4. Cellular Automata and Fractal Evolution

Cellular Automaton State Space

In general, we assume the state space is of infinite extent.

Any computer simulation must be finite, so an infinite state space cannot be faithfully represented.

Yet simply using a finite array (say cell 1 through cell K for a one-dimensional automaton) is not sufficient, because cells 1 and K, the boundary cells, are different from the other cells.

Cell 1 has a right neighbor (cell 2), but no left neighbor.

Similarly, cell K has a left neighbor but no right neighbor.

So this array is not homogeneous: not all cells have the same neighborhoods.

The simplest way of dealing with this problem is by wraparound.

This has the effect of making the one-dimensional state space into a circle.

For two-dimensional CA, there are two possibilities, one for each neighborhood type.

von Neumann nbhd wraparound	Moore nbhd wraparound

Return to State space.