another Game of Life question (infinite grid) ?

Question

Hi friends,

I have been playing around with Conway's Game of life and recently discovered some amazingly fast implementations such as Hashlife and Golly. (download Golly here - http://golly.sourceforge.net/)

One thing that I cant get my head around is how do coders implement the infinite grid? We can't keep an infinite array of anything, if you run golly and get a few gliders to fly off past the edges, wait for a few mins and zoom right out, you will see the gliders still there out in space running away, so how in gods name is this concept of infinity dealt with programmatically? Is there a well documented pattern or what?

Many thanks

Answer 1

Wikipedia explains it. The basic idea is that Conway's Game of Life exhibits locality, since information travels at a slow speed compared to the pattern size and the maximum density of filled cells is around 1/2 of the cells in any region. (More will kill off cells due to overcrowding.)

Since there is locality, you can seperate the field in different sections and simulate each section independently. If you choose your locality well, you will often see the same patterns. You can simulate how those evolve and store the results in a lookup table, so that other instances of the same pattern do not need to be simulated more than once. Combining adjacent patterns into larger 'metapatterns' allows you to precalculate those as well, and so on.

Answer 2

It is possible to represent living nodes with some type of sparse matrix in this situation. For instance, if we store a list of (LivingNode, Coordinate) pairs instead of an array of Nodes where each is either living or dead, we are simply changing the Coordinates rather than increasing an array's size. Thus, the space required for this is proportional to the number of LivingNodes.

This solution doesn't work for states where the number of living nodes is constantly increasing, but it works very well for gliders.

EDIT: So that was off the top of my head. Turns out Wikipedia has an article that shows a much more well-thought out solution. Oh well! :) Enjoy.