IfsCompose v0.6 - Interactively create IFS fractals

By Owen Taylor <otaylor@gtk.org>

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.

What's new in 0.6

The principle change in 0.6 is a major redesign of the design area.

Instead of having different operations bound to different mouse buttons, the current operation can be selected by button, pop-up menu, or keyboard.
Drawing is now done to an offscreen pixmap to reduce flashing.
The distortion operation has been replaced by a more intuitive stretching operation.
Multilevel undo/restore has been added.
When operations are done on all transformations at once, they now affect the fractal as a whole in a predictable manner. (i.e., "Move" on the whole fractal, simply moves the fractal.)
There is now a concept of "Center" - a point in the middle of the fractal used for display operations.

IFS Fractals

You may be familiar with IFS's from the screen hack 'Flame'. They are also the basis of fractal image compression.

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):

M. Barnsley, Fractals Everywhere, Academic Press Inc., 1988.
M. Barnsley and L. Hurd, Fractal Image Compression, Jones and Bartlett.

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.

Gallery

Here are a few examples of the wide variety of images it's possible to create with IfsCompose. Also, take at look at these really impressive images created by Spencer Kimball using IfsCompose. They clearly show who has actual artistic talent... If you manage to create cool pictures with IfsCompose, I'd be interested to hear about it.

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.