Note that this pattern will flip back and forth, There are many interesting patterns in the life Hence, the next generation looks like this: There are other cells with one or two neighbors but they were not alive to start with so they stay dead. The cells to the right and left of the center (currently not alive) have three neighbors, so they become alive. The cells directly above and below the center have only one neighbor so they die. You see that the middle cell was alive and has two neighbors, so that it stays alive. Here we have placed the neighbor count inside the cell position. Now we count the neighbors that each cell has. We start with three live cells in a central column. The white squares are dead cells, and the blue squares are live cells. That is, a cell can have vertical, horizontal, and/or diagonal neighbors. The neighborhood will be each square that a king could move to on a chessboard. But only 2,3/3 is the "Conway life" rule, which is a subset of a large number of "Cellular Automata" rules.) (Note: this shorthand allows us to write many rules - e.g. The shorthand way for writing this "rule" is 2,3/3, meaning that a living cell remains alive next generation if it has 2 or 3 neighbors, and a non-living cell comes to life if it has exactly three neighbors. (hence, if a living cell has two or three neighbors, it will remain alive for the next generation.)īirths: A cell will become alive if it has exactly 3 neighbors. THE NEIGHBORHOOD RULES FOR CONWAY'S "GAME"ĭeaths: A live cell will die if it has either too few or too many neighbors:
The cells live or die from generation to generation depending upon whether they are already alive or not, and how many living neighbors (hereafter called simply "neighbors") they currently have.
The "game" (placed in quotes because there are actually no players - the outcome is decided by the pattern initially chosen) is played on a grid of "cells" which are represented as squares). CELLULAR AUTOMATA AND CONWAY'S GAME OF LIFEĬonway's game of Life was invented by John Horton Conway and was described in Scientific American's Mathematical Games column back in the early 70's.