Abstract
Cellular automata (CA) are tools for computational modelling widely used to model systems that change some feature with time. They are suitable for modelling dynamic systems in which space and time are discrete, and quantities take on a finite set of discrete values. CA are highly suitable for modelling music: music is fundamentally time-based and it can be thought of as a system in which a finite set of discrete values (e.g. musical notes, rhythms, etc.) evolve in space and time. CA were originally introduced in the 1960s by John von Neumann and Stanislaw Ulam as a model of a self-reproduction machine (Cood 1968). They wanted to know if it would be possible for an abstract machine to reproduce; that is, to automatically construct a copy of itself. Their model consisted of a two-dimensional grid of cells, each cell of which could assume a number of states, representing the components from which they built the selfreproducing machine. Completely controlled by a set of rules, the machine was able to create several copies of itself by reproducing identical patterns of cells at another location on the grid. Since then, CA have been repeatedly reintroduced and applied to a considerable variety of purposes, from biomedical image processing (Preston and Duff 1984) and ecology (Hogeweg 1988) to biology (Ermentrout and Edelstein-Keshet 1993) and sociology (Epstein and Axtell 1996). Many interesting CA algorithms have been developed during the past 40 years. Since CA produce large amounts of patterned data and if we assume that music composition can be thought of as being based on pattern propagation and the formal manipulation of its parameters, it comes as no surprise that composers started to suspect that cellular automata could be related to some sort of music representation in order to generate compositional material. One of the first composers to use CA was Iannis Xenakis, who used them in the mid of the 1980s ‘to create complex temporal evolution of orchestral clusters’ for his piece Horos (Hoffman 2002; p. 122). A number of pioneering experiments
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