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).
Cellular automata provide a simple model to aid the understanding of excitable media. Each cell of the automaton is made to represent some section of the medium (for example, a patch of trees in a forest, or stress in 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 an excitable medium the general function is as follows:
This function can be refined according to the particular medium. For example, the effect of wind can be added to the model of the forest fire.
It is most common for a one-dimensional medium to form a closed circuit, i.e. a ring. For example, the Mexican wave can be modelled as a ring going around the stadium. If the wave moves in one direction it will eventually return to where it started. If, upon a wave's return to the origin, the original spot has gone through its refractory period, then the wave will propagate along the ring again (and will do so indefinitely). If, however, the origin is still refractory upon the wave's return, the wave will be stopped.
In the Mexican wave, for example, if for some reason, the originators of the wave are still standing upon its return it will not continue. If the originators have sat back down then the wave can, in theory, continue.
Several forms of waves can be observed in a two-dimensional medium.
A spreading wave will originate at a single point in the medium and spread outwards. For example a forest fire could start from a lightning strike at the centre of a forest and spread outwards.
Spiral waves constitute one of the mechanisms of fibrillation when they organize in long-lasting reentrant activities named rotors.