Also from The New Scientist, a report of studies finding fractal patterns, or at least self-similar patterns, underlying abstract art:

A TECHNIQUE designed to detect art forgeries using the maths of fractals may also help pinpoint why we instinctively like some abstract paintings more than others - even if we can't put our finger on why.

The abstract expressionist artist Jackson Pollock famously dripped paint onto large canvasses on the floor, manipulating it into abstract swirls using sticks or trowels. In 1999, an Australian group found that these swirls contained well-defined fractals - patterns that show self-similarity, that is, they are repeated at different magnifications (New Scientist, 5 June 1999, p 11).

The essence of pattern recognition, or self-simularity, as a primary characteristic of appealing art -- whether painting or music -- is not really a revelation.

Even while the charges that modern 20th century music was nothing but random chaos were relatively disproved by an "experiment" by the BBC (I believe), where "real" pieces of modern music were judged by an audience against a truly intentionally random, improvised piece of percussion music -- even with a made up backstory and an imaginary composer, etc. The audience did not like the random piece -- and instead prefered the other works, which, if I recall correctly, were of your garden-variety Darmstadt-type composers. Of course, underlying the seemingly abstract and chaotic work of the modernist school was a highly principaled and disciplined system of non-tonal relationships.

Fractals found the math for many naturally occuring relationships. Leaves, the coastline. Even Webern.