Conway's Game of Life Simulations

Conway's Game of Life is a cellular automaton devised by the British mathematician John Horton Conway in 1970. It is a zero-player game, meaning that its evolution is determined by its initial state, requiring no further input. One interacts with the Game of Life by creating an initial configuration and observing how it evolves. In this project I decided to test out different densities and see which ones would survive the longest. As a second part to the project, I decided to expand this to a hexagonal version of the game and see the survival rates in this new environment.

Here's a little environment that I have built to play the game with the famous glider already drawn.

In the design of the game, I decided to make the the board behave like a torus. This means that the board wraps around on itself, so that the top row is connected to the bottom row and the right is connected to the left. This allows the game to have a seemingly "infinite" board even though it is actually pretty small. This is useful since in an ideal world we would want to test the densities on an infinite board.

Results with the square grid

As we can see, the densities that provide the most survivability is in the range of 25% to 50%. I know that the axis on the graph are not labeled correctly. This project was done in cégep and to get the same graph would take another 10 hours of computation.

The transition from a square grid to a hexagonal grid

The challenging part in this new implementation of the game was to decide how to internally store the board and make the game play. I could have used a graph where every edge would be a neighbor but I decided to make the implementation more efficient. I found a pretty simple way to represent the hexagonal grid in a normal matrix.

Using the power of these matrices, I simulated again!

As we can see, the overall most surviving densities are still around 25% to 50%. The interesting thing here is how the graph is "Wider". Thus in general, on a hexagonal board, any pattern has a higher likelihood of surviving for longer than a similarily dense pattern on a square board. As a final note, the axis are not labeled correctly again.