This replicator repeats every two generations,
on a one-dimensional 1-unit grid. It works in several rules, the
simplest of which is B36/S124.
B36/S124 also has
several interesting spaceships
including a very small c/2 spaceship formed by
attaching a tail to a single replicator.
Dean Hickerson and I discovered that the small c/6 spaceship can
a row of replicators to form a pseudo-random number generator.
A more complicated pseudo-random number generator can be formed by
interacting replicators with a 2c/4 double-domino puffer (also by Hickerson):
Dean and I analyzed the average speed at which the replicator-domino
boundary moves, by examining the possible results
of a replicator-domino collision:
it may leave no residue, or a single domino,
the next collision with
which can again either leave no trace, or form a block;
hitting a block can again leave either no trace, or form a c/2 spaceship,
which finally must crash into the replicators leaving no trace.
The times between several of these events are exponentially-distributed
random variables depending on the state of the replicator field.
But, amazingly, the end result is that the boundary moves at the same
speed as the simpler spaceship-based generator: c/6!
Finally, arbitrarily high-period oscillators can be formed
by using period-4 oscillators to cap a row of replicators.