Rule equivalences [for cellular automata]

The table below gives basic equivalences between elementary cellular automaton rules. In each block the second entry is the rule obtained by interchanging black and white, the third entry is the rule obtained by interchanging left and right, and the fourth entry the rule obtained by applying both operations. (The smallest rule number is given in boldface.) For a rule with number n the two operations correspond respectively to computing 1 - Reverse[list] and list[[{1, 5, 3, 7, 2, 6, 4, 8}]] with list=IntegerDigits[n, 2, 8].