![]() ![]() In our universe, each cell will either be a 1 (alive) or 0 (dead). Let us start with a small universe consisting of a six-by-six grid. I am using numpy arrays to represent the universe, as they are easy to initialise and manipulate. Iterate steps 3–4 for the desired number of generations.Iterate this survival function over all the cells in the universe.Determine if a given cell survives to the next iteration, based on its neighbours.This is a rough overview of our plan of attack: The massive variety and complexity of the results, often starting from simple seeds, is what makes cellular automata so interesting. ![]() Thus, we have to provide the universe with a seed, i.e a set of initial living cells. A dead cell will spring to life if it has exactly three live neighbours ( reproduction).Ĭlearly, no cells can come to life unless there are already some living cells in the universe (Aquinas’ primum movens?). it has more than three live neighbours ( overpopulation).Ģ.it has fewer than two live neighbours ( underpopulation).A living cell will survive into the next generation by default, unless: It is so named because its rules can be interpreted as a very simplistic model of living cells.įirstly, let us define the the eight grid squares around a cell as its neighbours. One of the most widely-studied cellular automata is the Game of Life, sometimes just called ‘Life’, which was discovered (or ‘invented’ if you prefer) by John Conway. The automaton then iterates forward in time, with the new state of each cell being decided by a set of rules. I will refer to this grid as the universe, though this is non-standard terminology. automata) consists of a grid of cells each cell has a state - either alive or dead. I emphasise intuitive code than performance, so it could be a useful starting point for somebody to understand the logic before implementing a more efficient version.Ī cellular automaton (pl. Third, you create the animate() function that uses a for loop to iterate through the array and update each cell using the “Game of live rules” discussed above.įourth, the animation is displayed with the FuncAnimation() function from Matplotlib’s powerful animation capabilities.In this short post, I explain how to implement Conway’s Game of Life in python, using numpy arrays and matplotlib animations. Second, you define a create_universe() function that takes two parameters and returns a random array of 0’s and 1’s. The Python code creates an animation of Conway’s hugely famous “Game of Life”.įirst, you import the NumPy and Matplotlib libraries. Img = ax.imshow(universe, interpolation='nearest')Īni = FuncAnimation(fig, animate, fargs=(universe, img,), Return np.random.choice(, size=(N, N), p=) import numpy as npįrom matplotlib.animation import FuncAnimation The rules of the animation are defined in the animate() function, which iterates over each cell in the universe and applies the rules of Conway’s Game of Life. It then animates the universe for 200 frames with a 200ms interval between each frame, and displays it using Matplotlib. This code creates a universe of size NxN with a probability p of being populated. How to Implement the “Game of Life” in Python? The rules continue to be applied repeatedly to create further generations. The first generation is created by applying the above rules simultaneously to every cell in the seed births and deaths occur simultaneously, and the discrete moment at which this happens is sometimes called a tick.Įach generation is a pure function of the preceding one. The initial pattern constitutes the seed of the system. Any dead cell with exactly three live neighbors becomes a live cell, as if by reproduction.Any live cell with more than three live neighbors dies, as if by overpopulation.Any live cell with two or three live neighbors lives on to the next generation.Any live cell with fewer than two live neighbors dies, as if by underpopulation.Every cell interacts with its eight neighbors, which are the cells that are horizontally, vertically, or diagonally adjacent.Īt each step in time, the following rules apply: The game is played on a two-dimensional grid of square cells, each of which is in one of two possible states, alive or dead. ![]() The game is a zero-player game, meaning that its evolution is determined by its initial state, requiring no further input. In this article, you’ll learn how to make this beautiful and interesting animation using only Python, NumPy, and Matplotlib - nothing else: □īut how does the Game of Life work – and what’s behind the classical visualization anyways? The Game of LifeĬonway’s Game of Life is a cellular automaton devised by the British mathematician John Horton Conway in 1970. ![]()
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