cellular automata. the game the game of life is not your typical computer game. it is a 'cellular...

Cellular Automata

The Game

The Game of Life is not your typical computer game. It is a 'cellular automation', and was invented by the Cambridge mathematician John Conway.

This game became widely known when it was mentioned in an article published by Scientific American in 1970. It consists of a collection of cells which, based on a few mathematical rules, can live, die or multiply. Depending on the initial conditions, the cells form various patterns throughout the course of the game.

Cellular Automation

Formally, we must think of an infinite square grid in which each cell exists in one or two states, living or dead. Each cell is a simple automation that at every tick of a great clock must decide which state it will be in until the next tick. It makes this decision on the basis of not only its present state but also those of its eight neighbours, four adjacent along sides and four adjacentat corners.

The Rules

For a space that is 'populated': Each cell with one or no neighbours dies, as if by loneliness. Each cell with four or more neighbours dies, as if by overpopulation. Each cell with two or three neighbours survives. For a space that is 'empty' or 'unpopulated' Each cell with three neighbours becomes populated.

The algorithmbelow computes successive generations for Life in matrix L.A 1 represents a live cell in the i,jth entry, and a 0 represents a dead cell.

1. for i 1 to 1001. for j 1 to 1001. s 02. for p i -1 to i +1 /compute effectfor q j - 1 to j +1 /of neighbourss s + L(p,q)3. s s - L(i,j)4. if (s = 3) or (s + L(i,j) = 3)then X(i,j) = 1/store life or deathelse X(i,j) = 0/in auxiliary array X2. for i 1 to 1001. for j 1 to 1001. L(i,j) X(i,j)/refresh L2. display L(i,j)/display L

The Game of Life A java applet: A dos program:

Interesting links:

www.bitstorm.org/gameoflifewww.math.com/students/wonders/life/lif.htmlhensel.lifepatterns.nethttp://wwwhomes.uni-bielefeld.de/achim/gol.html