With Javascript enabled you would be able to experiment with color examples of the following parity based cellular automata rules:
Parity: new = (N + E + S + W + current) mod 2
Corner Parity: new = (NW + NE + SW + SE + current) mod 2:
Inner Replicator: new = (NW + N + NE + W + E + SW + S + SE + current) mod 2
Outer Parity Flip: new = (N + E + S + W + past) mod 2
Outer Corner Parity Flip: new = (NW + NE + SW + SE + past) mod 2
Replicator Flip: new = (NW + N + NE + W + E + SW + S + SE + past) mod 2
Outer Parity: new = (N + E + S + W) mod 2
Outer Corner Parity: new = (NW + NE + SW + SE) mod 2
Replicator: new = (NW + N + NE + W + E + SW + S + SE) mod 2
Parity Flip: new = (N + E + S + W + current + past) mod 2
Corner Parity Flip: new = (NW + NE + SW + SE + current + past) mod 2
Inner Replicator Flip: new = (NW + N + NE + W + E + SW + S + SE + current + past) mod 2