Life game with Python! (Conway's Game of Life)

Introduction

[Life game] [link01], which is famous as a cellular automaton, seemed to be interesting, so I wrote the code to generate the map array of the life game with Python and numpy. By giving an early generation map array written in 0 (dead) and 1 (live), iterative is implemented as a generator to generate the next generation map array. The map also supports periodic boundary conditions (end-to-end connection)!

lifegame.py

Import and use the following lifegame.py as a module. See the sample code below for an actual usage example. The evolution rules are based on the 23/3 featured on Wikipedia, but you can easily change them by tweaking in the code.

usage

>>> lg_map = lifegame.MapGenerator(map_init, periodic=False)
>>> lg_map.evolve()
array([...]) #0th generation map array(= map_init)
>>> lg_map.evolve()
array([...]) #1st generation map array
>>> ...

map_init: Early generation map array (list or numpy.ndarray)
periodic: Whether to use periodic boundary conditions for the map (bool)

lifegame.py

`lifegame.py`


import numpy as np
from itertools import product

class MapGenerator(object):
    def __init__(self, map_init, periodic=False):
        self.map_init  = np.array(map_init, np.int64)
        self.periodic  = periodic
        self.generator = self.map_evolver()

    def map_evolver(self):
        map_now   = self.map_init
        map_shape = self.map_init.shape

        while True:
            map_next = np.zeros_like(map_now, np.int64)
            for (i,j) in product(range(map_shape[0]), range(map_shape[1])):
                islive = bool(map_now[i,j])
                nlive  = self.num_live_neighbours(map_now, i, j)
                # write the rules of lifegame here!
                # ........................................
                if nlive == 2:
                    if islive: map_next[i,j] = 1
                elif nlive == 3:
                    map_next[i,j] = 1
                # ........................................

            yield map_now
            map_now = map_next

    def num_live_neighbours(self, map_now, i, j):
        if self.periodic:
            neighbours = np.roll(np.roll(map_now, -i+1, 0), -j+1, 1)[:3,:3]
        else:
            sl_i = slice(0,i+2) if i == 0 else slice(i-1,i+2)
            sl_j = slice(0,j+2) if j == 0 else slice(j-1,j+2)
            neighbours = map_now[sl_i,sl_j]

        return neighbours.sum() - map_now[i,j]

    def evolve(self):
        return self.generator.next()

Sample code using matplotlib

Below is a sample code of a type of oscillator called [pulsar] [link02] that evolves endlessly on a 15x15 map. Since it is just a sample, it seems that it is limited by the drawing efficiency of matplotlib rather than the calculation speed of the array ...

Sample code

`pulsar.py`


import time
import numpy as np
import matplotlib.pyplot as plt
import lifegame

pulsar = np.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, 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, 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, 1, 0, 1, 0, 1, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]])

lg_map = lifegame.MapGenerator(map_init=pulsar, periodic=False)
plt.ion()
while True:
    plt.pcolormesh(lg_map.evolve())
    plt.xlim([0, pulsar.shape[1]])
    plt.ylim([0, pulsar.shape[0]])
    plt.draw()
    plt.clf()
    time.sleep(0.05)

State of drawing

![lifegame-pulsar.png][link03]

Future plans?

At the moment, it is necessary to prepare the map array of the early generation in text in advance, so I would like to use matplotlib.widgets so that the map array can be input from the screen. It's a play, so it's undecided when to make it (laughs)

[link01]: http://ja.wikipedia.org/wiki/ Conway's Game of Life [link02]: http://ja.wikipedia.org/wiki/pulsar_ (life game) [link03]: https://qiita-image-store.s3.amazonaws.com/0/44000/18e4ac52-9120-dae6-b683-8ca29cd1d507.png