# Stride tricks for the Game of Life

This is similar to 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

In [1]: import numpy as np In [2]: from numpy.lib import stride_tricks In [3]: x = np.arange(20).reshape([4, 5]) In [4]: xx = stride_tricks.as_strided(x, shape=(2, 3, 3, 3), strides=x.strides + x.strides) In [5]: x Out[5]: array([[ 0, 1, 2, 3, 4], [ 5, 6, 7, 8, 9], [10, 11, 12, 13, 14], [15, 16, 17, 18, 19]]) In [6]: xx Out[6]: 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]]]]) In [7]: xx[0, 0] Out[7]: array([[ 0, 1, 2], [ 5, 6, 7], [10, 11, 12]]) In [8]: xx[1, 2] Out[8]: array([[ 7, 8, 9], [12, 13, 14], [17, 18, 19]]) In [9]: x.strides Out[9]: (20, 4) In [10]: xx.strides Out[10]: (20, 4, 20, 4)