<a title="Conway's Game of Life" href="http://en.wikipedia.org/wiki/Conway%27s_Game_of_Life">Conway's Game of Life</a> is a popular zero player cellular automaton game devised by the John Horton Conway in 1970. Each cell has 2 states: live or dead. There are 4 simple rules that determine this:
<ul>
<li>Any live cell with fewer than two live neighbours dies, as if caused by under-population.</li>
<li>Any live cell with two or three live neighbours lives on to the next generation.</li>
<li>Any live cell with more than three live neighbours dies, as if by overcrowding.</li>
<li>Any dead cell with exactly three live neighbours becomes a live cell, as if by reproduction.</li>
</ul>

The game makes for a fun evolution as the player sets the initial condition and then observes the evolution of the game.

From a programmer's perspective, the game is closer to an image processing algorithm. The "world" is a 2D image, where each pixel is a cell.
The state of a cell at a time is solely determined by the number of neighbours at the previous step. Hence this makes for an embarrassingly parallel image processing algorithm. Ting Ting Ting. GPUs!!!

The number of neighbours can be computed using a convolution kernel:
<a href="http://sandbox.arrayfire.com/wp-content/uploads/2014/12/kernel_CodeCogsEqn1.png"><img class="size-full wp-image-7582 aligncenter" src="http://sandbox.arrayfire.com/wp-content/uploads/2014/12/kernel_CodeCogsEqn1.png" alt="kernel_CodeCogsEqn" width="159" height="67" /></a>

Since the value of the a cell can be represented as 1 (live) and 0 (dead), using convolution will give us the number of neighbours of any cell. The center value of the kernel is 0 as we do not want to count the cell itself.

Here is a general overview of a convolution operation:
<a href="http://sandbox.arrayfire.com/wp-content/uploads/2014/12/convolve_CodeCogsEqn.png"><img src="http://sandbox.arrayfire.com/wp-content/uploads/2014/12/convolve_CodeCogsEqn.png" alt="convolve_CodeCogsEqn" width="978" height="150" class="alignnone size-full wp-image-7588" /></a>
