# A Strategy for Exploring k=2, r=2 Cellular Automata

A Strategy for Exploring k=2, r=2 Cellular Automata

The 256 elementary cellular automata (ECA) rules can all be found somewhere among the four billion rules of the , cellular automata (CA). To find this correspondence, associate each three-bit neighborhood of the ECA with the four specific five-bit neighborhoods of the CA that have the same three middle bits as the ECA. The resulting pattern is determined solely by the inner three bits, exactly like an rule. Essentially, the status of the outermost bits does not matter. But now, what about slight perturbations of this mapping? Will there be similarly shaped CA patterns or radically different patterns?

r=1

k=2

r=2

r=2

r=1