Stride tricks for the Game of Life

This is similar to [:../SegmentAxis:Segment axis], but for 2D arrays with 2D windows.

The Game of Life is a cellular automaton devised by the British mathematician John Horton Conway in 1970, see [1].

It consists of a rectangular grid of cells which are either dead or alive, and a transition rule for updating the cells’ state. To update each cell in the grid, the state of the 8 neighbouring cells needs to be examined, i.e. it would be desirable to have an easy way of accessing the 8 neighbours of all the cells at once without making unnecessary copies. The code snippet below shows how to use the devious stride tricks for that purpose.

[1] Game of Life) at Wikipedia

import numpy as np
from numpy.lib import stride_tricks
x = np.arange(20).reshape([4, 5])
xx = stride_tricks.as_strided(x, shape=(2, 3, 3, 3), strides=x.strides + x.strides)

x

 array([[ 0,  1,  2,  3,  4],
        [ 5,  6,  7,  8,  9],
        [10, 11, 12, 13, 14],
        [15, 16, 17, 18, 19]])

xx

 array([[[[ 0,  1,  2],
          [ 5,  6,  7],
          [10, 11, 12]],

         [[ 1,  2,  3],
          [ 6,  7,  8],
          [11, 12, 13]],

         [[ 2,  3,  4],
          [ 7,  8,  9],
          [12, 13, 14]]],

        [[[ 5,  6,  7],
          [10, 11, 12],
          [15, 16, 17]],

         [[ 6,  7,  8],
          [11, 12, 13],
          [16, 17, 18]],

         [[ 7,  8,  9],
          [12, 13, 14],
          [17, 18, 19]]]])

xx[0,0]

 array([[ 0,  1,  2],
        [ 5,  6,  7],
        [10, 11, 12]])

xx[1,2]

 array([[ 7,  8,  9],
        [12, 13, 14],
        [17, 18, 19]])

x.strides

 (40, 8)

xx.strides

 (40, 8, 40, 8)