Game of Life

How it works

The Game of Life is a cellular automaton: every cell is alive or dead, and its state in the next generation depends on how many of its eight neighbours, diagonals included, are alive. A dead cell comes to life with exactly 3 live neighbours, and a live cell survives with 2 or 3; otherwise it dies. The rule is written B3/S23, and all cells update at the same time. The evolution is completely deterministic, yet it produces still lifes, oscillators and patterns that travel across the grid.

birth: exactly 3 live neighbourssurvival: 2 or 3 live neighboursB3/S23

Try it yourself

1. Add a “Glider” and advance with “Step”. After 4 generations the glider has the same shape again, shifted by one cell diagonally.
2. Add a “Blinker”, a “Toad” and a “Block”. The blinker and the toad return to their original state after 2 generations; the block never changes.
3. Turn on “Show fading trails”, click “Add all” and start the evolution. The LWSS moves 2 cells sideways every 4 generations. Watch what happens when patterns collide.
4. Click “Random sample · 25%”. Out of the initial chaos usually only still lifes, oscillators and escaping gliders remain. Turn off “Connect opposite edges” and compare what happens at the edges.

Model limitations

The grid is finite, at most 90 × 60 cells. With connected edges it forms a torus – what leaves on one side comes back on the other – and without them the cells beyond the edge stay dead. The evolution may therefore differ from an infinite plane. Trails are only a visual aid and do not affect the computation.

Related experiments

• Logic circuits
• Fractals
• Radioactive decay