Conway’s Game of Life

The Game of Life is a cellular automaton devised by the British mathematician John Horton Conway in 1970. It is the best-known example of a cellular automaton – Wikipedia

The universe of the Game of Life is an infinite two-dimensional orthogonal grid of square cells, each of which is in one of two possible states, live or dead. Every cell interacts with its eight neighbours, which are the cells that are directly horizontally, vertically, or diagonally adjacent. At each step in time, the following transitions occur:

  1. Any live cell with fewer than two live neighbours dies, as if by loneliness.
  2. Any live cell with more than three live neighbours dies, as if by overcrowding.
  3. Any live cell with two or three live neighbours lives, unchanged, to the next generation.
  4. Any dead cell with exactly three live neighbours comes to life.

Gospers glider gun from Wikipedia

Dowload Excel Game of Life

The Excel document uses macros to simulate the birth and death of the cells according to the rules outlined above. There is a macro that will seed the game with a random configuration of cells. You can then increment this a single generation at a time or run ‘life’, where you will see the evolution of the cells over one hundred generations. There are also some interesting configurations stored on other worksheets. You can cut and paste these into the start generation and run life from there. There are a numbert of interesting ‘creatures’ outlined in Martn Gardiner’s Scientific American article from 1970.


Here are two screenshots of the population when life is running.


The macro also records and plots the population change over time. The plots for xbar and ybar give the average location of all the cells – when looking as single creatures such as a ‘glider’ you can see the aggregate direction they take.

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One Response to Conway’s Game of Life

  1. […] I have posted a previous model of Conway’s Game of Life that runs in Excel – click here to view. I’ve just been reading Daniel Dennet’s book, Freedom Evolves, which uses examples of […]

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