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. Cell excitability is the change in membrane potential that is necessary for cellular responses in various tissues. The resting potential forms the basis of cell excitability and these processes are fundamental for the generation of graded and action potentials. Normal and 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).

Modelling excitable media

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

With 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:

thumb|right|220px|Traveling waves in a model of an excitable medium (White – Quiescent, Green – Excited, Yellow – Refractory)

  • Quiescent or excitable – the cell is unexcited, but can be excited. In the forest fire example, this corresponds to the trees being unburnt.
  • Excited – the cell is excited. The trees are on fire.
  • Refractory – the cell has recently been excited and is temporarily not excitable. This corresponds to a patch of land where the trees have burnt and the vegetation has yet to regrow.

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