The Game of Life in this visualization
In Conway’s Game of Life, every square x of an endless grid is alive, , or dead, . With N(x) the number of live squares among the 8 around x, diagonals included, the next generation is
the rule B3/S23. Here you can draw patterns, watch them evolve, go back to earlier generations, look one generation ahead, and see when a pattern has provably settled.
Every square is updated from the same old generation at the same moment. Paused, Next generation shows a step before it is taken: squares about to be born get an open frame, squares about to die are struck through, and pointing at a square shows its 8 neighbours and its count. The board has no edge and does not wrap. A chevron at the edge says how many live squares lie beyond it. The curve in the panel counts the live squares in each generation since the board last changed.
A few kinds of object come up again and again. A still life never changes, like the block and the beehive. An oscillator returns to itself, like the blinker every 2 generations. A spaceship returns to its shape somewhere else: the glider after 4 generations, one square across and one down. A gun returns to itself and leaves something behind each time, and the Gosper gun fires a glider every 30 generations. Small patterns that take a long time to settle, such as the R-pentomino, are called methuselahs. Since a square’s next state depends only on the 3 × 3 block around it, no effect travels faster than one square per generation, a diagonal step counting as one. This is the speed of light c, and the glider moves at c/4.
The page says a pattern has settled only when it can prove it. The proof rests on one fact. Write F for one generation. If two groups of live squares X and Y are at least 3 squares apart, again counting a diagonal step as one, then
because no 3 × 3 block reaches both. So once the ash left in place repeats on its own, and every ship stays at least 3 squares from it and from the other ships as it flies off, nothing can disturb them again. The curve marks with a dashed line the first generation from which the board is that ash plus those ships. When the page cannot prove this, as with ships about to collide or a gun still firing, it says nothing about settling, and it never claims that a pattern will not settle.
John Horton Conway devised the game in 1970, and Martin Gardner made it famous in Scientific American that October.
Things to notice
- Colour and afterglow are display, not part of the rule. Afterglow fades by the second, not by the generation, so it does not tell a square’s age.
- Settled does not always mean still: oscillators keep blinking and ships keep flying, and the readout says which. A flat curve is not settling either, because the board can change while the count stays level.