Lookup tables cellular automata

Similarly to Karplus-Strong synthesis, the cellular automata lookup table also employs a recirculating wavetable to simulate the behaviour of a vibratory medium. The main difference is that the new sample values of the delay line are computed here by means of cellular automata, rather than by the averaging method. 

Cellular automata are computer modelling techniques widely used to model systems in which space and time are discrete and quantities take on a finite set of discrete values (Wolfram, 1986). Physical systems containing many discrete elements with local interaction can be modelled using cellular automata. In principle, any physical system described by differential equations may be modelled as cellular automata. 

Cellular automata are implemented as regular arrays of variables called cells. Each cell may assume values from a finite set of integers. Each value is normally associated with a colour. 

An example set of rules for the functioning of such types of automata can be defined as follows  

The synthesis method works by considering the array of cells of the one-dimensional cellular automaton as a lookup table each cell of the array corresponds to a sample. The states of every cell are updated at the rate of the cellular automaton clock and these values are then heard by piping the array to the digital-to-analog converter (DAC). 

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The LASy program for Macintosh on the CD-ROM was especially designed for experimentation with the cellular automata lookup table (see also Chapter 8). 

LASy (Linear Automata Synthesis) is a program made specifically for cellular automata lookup table synthesis. It was designed by Jacques Chareyron (1990), at the University of Milan s Laboratorio di Informatica Musicale (LIM), Italy. LASy runs on Macintosh computers and it is part of a pool of programs developed at LIM, which together form a larger integrated computer music workbench called Intelligent Music Workstation, or IMW. 

The cellular automata lookup table synthesis technique is discussed in Chapter 4. LASy basically works by applpng a cellular automaton to a lookup table containing an initial waveform. At each playback cycle of the lookup table, the cellular automaton algorithm processes the waveform. The intention is to let the samples of the lookup table be in perpetual mutation, but according to a sort of genetic code. ... 

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