Various applications have been written that are designed for composing music algorithmically. They use various techniques including fractals, cellular automata, and genetic algorithms.
Works on Windows (XP and Vista, at least, may work on newer versions). Commercial software with a free trial available.
Windows software released sometime around 1999.
(Dead Link - No longer available, no clue how to contact the original author)
Cellular-automata-based software for Windows created by Phil Thompson. Current status unknown.
Works on Windows 3.1, 2000, XP, and Vista. It is a 16-bit application and will not run on Windows 7 or newer. It can also be used on Linux with Wine and Timidity.
The Music In Numbers - http://reglos.de/musinum/
As far as I'm aware this program does not have a website. You can download version 1.02 HERE. I suspect there are newer versions than 1.02, but I have not seen them. Feel free to Contact Me if you can hook me up with a newer version. It seems to run well enough on Windows Vista.
As far as I'm aware this shareware program also does not have a website. You can download an unregistered copy of version 1.00 HERE. I'm not aware of any way to buy a registered copy of Tangent. It seems to run well enough on Windows Vista.
Please, let us know about any fractal/mathematical/cellular-automata-based music composition software we do not have listed.