Frankly, I don't understand this replicator's behavior very well. It does not follow the typical parity-rule replicator pattern. Instead, each shuttle above, if sufficiently far from everything else, repeats its shape in 102 generations, flipped 180 degrees, after laying a pair of "eggs" (period 4 oscillators). But, if an egg is already present, it produces a collection of sparks, which in the presence of the symmetrically placed shuttle end up hatching another replicator after 96 generations. So, the first few generations at which a copy of the replicator reappears are 102, 204, 300 (the first hatched egg), 306, 402, 504, 606, 702, and 708. There is no replicator e.g. at generation 408 because the replicator that should form then crashes with another formed by the generation-306 replicator. Somehow, despite all this asynchrony, the replication of shuttles and eggs always continues with the usual sawtooth growth pattern instead of degenerating into chaos.
Rule B36/S245 is also interesting because, like Life, it has many small spaceships, including a 3x3 period-7 diagonal glider, and a 4c/23 spaceship I found based on a combination of a form of the shuttle with two p4 oscillators.
As Niemiec discovered, replicator-based oscillators can be used to form a glider gun.
Later, Hickerson, investigating other ways of combining pairs of shuttles to make replicators, found that they could instead be used to make puffers, moving 28 steps every 600 or 1200 generations:
Finally, these puffers can be tamed, to produce spaceships which move at speed 14c/300
and 28c/1200
Replicators -- Cellular Automata -- D. Eppstein -- UCI Inf. & Comp. Sci.