Charles Wuorinen

In the text accompanying Charles Wuorinen's A Winter's Tale, Peter Paul Nash describes Wuorinen's transformation in the mid 70s to early 80s. While some American composers abandoned dissonance for romanticism, Wourinen's
"transformation was more subtle and fundamental,originating in his discovery of the fractal geometry and chaos theory pioneered during the 1960s by Benoit Mandelbrot..."
Fractal geometry
"could be the most radical way of reconsidering the world since the great modernist and reductive theories of the early 20th century; since it is so anti-reductive, and admits the irregularities, proportionalities, hierarchies and sheer messiness of 'real life.' The implications for music are obvious. Indeed a succession of 'proto-fractal' composers can be traced back into the past: Sibelius, Beethoven, J. S. Bach, and even further back."
Here is the CD jacket for A Winter's Tale.
In his essay "Music and Fractals," Wuorinen describes some of the fractal characteristics of music, including this
"... in traditional western diatonic-tonal music, there is a strong tendency for similar structures to appear on different time-scales. Thus the same harmonic progression may determine the course of a whole movement, of a sizable section of it, or of a single short phrase. Traditional terminology shows, by its indifference to scale, how deeply imbedded self-affine structures in compositions are: "C major" can refer to a single sonority, the key of a phrase, a movement-section, a whole movement, or the key of an entire work. And in post-tonal music similar structures on differing time-scales are certainly present."
Wuorinen continues, describing a method of fractal composition he developed.
"The 'nesting method' typically begins with an ordered set of pitch-classes, whose intervals are chosen not merely for their appropriateness in the design of satisfactory harmony, but also so that, when these same intervals are temporally interrupted, they can conduce to the development of meaningful large-scale structure. The total interval span of the ordered set is flung over the duration of the whole work or movement. The set is defined by a succession of intervals of varying sizes, and these intervals may be used to divide a large span of time into sections whose lengths are directly proportional to the interval-sizes of the original succession. Within each of these large sections, then, a similar process is effected. Usually, three levels of such divisions are sufficient to produce a set of nested self-affine temporal intervals which can then be used to define the structure of the composition, ... .
"It should be clear that what I have sketched above is not really 'composing' in the sense we might historically apply to the familiar figures of the western tradition. It is rather the preparation for the composing, ... . Having made such preparation, then, I have found it possible to compose with a kind of intuitive freedom which still assures macrostructural coherence. Those who try for this coherence without structural underpinnings usually fail."