I found this replicator on Oct. 27, 2001. It repeats every 4 generations, on a one-dimensional 2-unit grid.
This rule has a few known spaceships. It is unknown whether the replicator can lead to high-period oscillators, spaceships, guns, or other interesting technology.
Replicators -- Cellular Automata -- D. Eppstein -- UCI Inf. & Comp. Sci.