Sonification is the act of representing data as sound. Any data will do, but data that has a pattern will make better music, and if you don't know whether your data has a pattern or not, sonification may help you find out.

A fractal is "a rough or fragmented geometric shape that can be subdivided in parts, each of which is (at least approximately) a reduced-size copy of the whole", according to Wikipedia. Many musicians have experimented with converting fractal shapes into music. Fractal Vibes has examples and links to more fractal music.
Your chance to hear music from brain waves, gene sequences, and more after the jump.

This piano piece was created by assigning notes to the digits 0 through 9 in the constant known as pi. Pi has no repetitive patterns, so the piece sounds random, but has a mathematical beauty all its own. Hear more examples of turning math into music at Math Sonification and The Sound of Mathematics.
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In the news just last week, scientists at UCLA are working to convert genome-encoded protein sequences into musical notes in order to hear auditory protein patterns. Listen to the conversion of the sequence found in horse hemoglobin.

Paras Kaul of mississippi State University, known as The Brainwave Chick, uses converted brain wave music in her recording. Hear some examples of brain wave conversions here, and a musical composition entitled The Brain on Om here.

Musician Roberto Morales-Manzanares, a student at UC Berkeley, worked with physicists to convert electrons from the sun (solar wind) to music. Listen to a section of Turning Point.

Berkeley has more on the process of sonification, including software you can use to convert data to sound waves.