This is an incredibly simple screensaver. One of my first for windows. All it does is draw out an IFS with maybe two or three branches for maybe ten or twelve iterations, then switches to the next. Because I wrote it so long ago, and because it was one of my first projects, you have to wait between each set render before you can terminate the screensaver. Don't worry, this delay isn't for very long. For the most part the designs will look like noise, but every once in a while a good one will come out of it all. Naturally, the better ones are those that I made into the screenshots.
Hand in hand with my interest in fractal structure and applying it and observing it in nature, I once put a lot of effort into studying geometric sums of complex numbers. These work hand in hand with such simple IFS systems as this one. I remember once seeking out to chart out the area an IFS would cover based upon its transformation matrices. No luck, but if you know anything about it give me a holler.