On April 11, 2020 John Conway died of Covid. Conway made contributions to many branches of mathematics, but is most famous for his invention The Game of Life. Reading about The Game of Life in the Dutch popular scientific magazine “KIJK” made a big impact on me and was one of the factors that lead me to pursue a career in computer science. So when I heard about Conway’s passing I decided to create a little cellular automaton as a tribute. This post is about that tribute.

Game of Life

A cellular automaton consists of a regular grid of cells, each in one of a finite number of states, Each cell changes state based on a set of fixed rules and its neighborhood. The neighborhood of a cell is made up of the cells nearby and in particular of the states of those cells.

The brilliance of the Game of Life is its simplicity of rules that power configurations that show highly complex behaviors. There are only two states: on and off. Only the eight direct neighbors are taken into account. As for the rules, a cell that is off, remains off unless three of its neighbors are on. A cell that is on, remains on only when two or three of its neighbors are on. That’s it!

Take for example this configuration, where the blue cells are on, the white ones off:

The middle cell has exactly two neighbors that are on, so it will remain on. The two blue cells on the left and the right though have only one neighbor that is on, so they will switch off. The two white cells just above and below the middle cell have both three neighbors that are switched on and so they will switch on themselves.

With the result:

Of course now the roles are reversed and in the next generation the cells above and below will switch off and the cells to the left and right will switch on again.

**Using these primitives you can create all kinds of complex mechanisms. A popular building block is the glider, a group of cells that ‘moves’ in a certain direction by changing its shape a few times until it reappears just the same, but now one cell down and **more to the right:

Glider in action

**It doesn’t stop there; people have created **guns that produce new gliders every so many generations, discovered or designed hundreds of space ships and even build systems that behave like computers which proves that the Game of Life is Turing Complete; anything that can be calculated, can be calculated using the right game of life setup (though the boards might be very big indeed).

#processing #artificial-life #artificial-intelligence