QuasiMusic is a Java applet that generates music, functioning a lot like a player-piano roll, by exploiting the patterns in quasiperiodic tilings of the 2 dimensional plane. The animations show two different instances of the applet in action.
These are tilings that fill the entire infinite plane using different shapes called tiles that are arranged in a certain way with out overlapping each other and without leaving any empty space.
If its possible to take a copy of a tiling and shift it over in some direction by a certain amount relative to the original tiling and have it line up exactly with the original, then that tiling is periodic. This minimum shifting distance needed to make the tiling match itself is called the period.
Whats special about quasiperiodic tilings is that there is no such period. So no matter which direction you shifted the tiling, it would never exactly line up with itself.
Using these quasiperiodic tilings has interesting consequences for the music they generate. Since the pattern never repeats, this implies that the music will never repeat. Although there may be moments which sound similar they can never be exactly the same when considered in a longer time interval.
To understand how the applet creates the music from a given tiling first assign to each type of tile a sound (instrument and pitch). Next, imagine a series of vertical lines passing over the tiling. Then as the whole tiling moves upwards passing a horizontal axis, play a sound each time one type of tiling changes to another type on one of these vertical lines. In the animations, the tiles light up when they trigger a sound, and the series of vertically arranged white dots specify when the tiles change. These white dots are reminiscent of the holes in a player-piano roll.
The applet allows the user to control many different parameters, and their are over 350 different instruments and sounds to choose from literally allowing for endless possibilities. Check it out here.
Also check out a recently released dark ambient album which makes use of QuasiMusic on some tracks by master mathematics expositor John Baez.