{"id":396,"date":"2015-08-24T14:10:08","date_gmt":"2015-08-24T14:10:08","guid":{"rendered":"http:\/\/drsfenner.org\/blog\/?p=396"},"modified":"2016-02-05T16:25:34","modified_gmt":"2016-02-05T16:25:34","slug":"game-of-life-in-numpy-2","status":"publish","type":"post","link":"https:\/\/drsfenner.org\/blog\/2015\/08\/game-of-life-in-numpy-2\/","title":{"rendered":"Game of Life in NumPy"},"content":{"rendered":"
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In a previous post, we explored generating the grid-neighborhoods of an element in a NumPy array. The punch line of that work was grid_nD<\/code>, shown below.<\/p>\n<\/div>\n<\/div>\n<\/div>\n

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import<\/span> numpy<\/span> as<\/span> np<\/span>\r\nimport<\/span> matplotlib.pyplot<\/span> as<\/span> plt<\/span>\r\nimport<\/span> time<\/span>\r\nfrom<\/span> IPython<\/span> import<\/span> display<\/span>\r\n\r\n%<\/span>matplotlib<\/span> inline\r\n\r\nfrom<\/span> numpy.lib.stride_tricks<\/span> import<\/span> as_strided<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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def<\/span> grid_nD<\/span>(<\/span>arr<\/span>):<\/span>\r\n    assert<\/span> all<\/span>(<\/span>_len<\/span>><\/span>2<\/span> for<\/span> _len<\/span> in<\/span> arr<\/span>.<\/span>shape<\/span>)<\/span>\r\n    \r\n    nDims<\/span> =<\/span> len<\/span>(<\/span>arr<\/span>.<\/span>shape<\/span>)<\/span>\r\n    newShape<\/span> =<\/span> [<\/span>_len<\/span>-<\/span>2<\/span> for<\/span> _len<\/span> in<\/span> arr<\/span>.<\/span>shape<\/span>]<\/span>\r\n    newShape<\/span>.<\/span>extend<\/span>([<\/span>3<\/span>]<\/span> *<\/span> nDims<\/span>)<\/span>\r\n    \r\n    newStrides<\/span> =<\/span> arr<\/span>.<\/span>strides<\/span> +<\/span> arr<\/span>.<\/span>strides<\/span>\r\n    return<\/span> as_strided<\/span>(<\/span>arr<\/span>,<\/span> shape<\/span>=<\/span>newShape<\/span>,<\/span> strides<\/span>=<\/span>newStrides<\/span>)<\/span>\r\n<\/pre>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
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Using grid_nD<\/code>, coding the game of life becomes really, really easy. Given the neighborhood around a cell, we can simply make use of two lookup tables: (1) the rules to use if the center cell is alive and (2) the rules to use if the center cell is dead. Normally, the Game of Life is implemented with these rules encoded as if-then-else<\/code> or case<\/code> statements. Instead, we’re going to use np.where<\/code> which allows us to specify an array of boolean values (true\/false, 1\/0, alive\/dead) and then pick from a "true\/1\/alive" value or a "false\/0\/dead" value.<\/p>\n
We’ll create a table of the living values and a table of the dead values in two separate NumPy arrays. For a given number of neighbors, we can lookup the state of the center cell for the next time point.<\/p>\n
Recall the rules for a currently living cell:<\/p>\n