Self-complementary

A (totalistic) rule is said to be self-complementary if it remains unchanged under black/white reversal, i.e. if a pattern composed of live cells in a dead universe behaves the same as an equivalent pattern composed of dead cells in a live universe.

A self-complementary rule's birth conditions completely determine its survival conditions, and vice versa, but no other constraints exist; as such there are 2⁹ = 512 distinct self-complementary totalistic rules.

Examples

The most well-known and well-investigated self-complementary rule is Day & Night (B3678/S34678).