Saturday, March 12, 2011

The Game of Life, part 1

Update: See part 2 for the implemented HashLife algorithm.

The Game of Life is a fascinating system. It was invented by John Conway in 1970 and has been studied continuously ever since. For those reading who haven’t heard of it before, a brief explanation: The world is an infinite grid of points, all either alive or dead. After each generation – or ‘iteration’ if you’d prefer – cells are updated according to the following three rules:

1. If a cell is alive and it has two or three live neighbours, it stays alive.
2. If a cell is dead and it has exactly three live neighbours, it becomes alive (tripartite reproduction?).
3. Any other cell is dead.

From these simple rules amazing complexity can arise. Some configurations are stable, like the period two “blinker” [above left], or the period four “glider” [above right] that moves one row over and one row down with every cycle. Other configurations, like the one above centre, grow infinitely – this one spits out two gliders then lays down a zig-zag strip of blocks forever after.

There is more to the Game of Life than pretty patterns and curious growth, I must hasten to add. It has been studied by a host of people in a variety of fields and has gone on to start a new branch of mathematics (cellular automata) and spur discussions on whether a sufficiently complicated pattern could be considered intelligent. It has also been proven to be Turing complete, so any computation your computer can run can be run by simulating the Game of Life with the correct starting state.

I have implemented a basic python program for simulating the Game of Life on GitHub. It allows for infinite patterns, grows the field of view automatically, and allows speed to be controlled with Up/Down, but otherwise is a very simple implementation. The goal here is to eventually implement some of the more interesting algorithms for speeding up the simulation.  There are numerous such algorithms, although the one I find the most interesting is called Hashlife and exploits repeated patterns through space and time to achieve an exponential speedup in running the simulation. More details in part 2, whenever I write it :).