Replicators: B36/S124

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 c/2 replicator

B36/S124 also has several interesting spaceships including a very small c/2 spaceship formed by attaching a tail to a single replicator.

B36/S124 c/2 spaceship

Dean Hickerson and I discovered that the small c/6 spaceship can interact with a row of replicators to form a pseudo-random number generator.

B36/S124 replicator-c/6 interaction

A more complicated pseudo-random number generator can be formed by interacting replicators with a 2c/4 double-domino puffer (also by Hickerson):

B36/S124 replicator-puffer interaction

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.

B36/S124 p48 oscillator

Replicators -- Cellular Automata -- D. Eppstein -- UCI Inf. & Comp. Sci.