Replicators: B01367/S012

B01367/S012 has an 11c/22 replicator:

B01367/S012 11c/22 replicator

It also has a larger 10c/20 replicator:

B01367/S012 10c/20 replicator

This pattern, based on the smaller replicator, is a rake, moving in one direction at 11c/22 and, every 22 steps, spitting out a small c/2 glider moving in the opposite direction.

B01367/S012 11c/22 backwards rake

A different tail turns the 11c/22 replicator into a more conventional spaceship.

B01367/S012 11c/22 spaceship

Finite oscillators with periods that are multiples of 22 can be made from the replicator by blocking it by small p2's. The following example repeats with period 44.

B01367/S012 p44 oscillator

Combinations of oscillators can be used to make glider guns; for instance this p44 gun produces 11c/22 spaceships. By adjusting the lengths of the oscillators, higher multiple-of-22 periods can also be achieved. It seems likely that guns for simpler gliders (such as the 3x2 or 4x2 c/2's) can be constructed similarly.

B01367/S012 p44 11c/22 gun

A simpler pattern can be used for higher period 11c/22 spaceship guns. Here, the period is 88.

p88 11c/22 gun

Another interesting replicator-based pattern is the following breeder, which moves at 12c/24, at each repetition leaving behind a replicator at right angles to its path. As the pattern evolves the system of replicators behind the breeder forms a two-dimensional Sierpinski triangle fractal pattern.

B01367/S012 12c/24 replicator breeder

The breeder produces O(n1.585) live cells after n generations.

With random initial conditions, this rule eventually develops into a chaotic pattern in which small patches of dead cells are filled with live oscillators or vice versa. Therefore, it seems likely that most patterns eventually lead to a quadratic growth in the number of live cells. However, an explicit quadratic growth pattern remains unknown.

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