John Conway’s Game of Life is of the most addictive recreative mathematics I’ve ever met. An initial configuration and a simple set of rules are enough to create an extremely complex world, in which it would be possible to, for instance, calculate the primes.

Each stage, new cells are born and old ones die according to this rules:

  • A living cell with 2 or 3 neighbours stays alive.
  • A living cell with 4 or more neighbours dies (“overpopulation”).
  • A living cell with 0 or 1 neighbours dies (“loneliness”).
  • A dead cell with exactly 3 neighbours becomes alive (“reproduction”).

With a “neighbour” one means a living cell from the 8 surrounding cells. All transitions take place at the same time and each stage is called a “generation”.

Within this Game of Life, one can build spaceships, billiard tables, pulsars, even complete working computers (Turing machines)!!! The first image above is Gosper’s gliding gun, a construction emitting a stream of gliders (spaceships).