this is a version of the game of "life". Anyone remember that one? It
was in a Scientific American article many years ago. Used a board
something like a Go board, but with a theoretically infinite number
of intersections but a Go board works for most iterations.
You have black and white stones, put down some initial pattern
then some stones die, some reproduce and the pattern changes
in response to a simple set of rules. Each intersection has 8 surrounds
and depending on the count of black and white stones in those
surrounds, the pieces live or die. Like if there is only one of its color
in the 8 surrounds, it dies of loneliness, if there are two and only two
it reproduces, etc. Each generation produces a new pattern that,
depending on the original configuration, can make a self reproducing
shape that eventually runs off the board. Some shapes sit there
and go back and forth between two configurations, a stalemate
and others dribble into a static state or dies off completely.