The Game of Life is a cellular automaton devised by the British mathematician John Conway in 1970. The game is a zero-player game, meaning that its evolution is determined by its initial state. The Game of Life is played on a two-dimensional orthogonal grid of square "cells." Each cell has 2 states, either alive or dead, and also interacts with each of its 8 neighbors. Its neighbors are the cells that are horizontally, vertically, and diagonally adjacent to the cell. At each step in time, the following transitions take place...

• Any live cell with fewer than two live neighbors dies, as if by underpopulation.

• Any live cell with two or three live neighbors lives on to the next generation.

• Any live cell with more than three live neighbors dies, as if by overpopulation.

• Any dead cell with exactly three live neighbors becomes a live cell, as if by reproduction.