game of life

A computer science classic Game of life.

How

Game of life is really just counting neighbors. We can speed that up that by leverging the optimized scipy.convolve function. The kernel would be:

1 1 1
1 0 1
1 1 1

Convolution of state I (suppose living = 1, dead = 0) with kernel is the count of living neighbors:

neighbors = convolve(self.I, self.kernel, mode='same')

We map living cells to 8 and dead cells to -9:

I = 8 * I + (-9) * (1 - I)

Now I + neighors alone can represent the state of a cell and the number of its living neighbors. The range of cell states is from -17 to 16. For example, -6 represents a dead cell with 3 living neighbors, which will live.

Combining the above logic, the state update is a two-liner:

t = convolve(self.I, self.kernel, mode='same') + 17 * self.I - 9 # compute state variables
self.I = np.where((t == -6)|(t == 10)|(t == 11), 1, 0).reshape(self.I.shape)  # new state I

List of patterns

Great library of game of life patterns: Link.