The basics of cellular automata

CA are mathematical models of dynamic systems in which space and time are discrete and quantities take on a finite set of discrete values. CA are often represented as a regular array with a discrete variable at each site, referred to as a cell. The state of the CA is specified by the values of the variables at each cell. It evolves in synchronisation with the tick of an imaginary clock, according to an algorithm, which determines the value of a cell based upon the value of its neighbourhood [11, 6, 12]. This algorithm is called global transition function, or simply F. As implemented on a computer, the cells are represented as a grid of tiny rectangles, whose states are indicated by different colours.

CA were originally introduced in the 1960's by John von Neumann [13] as a model of biological self-reproduction. He wanted to know if it is possible for a machine to reproduce, that is, to automatically construct a copy of itself. His model consisted of a two dimensional grid of cells, each of which is in one of a number of states; each state represented the components of the self-reproducing machine. Controlled completely by the global transition function designed by von Neumann, the machine (a pattern of cells in the grid) would extend an arm into a virgin portion of the universe (that is, the grid), then slowly scan it back and forth, creating a copy of itself.

A wide variety of CA and global transition functions have been invented and adapted for many modelling purposes. CA have also attracted the interest of musicians, because of their organisational principles. Various composers and researchers have used CA to aid the control of both higher level musical structures (musical form) and lower level sound structures (that is, the spectrum of a sound event) ([14, 15, 16, 17, 18, 19, 20], to cite but a few). Chaosynth uses CA to control the low-level structure of sounds.


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Laboratório de Música Eletroacústica de Santa Maria
Brasil