How does fractal geometry apply to music and art?
A piece of music is an organized “whole” that obeys diverse structures. Many have long been identified by musicians, investigated very explicitly and taught to students. For example, scales were known to musicians long before they were understood by science. However, one structure was left for teachers to enforce informally. “Wallpaper music” and “musak” can be repetitive, but real music cannot. For example, it is important that the movements of a sonata are distinguished by different speeds — such as fast, slow and fast. Moreover, features other than speed vary within each movement and also within smaller portions of a movement. Besides, the “degrees of variability” on the small, medium and large sections of music must “balance” one another. Curiously, musicians did not know how to express this notion of balance in useful formal fashion. But, once they saw fractal pictures, several prominent musicians immediately commented that balance is a form of self-affinity, one aspect of fracta
