Cellular automata transition rules

Some or all of the vertices in each fragment may be representative of a water molecule. The trace of each fragment may be mapped onto a two-dimensional grid (Figure 3.1c). This trace is equated with the mapping of a cellular automaton von Neumann neighborhood. The cellular automata transition rules operate randomly and asynchronously on the central cell, i, in each von... 

The evolution of a one-dimensional, two-state cellular automaton. The starting state is at the bottom of the figure and successive generations are drawn one above the other. The transition rules are given in the text. 

Many important natural processes ranging from nuclear decay to uni-molecular chemical reactions are first order, or can be approximated as first order, which means that these processes depend only on the concentration to the first power of the transforming species itself. A cellular automaton model for such a system takes on an especially simple form, since rules for the movements of the ingredients are unnecessary and only transition rules for the interconverting species need to be specified. We have recently described such a general cellular automaton model for first-order kinetics and tested its ability to simulate a number of classic first-order phenomena.70... 

LASy instruments are defined in terms of an initial waveform, a rule for the cellular automaton (referred to as the transition rule) and envelopes for amplitude and pitch. The system provides tools for the individual specification of these components so that the user can build their own library of waveforms, rules and envelopes (Figure 8.16). Instruments are either created by combining components selected from these libraries or from scratch on a window, where the user can set up all these parameters at once (Figure 8.17). 

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