Fractal Sound

The concept of fractals (mathematical structures that sometimes pop up in nature that are self-similar, which is to say if you look at them on any scale they will tend to roughly look the same, often constructed by taking a pattern, replacing each element with the original pattern, then replacing the tiny elements of those smaller patterns with the whole pattern, etc etc etc) has occasionally been applied to music but almost always through generating non-random sequences of notes or attempting to play the pictures fractals generate through various sonification techniques.

However, sound is just periodic variations in pressure. Music is organized sound, or to state it with consistent terminology, patterned variations of periodic variations in pressure. Timbre can also be said to be periodic variations the pitch of a sound (but at audio rates if you want to generate all possible timbres, otherwise known as FM synthesis), with the pitch of a sound being the rate at which it's varying.

So, it should be possible to create fractal Music, which is not only self-similar in it's structure of notes, but down to the timbre from note to note. By using self-similar patterns across all scales of time the waveforms will resemble the phrases will resemble the entirety of the piece. Variation could be made by varying the rules. You could also apply a different kind of rule (like variations in pressure or harmonic content rather than pitch).

Given a certain kind of rule or a rule with significant complexity the self-similarity could be obscured a bit, making it seem more organic or human. Another possibility to add richness would be to add chaos. Human input could alter the rules or jar the results in unpredictable ways. Sensor based input or semi-random systems could fight with the fractal patterns in an endless and varying battle between order and chaos, noise and music.

Whether the aesthetics are better when the system tends towards regularity, unity or chaos and where the balance is remains to be heard.

Also what all this would sound like remains unknown, at least until my programing work progresses more.