Friendly Fire

Here’s a little oddity that I just came across. John Conway’s Game of Life is a familiar recreation that takes place on a grid of squares. At the start each square is either “alive” or “dead,” and then on each turn the status of each square is updated:

  1. Any live cell with fewer than two live neighbors dies (as if by underpopulation)
  2. Any live cell with two or three live neighbors lives on
  3. Any live cell with more than three live neighbors dies (as if by overpopulation)
  4. Any dead cell with exactly three live neighbors becomes a live cell (as if by reproduction)

This produces some surprising creatures, such as the “glider,” a self-propagating “spaceship” that travels diagonally:

Gliders can be generated by an oscillating factory called a “gun”:
Image: Wikimedia Commons

Here’s the oddity: It would seem that each gun will produce an infinite fleet, since its gliders all depart in the same direction. But that’s not true if the grid of squares is written on a torus — then the gliders snake around the figure and destroy their maker: