Excitable medium

An excitable medium is a nonlinear dynamical system which has the capacity to propagate a wave of some description, and which cannot support the passing of another wave until a certain amount of time has passed (known as the refractory time).

A forest is an example of an excitable medium: if a wildfire burns through the forest, no fire can return to a burnt spot until the vegetation has gone through its refractory period and regrown. In chemistry, oscillating reactions are excitable media, for example the Belousov–Zhabotinsky reaction and the Briggs–Rauscher reaction. Pathological activities in the heart and brain can be modelled as excitable media. A group of spectators at a sporting event are an excitable medium, as can be observed in a Mexican wave (so-called from its initial appearance in the 1986 World Cup in Mexico).

Excitable media can be modelled using both partial differential equations and cellular automata.

Cellular automata provide a simple model to aid in the understanding of excitable media. Perhaps the simplest such model is in. See Greenberg-Hastings cellular automaton for this model.

Each cell of the automaton is made to represent some section of the medium being modelled (for example, a patch of trees in a forest, or a segment of heart tissue). Each cell can be in one of the three following states:

As in all cellular automata, the state of a particular cell in the next time step depends on the state of the cells around it—its neighbours—at the current time. In the forest fire example the simple rules given in Greenberg-Hastings cellular automaton might be modified as follows:

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