As a new technique of computer-assisted composition, measures of attractors of iterated functions systems codes (Barnsley 1989) can be interpreted as musical scores. The technique is called here music. In some important respects, it appears to be more general and more powerful than previous methods for generating musical scores from fractals, such as Koch curves (Dodge and Bahn 1986), 1/If distributions (Voss and Clarke 1978; Bolognese 1983; Dodge 1988), and nonlinear dynamical systems of the general type z # z2 + c. (Pressing 1988) Unlike these earlier methods, iterated functions systems can produce either connected or disconnected fractals, self-similar or non-self-similar fractals, and fractals which appear to contain nonfractal elements. There is theoretical and experimental reason, discussed below, to believe that IFS music can produce, in principle, any arbitrary score specifying pitch and time. The technique brings computer-assisted composition several steps towards what increasingly appears to be a fundamental goal-a universal compositional algorithm with a coherent parametric map. I have written a small-scale IFS music program, IFSMUSIC, in GFA BASIC version 2.0 for the Atari 520ST computer. The program generates standard MIDI file sequences to be used either as selfcontained compositions or as raw material for manipulation and combination with commercial sequencers. This article introduces the mathematics underlying iterated functions systems, outlines the algorithm for approximating the measure of an IFS attractor and interpreting the measure as music, illustrates some basic geometric techniques for generating and manipulating scores, and concludes with a brief discussion of coherent parametric maps of compositionally universal algorithms. For proofs of the theorems used here about iterated functions systems, see (Barnsley 1989). Mathematics of Iterated Functions Systems