison Wesley, 1990).
The standard references in the field are Michael Barnsley's books (though I haven't looked at them yet):
Briefly, you take a point and repeatedly apply one of a set of transformations to it, choosing randomly between them, and plot the point at each step. An interesting result (the Collage Theorem) says that if you can find a set of transformations that break up an image into smaller copies of itself, then the resulting fractal exactly reproduces the original image. For example, here is a classic image of a leaf and the same image with the four component transforms colored distinctively.
But the best way to appreciate this may to install this program and try it out. I've extended the basic concept as found in Foley and van Dam to include transformations in color space as well as in real space.
This last one's a bit different. To get a tileable image like this, I had to paste together several copies of the triangular fractal.