Critters (cellular automaton)

Critters is a reversible block cellular automaton with similar dynamics to Conway's Game of Life,[1][2] first described by Tommaso Toffoli and Norman Margolus in 1987.

[1][2][3] It has been conjectured, but not proven, that for periodic boundary conditions (so that the entire space of the cellular automaton is finite) initial fields of random cells that are sufficiently smaller than the whole space will lead with high probability to states in which a single glider follows a random walk through a field of oscillating debris.

[5] In Conway's life, collisions of gliders may result in a completely dead state, a stable pattern, or an oscillator, but this is not possible in Critters.

[1] The Critters rule can also support more complex spaceships of varying speeds as well as oscillators with infinitely many different periods.

For instance, the parity of the number of live cells along certain diagonals of the grid is not changed by the update rule, and remains unchanged throughout the evolution of any Critters pattern.

Gliders escape from a central random seed region
The transition rule for Critters. Live cells are shown as green and dead cells as white. Each of the 16 possible 2 × 2 blocks (outlined in blue) is transformed as shown. The rule alternates between using the blocks outlined in blue and the blocks outlined by the dashed red lines.