It would be really interesting to try to make a waveform that is fractal in nature, and actually sounds interesting and musical at whatever frequency you play it at. As you speed it up, some frequencies will go so high they become inaudible and new frequencies move into the audible range at the low end. In normal music, the pitches, effects, tempos and structures all happen at different timescales but in fractal music they would all interact with each other in interesting ways.
Re: Fractal waveform ... https://www.reenigne.org/blog/fractal-waveform/
http://en.wikipedia.org/wiki/Shepard_tone ?