This is the periodic cycle of period 52 of an automata using a Z13 based rule and a 13x13 grid. The rule uses a clockwise multiplication of all of the cells in the nine point rule except the center. The identity is red.
This period 100 automata has a 50x50 grid and uses a Z5 based rule. However, this rule uses only the three cells above and to the right of the center cell. Notice that by changing the rule, you can change the direction in which information propagates through the grid. The identity is white.
This is a periodic cycle of period 124 of a D4 based rule automata with a 64x64 grid. As in the previous example, this rule uses only the three cells above and to the right of the center cell. The non-zero rotations are shades of purple, the reflections are shades of green, and the identity is white.