Conway's Game of Life: Rules & Instructions

Instructor: Sharon Linde

Sharon has a Masters of Science in Mathematics

This lesson goes over the four simple rules for Conway's Game of Life, a single-person logic game created in 1970. Read on to learn how the simple rules lead to many interesting patterns.

Brief History of Conway's Game of Life

The Game of Life, created by mathematician John Horton Conway, first appeared in the October 1970 edition of Scientific American. The rules of this single-person logic game are very simple, as we'll see below, but often lead to very surprising results. Conway originally recommended playing the game using tokens on a flat game board that was just a square grid. This method is fine for keeping track of starting positions of up to four initial counters and most of the patterns with five counters. However, with more counters this method doesn't work as well.

As personal computers became more popular, interest in the playing the electronic game grew, allowing for investigation of increasingly complex initial set-ups. Today there are online communities of players, programmers, and enthusiasts continuing to investigate the complexities these simple rules create. Let's take a closer look.

Instructions for the Game of Life

So, let's get to the details. Conway's Game of Life was originally played on a flat grid made up of square cells. These cells can be either live (with a token in it) or dead (no tokens in it). In computer versions, live cells are represented by one color, and dead cells by another color. In theory the size of the grid is infinite, but small boards will do for initial play.

This is a solitary game, or one with just one player, and the play of a typical game goes like this:

  1. Player chooses an initial set up.
  2. Rules are applied to see what happens in the next generation.
  3. Play continues until one of three things happens: all cells are dead, no cells change from one generation to the next, or the pattern flips back and forth between two or more positions.

Of course, like any game, there are rules! Here's a quick overview.

Rules for Conway's Game of Life

At the heart of this game are four rules that determine if a cell is live or dead. All depend on how many of that cell's neighbors are alive.

  1. Births: Each dead cell adjacent to exactly three live neighbors will become live in the next generation.
  2. Death by isolation: Each live cell with one or fewer live neighbors will die in the next generation.
  3. Death by overcrowding: Each live cell with four or more live neighbors will die in the next generation.
  4. Survival: Each live cell with either two or three live neighbors will remain alive for the next generation.

Another important fact about the rules for the game of life is that all rules apply to all cells at the same time.

Starting Points

What happens in the first generation if you start with a single cell that is alive? Well, let's apply the rules to that single live cell. How many live neighbors does it have? Because it is the only live cell on the board, it has zero live neighbors and the rules say it will die due to isolation. Since there are no dead cells that could possibly have three live neighbors, there will be no births. So, all starting configurations with only a single live cell will only contain dead cells in the next generation.

The same thing happens when you start with only two live cells. In that case, each cell will only have a maximum of one live neighbor and will die of isolation. There will be no births, since there are fewer than three live cells. So, all initial configurations die in the first generation.

Things start to get more interesting with three live cells. Most configurations will be far enough apart that they will also die out in one or two generations, but there are two exceptions to this rule. The first is a line of three live cells. The two end cells will die, because they each have one neighbor. The middle cell will survive, because it has two live neighbors, and there will be two births. The births occur in the two cells next to the surviving cell that were dead because each of those positions is next to all three live starting positions. If we started with a vertical line of three, the first generation will be a horizontal line of three. This pattern will repeat every second generation and was named a blinker by Conway.

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