These cellular automata are derivative of the classic Conway's Game of Life. Each cell is 'alive' or 'dead', and iteratively dies, survives, or is born again depending upon how many living neighbors it has. This implementation extends that concept by assigning each cell one of four colors. If a cell is born (becomes alive), it then inherits the color of one of its alive neighbors. When cells die, they fade away rather than immediately clearing, to give the appearance of continuity.
Conway's Game of Life can be described as a 23/3 rule-set: An alive cell survives if 2 or 3 of its neighbors is alive; A dead cell is born if three of its neighbors are alive. You can explore different rule-sets using the UI below, and restart the simulation by clicking on it.
-- Alec McEachran, November 29, 2015