I have always admired Islamic art, especially because of the geometrical, mathematical basis for its beautiful and intricate patterns. Recently I purchased a Dover clipart book full of copyright-free Islamic designs, and I absolutely love it. Here is a sample:

Personally I am very intrigued by art based on math. To the uninitiated, mathematical art may sound very plain, rigid, boring. However, it is possible to mathematically construct very beautiful and intricate designs. Fractal theory suggests that many objects in the natural world, appearing complex or even chaotic as a whole, are actually built from relatively simple mathematical repetitions (examples would be tree branches, sea shell patterns, snowflakes).

Music is also a prime example of art with a mathematical basis: timing, rhythm, and harmonics are all based on math. (The degree to which two given notes harmonize is related to the alignment/correlation of the “peaks” in their respective sine waves.) It is often alleged that many of the great classical works have strong patterns that can be mathematically derived, and this is perhaps true on a lesser scale for other genres of music.