# 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

In [7]:
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)

In [8]:
x

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

Out[9]:
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 [11]:
xx[0,0]

Out[11]:
array([[ 0,  1,  2],
[ 5,  6,  7],
[10, 11, 12]])
In [12]:
xx[1,2]

Out[12]:
array([[ 7,  8,  9],
[12, 13, 14],
[17, 18, 19]])
In [13]:
x.strides

Out[13]:
(40, 8)
In [14]:
xx.strides

Out[14]:
(40, 8, 40, 8)

Section author: RobertCimrman