Conway’s Game Of Life (Python Implementation)

Conways’s Game Of Life is a Cellular Automation Method created by John Conway. This game was created with Biology in mind but has been applied in various fields such as Graphics, terrain generation,etc..


The “game” is a zero-player game, meaning that its evolution is determined by its initial state, requiring no further input. One interacts with the Game of Life by creating an initial configuration and observing how it evolves, or, for advanced “players”, by creating patterns with particular properties.

How the game works

Because the Game of Life is built on a grid of nine squares, every cell has eight neighboring cells,as shown in the given figure. A given cell (i, j) in the simulation is accessed on a grid [i][j], where i and j are the row and column indices, respectively. The value of a given cell at a given instant of time depends on the state of its neighbors at the previous time step. Conway’s Game of Life has four rules.

  1. If a cell is ON and has fewer than two neighbors that are ON, it turns OFF
  2. If a cell is ON and has either two or three neighbors that are ON, it remains ON.
  3. If a cell is ON and has more than three neighbors that are ON, it turns OFF.
  4. If a cell is OFF and has exactly three neighbors that are ON, it turns ON.


So since we know how it works, the next thing we need to figure it out that how to make it work.


1. Initialize the cells in the grid.
2. At each time step in the simulation, for each 
   cell (i, j) in the grid, do the following:
   a. Update the value of cell (i, j) based on 
      its neighbors, taking into account the 
      boundary conditions.
   b. Update the display of grid values.

After we done here lets get our hands on code.


  1. numpy
  2. :For 2D array(matrix) manipulation.

  3. matplotlib
  4. :For update the simulation or in easy words to make stuffs move.

  5. argparse
  6. :To pass command line arguments in the code.

Now lets get it started

The Code





# Python code to implement Conway's Game Of Life
import argparse
import numpy as np
import matplotlib.pyplot as plt 
import matplotlib.animation as animation
# setting up the values for the grid
ON = 255
OFF = 0
vals = [ON, OFF]
def randomGrid(N):
    """returns a grid of NxN random values"""
    return np.random.choice(vals, N*N, p=[0.2, 0.8]).reshape(N, N)
def addGlider(i, j, grid):
    """adds a glider with top left cell at (i, j)"""
    glider = np.array([[0,    0, 255], 
                       [2550, 255], 
                       [0255, 255]])
    grid[i:i+3, j:j+3] = glider
def addGosperGliderGun(i, j, grid):
    """adds a Gosper Glider Gun with top left
       cell at (i, j)"""
    gun = np.zeros(11*38).reshape(11, 38)
    gun[5][1] = gun[5][2] = 255
    gun[6][1] = gun[6][2] = 255
    gun[3][13] = gun[3][14] = 255
    gun[4][12] = gun[4][16] = 255
    gun[5][11] = gun[5][17] = 255
    gun[6][11] = gun[6][15] = gun[6][17] = gun[6][18] = 255
    gun[7][11] = gun[7][17] = 255
    gun[8][12] = gun[8][16] = 255
    gun[9][13] = gun[9][14] = 255
    gun[1][25] = 255
    gun[2][23] = gun[2][25] = 255
    gun[3][21] = gun[3][22] = 255
    gun[4][21] = gun[4][22] = 255
    gun[5][21] = gun[5][22] = 255
    gun[6][23] = gun[6][25] = 255
    gun[7][25] = 255
    gun[3][35] = gun[3][36] = 255
    gun[4][35] = gun[4][36] = 255
    grid[i:i+11, j:j+38] = gun
def update(frameNum, img, grid, N):
    # copy grid since we require 8 neighbors 
    # for calculation and we go line by line 
    newGrid = grid.copy()
    for i in range(N):
        for j in range(N):
            # compute 8-neghbor sum
            # using toroidal boundary conditions - x and y wrap around 
            # so that the simulaton takes place on a toroidal surface.
            total = int((grid[i, (j-1)%N] + grid[i, (j+1)%N] + 
                         grid[(i-1)%N, j] + grid[(i+1)%N, j] + 
                         grid[(i-1)%N, (j-1)%N] + grid[(i-1)%N, (j+1)%N] + 
                         grid[(i+1)%N, (j-1)%N] + grid[(i+1)%N, (j+1)%N])/255)
            # apply Conway's rules
            if grid[i, j]  == ON:
                if (total < 2) or (total > 3):
                    newGrid[i, j] = OFF
                if total == 3:
                    newGrid[i, j] = ON
    # update data
    grid[:] = newGrid[:]
    return img,
# main() function
def main():
    # Command line args are in sys.argv[1], sys.argv[2] ..
    # sys.argv[0] is the script name itself and can be ignored
    # parse arguments
    parser = argparse.ArgumentParser(description="Runs Conway's Game of Life simulation.")
    # add arguments
    parser.add_argument('--grid-size', dest='N', required=False)
    parser.add_argument('--mov-file', dest='movfile', required=False)
    parser.add_argument('--interval', dest='interval', required=False)
    parser.add_argument('--glider', action='store_true', required=False)
    parser.add_argument('--gosper', action='store_true', required=False)
    args = parser.parse_args()
    # set grid size
    N = 100
    if args.N and int(args.N) > 8:
        N = int(args.N)
    # set animation update interval
    updateInterval = 50
    if args.interval:
        updateInterval = int(args.interval)
    # declare grid
    grid = np.array([])
    # check if "glider" demo flag is specified
    if args.glider:
        grid = np.zeros(N*N).reshape(N, N)
        addGlider(1, 1, grid)
    elif args.gosper:
        grid = np.zeros(N*N).reshape(N, N)
        addGosperGliderGun(10, 10, grid)
    else:   # populate grid with random on/off -
            # more off than on
        grid = randomGrid(N)
    # set up animation
    fig, ax = plt.subplots()
    img = ax.imshow(grid, interpolation='nearest')
    ani = animation.FuncAnimation(fig, update, fargs=(img, grid, N, ),
                                  frames = 10,
    # # of frames? 
    # set output file
    if args.movfile:, fps=30, extra_args=['-vcodec', 'libx264'])
# call main
if __name__ == '__main__':


Without passing any command line arguments.

Now lets turn up things a little, let’s see what happens if add updates the animation every 500 milliseconds and setting up the dimensions 32X32 and also using the initial glider pattern.

python '' --grid-size 32 --interval 500 --glider

You can try manipulating this code to create different simulation using this.

Reference Links:

  1. Github Code for this article
  2. Book: Python Playground: Geeky Projects for the Curious Programmer
  3. docs-numpy
  4. docs matplotlib

This article is contributed by Subhajit Saha. If you like GeeksforGeeks and would like to contribute, you can also mail your article to See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.

My Personal Notes arrow_drop_up

Article Tags :
Practice Tags :

Be the First to upvote.

Please write to us at to report any issue with the above content.