The Game of Life is a two dimensional universe in which patterns evolve through time. It is one of the best examples in science of how a few simple rules can result in incredibly complex behaviour. It’s also incredibly cool and gorgeous to watch.

The Life universe is terrifically simple. A square grid contains cells that are either alive or dead. The behaviour of each cell is dependent only on the state of its eight immediate neighbours, according to the following rules:

Live cells:

a live cell with zero or one live neighbours will die.

a live cell with two or three live neighbours will remain alive

a live cell with four or more live neighbours will die.



Dead cells:



a dead cell with exactly three live neighbours becomes alive

in all other cases a dead cell will stay dead.

Facebook Twitter Pinterest Every cell has exactly eight neighbours

We start with a pattern on the grid (generation 0) and we apply the rules simultaneously on all cells. This action results in a new pattern (generation 1). We then apply the rules again on all the cells, which creates another pattern (generation 2), and so on, and so on.

That’s it. There are no other rules.

The British mathematician John Conway, who is currently at Princeton University, invented the Game of Life in the late 1960s. He chose rules that produced the most unpredictable behaviour.

One of the most interesting early shapes was the R-pentomino.

All patterns made up of up to five live cells die out or become stable after ten generations. But the R-pentomino is active for more than a thousand! Check out its dazzling life cycle:



Facebook Twitter Pinterest Snap, crackle and pop

The five-cell pattern that moves diagonally across the screen from the 69th generation is called a glider, and is probably the most famous pattern in Life. It moves one cell vertically and one horizontally every four generations, giving the impression that it is crawling across the screen.

Another important pattern is the eater, so called because it eats gliders and other spaceships.

Facebook Twitter Pinterest Dinner time

When Conway came up with the Life rules, he was not sure if a pattern existed with a total number of live cells that kept on growing.

Bill Gosper at MIT answered this question in the affirmative by building the glider gun, a pattern which produces a new glider every 30 generations.

Facebook Twitter Pinterest Gun nation

Gosper also engineered the first pattern with a total number of live cells that grows faster and faster. It’s called Gosper’s breeder.

Facebook Twitter Pinterest Breeds glider guns, and lots of them

One of Conway’s early interests was whether or not the Game of Life could emulate the internal workings of a computer.

To do this, Life patterns had to be designed that could emulate the behaviour of the three basic logic gates: the NOT, AND and OR gates:

Facebook Twitter Pinterest How to build a computer in the Game of Life

It is remarkable to think that with all these patterns each cell is only listening to its immediate neighbour.

If you are curious to find out more about the Game of Life, I cover the area in some detail in my most recent book Alex Through The Looking-Glass. (The US title is the Grapes of Math).

It’s great fun to have a go at making patterns yourself. This is easier than ever now with the free software Golly, the Game of Life simulator, which is what I used for all the videos.

For historical context, Numberphile recently interviewed John Conway about the origins of the Game of Life: