A note on the recent passing of the mathematician Benoît B. Mandelbrot. Whether directly, via close study, or indirectly, even impressionistically, from a condensed version in the popular science press or from the illustrations in his coffeetable book The Beauty of Fractals, Mandelbrot had an impact on contemporary music. While the heyday of enthusiasm for compositional applications of fractals and other related self-similar and non-linear phenomena was probably back in the 1980's, the resonance has been long and lively. As each piece of information about this stuff came out in the press or from battered photocopies of off-prints, many composers would immediately start to ponder how to turn these things into sounds. How about a Nancarrowish canon with tempos based around the Feigenbaum number? One of the first pieces directly citing Mandelbrot which I can recall was Larry Austin's Canadian Coastlines (1981) and another composer with a lasting relationship to Mandelbrot's ideas was György Ligeti. I believe that Ligeti's approach to these ideas was not formal, down to the details, but many younger composers, particularly those working in computer music, found stricter applications. (The coincidence of the emergent chaos theory and more accessible computing power was not unimportant for scientists and mathematicians, nor was it for musicians.)
Fractals were only one of the ideas that composers in the last generation or so have eagerly grabbed at, if only from readingf over the shoulder's of our friends in the natural sciences. That Scientific American article about generating music from pink and white noise sent many composers productively back to their manuscript paper and their computers. Many of us were enthusiastic for Gregory Bateson's Mind and Nature, others for the ideas of Buckminister Fuller still more for cybernetics, information theory and algorithmic composition. Linguistic theory has had a long resonance with composers. I never found a compositional interest in chaos theory myself, but one of my youthful yet enduring enthusiasms was for another area of dynamical systems, catastrophe theory; René Thom's Structural Stability and Morphogenesis (1972) was an eye opener, and perhaps more importantly, it sent me to the pages of D'arcy Wentworth Thompson's classic On Growth and Form (1917) which had a tremendous effect on my sensibility for the overall shape and continuity of a piece and its relationship to particular events or details in the music. Inasmuch as no calculation I ever use in a piece of music is larger than can fit on an index card, I fall more into the impressionistic than calculating category of science-indebted composers, but however modest my own scientific insights may be, this stuff has registered in my music in an honest, useful, and productive way.