The definition of cellular automata requires the lattice to be regular. We consider the different possibilities for one, two, and three dimensions in turn. A one-dimensional realization of our example automaton is shown in Applet 2.1 below. In this case only simple traveling waves are observed. Example automaton in one dimension.
Subsequent lines show the state one step apart.
In two dimensions there are three regular lattices, namely triangular, square, and hexagonal lattices. Spiral wave in the example automaton in two dimensions on a hexagonal lattice. More difficult to represent and visualize, since it must be mapped to square arrays and display pixels. The mapping is described in Section 2.1.3 . In some cases the square lattice has insufficient isotropy.