# Game of Life With Python

# Game of Life With Python

### Love coding and Python and have a god complex? Well, even if you don't meet that second criterion, you'll probably still enjoy this post on using data patterns in Python.

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The game of life consists of a grid of cells where each cell can be dead or alive and the state of the cells can change at each time step. The state of a cell at the time step depends on the state of the grid at time *t-1* and it is determined with a very simple rule:

*A cell is alive if it's already alive and has two living neighbors, or if it has three live neighbors*.

We call the grid *universe* and the alive cells *population*. At each time step, the population evolves and we have a new *generation*. The evolution of the population is a fascinating process to observe because it can generate an incredible variety of patterns (and also puzzles!).

Implementing the game of life in Python is quite straightforward:

```
import numpy as np
def life(X, steps):
"""
Conway's Game of Life.
- X, matrix with the initial state of the game.
- steps, number of generations.
"""
def roll_it(x, y):
# rolls the matrix X in a given direction
# x=1, y=0 on the left; x=-1, y=0 right;
# x=0, y=1 top; x=0, y=-1 down; x=1, y=1 top left; ...
return np.roll(np.roll(X, y, axis=0), x, axis=1)
for _ in range(steps):
# count the number of neighbours
# the universe is considered toroidal
Y = roll_it(1, 0) + roll_it(0, 1) + roll_it(-1, 0) \
+ roll_it(0, -1) + roll_it(1, 1) + roll_it(-1, -1) \
+ roll_it(1, -1) + roll_it(-1, 1)
# game of life rules
X = np.logical_or(np.logical_and(X, Y ==2), Y==3)
X = X.astype(int)
yield X
```

The function *life* takes in input a matrix *X* which represents the universe of the game where each cell is alive if its corresponding element has value 1 and dead if 0. The function returns the next *steps* generations. At each time step, the number of neighbors of each cell is counted and the rule of the game is applied. Now we can create a universe with an initial state:

```
X = np.zeros((40, 40)) # 40 by 40 dead cells
# R-pentomino
X[23, 22:24] = 1
X[24, 21:23] = 1
X[25, 22] = 1
```

This initial state is known as the R-pentomino. It consists of five living cells organized as shown here (image from Wikipedia):

It is by far the most active polyomino with fewer than six cells, all of the others stabilize in at most 10 generations. Let's create a video to visualize the evolution of the system:

```
from matplotlib import pyplot as plt
import matplotlib.animation as manimation
FFMpegWriter = manimation.writers['ffmpeg']
metadata = dict(title='Game of life', artist='JustGlowing')
writer = FFMpegWriter(fps=10, metadata=metadata)
fig = plt.figure()
fig.patch.set_facecolor('black')
with writer.saving(fig, "game_of_life.mp4", 200):
plt.spy(X)
plt.axis('off')
writer.grab_frame()
plt.clf()
for x in life(X, 800):
plt.spy(x)
plt.axis('off')
writer.grab_frame()
plt.clf()
```

The result is as follows:

In the video, we can notice few very well known patterns like gliders and blinkers. Also, an exploding start at 0:55!

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Published at DZone with permission of Giuseppe Vettigli , DZone MVB. See the original article here.

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