︠ac12bda9-3eac-4b4d-90aa-0f96bac05be7︠
import numpy
def one_tick(B):
    # Count neighbours
    N = (B[0:-2,0:-2] + B[0:-2,1:-1] + B[0:-2,2:] +
         B[1:-1,0:-2]                + B[1:-1,2:] +
         B[2:  ,0:-2] + B[2:  ,1:-1] + B[2:  ,2:])

    # Apply rules
    birth = (N==3) & (B[1:-1,1:-1]==0)
    survive = ((N==2) | (N==3)) & (B[1:-1,1:-1]==1)
    B[...] = 0
    B[1:-1,1:-1][birth | survive] = 1
    return B
︠3df07e4a-1073-49db-b31d-1c01118af36f︠
# Create a simple glider
Z = numpy.array([[0,0,0,0,0,0],
                [0,0,0,1,0,0],
                [0,1,0,1,0,0],
                [0,0,1,1,0,0],
                [0,0,0,0,0,0],
                [0,0,0,0,0,0]])
Z
︠c8139636-4781-458b-aa21-f54a4c6704d5︠
matrix_plot(Z, cmap=["white", "red"])
︠f4342c11-3f4b-4faf-9958-d7048fe1a12c︠
Z = one_tick(Z)
matrix_plot(Z, cmap=["white", "red"])
︠047173b4-0ace-4d69-8b30-21d741c3147c︠
# Back to the start
Z = one_tick(one_tick(one_tick(Z)))
matrix_plot(Z, cmap=["white", "red"])
︠fd01dbf1-fe4e-4c92-8560-5615745c6b91︠
# This uses python generators which we don't discuss until MCS275
# For now, it will iterate the one_tick function total number of times,
# producing a list
class GameOfLife:
    def __init__(self, total, board):
        self.board = board
        self.num = total
    def __iter__(self):
        return self
    def next(self):
        if self.num <= 0:
            raise StopIteration
        self.num -= 1
        self.board = one_tick(self.board)
        return matrix_plot(self.board.copy(), cmap=["white", "red"])
︠f92cb639-7692-4538-a849-080c434f0d5a︠
animate(GameOfLife(10,
                   numpy.array([[0,0,0,0,0,0, 0, 0, 0],
                                [0,0,0,1,0,0, 0, 0, 0],
                                [0,1,0,1,0,0, 0, 0, 0],
                                [0,0,1,1,0,0, 0, 0, 0],
                                [0,0,0,0,0,0, 0, 0, 0],
                                [0,0,0,0,0,0, 0, 0, 0],
                                [0,0,0,0,0,0, 0, 0, 0],
                                [0,0,0,0,0,0, 0, 0, 0],
                                [0,0,0,0,0,0, 0, 0, 0]])))
︠5aa7ba35-a991-4245-a256-6db1624153ff︠
# Here is the Gosper Glider Gun http://en.wikipedia.org/wiki/Gun_%28cellular_automaton%29
glider_gun = numpy.array([[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0],
     [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0],
     [0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,1,1],
     [0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,1,1],
     [1,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
     [1,1,0,0,0,0,0,0,0,0,1,0,0,0,1,0,1,1,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0],
     [0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0],
     [0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
     [0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]])

X = numpy.zeros((50, 70))
X[1:10,1:37] = glider_gun
animate(GameOfLife(50, X))
︠cf8fb8ef-91a1-471a-a2d9-ec94c09db656︠