The evolution takes place in discrete time steps. Each cell is characterized by a state taken from a finite set of states. Each cell evolves according to the same rule which depends only on the state of the cell and a finite number of neighboring cells. The neighborhood relation is local and uniform. 1.2 Simple Example Let us first consider a simple example of cellular automata.
Excitable media appear in several different situations.
This sequence appears e.g., in the heart muscle, where a wave of excitation travels through the heart at each heartbeat. Another example is a forest or prairie fire. There are also many chemical systems involving some form of auto-catalysis which exhibit excitable behavior. The most notable among these are the Belousov-Zhabotinsky reaction, and reactions in heterogeneous catalysis. The evolution takes place on a regular lattice, in the first case we use a rectangular lattice.