In a cellular automaton the individuals are entities which have a finite number of states. These individuals are referred to as cells. We will typically be thinking of states abstractly, with labels . Applications in the natural sciences require assigning meanings to the cells and their states. This representation of an individual is among the simplest imaginable.
Cells occupy positions in space, they sit on a regular lattice.
The meaning of this spatial dimension depends on the application, its importance is to limit the interactions between individuals to a neighborhood. Like space, time is discrete. At each time step individuals change their state according to a rule which determines the new state as a function of the previous states of cells in the neighborhood. The simplest choice is to make all individuals identical, obeying the same rule, and apply that rule in synchrony to all individuals. This choice completes the specification of cellular automata.