I've been tinkering with the Chaoscope program, a fascinating little free program that lets you render "strange attractors" in 3D. These are mathematical constructs, a special subset of fractals.
You can find the program here:Chaoscope
Check it out; it's well worth your time.
I'll post some of my favorite renders here. These are all my work, and are all straight from the Chaoscope renderer. I'll have another thread for postprocessed pieces.