Play John Conway’s Game of Life

OOO ..O .O.

Life Lexicon

(CC BY-SA 3.0)

This Life lexicon is compiled by Stephen A. Silver from various sources and may be copied, modified and distributed under the terms of the Creative Commons Attribution-ShareAlike 3.0 Unported licence. See the original credit page for all credits and the original download location. The styling has been adjusted to fit this website.

Colour of a glider

:colour of a glider The colour of a glider is a property of the glider that remains constant while the glider is moving along a straight path, but that can be changed when the glider bounces off a reflector. It is an important consideration when building something using reflectors.

The colour of a glider can be defined as follows. First choose some cell to be the origin. This cell is then considered to be white, and all other cells to be black or white in a checkerboard pattern. (So the cell with coordinates (m,n) is white if m+n is even, and black otherwise.) Then the colour of a glider is the colour of its leading cell when it is in a phase that can be rotated to look like this:

Game of Life pattern ’colour_of_a_glider’

A reflector that does not change the colour of gliders obviously cannot be used to move a glider onto a path of different colour than it started on. But a 90-degree reflector that does change the colour of gliders is similarly limited, as the colour of the resulting glider will depend only on the direction of the glider, no matter how many reflectors are used. For maximum flexibility, therefore, both types of reflector are required.

Small periodic colour-changing glider reflectors (bouncers) are known, and also small periodic colour-preserving glider reflectors (bumpers). Among stable patterns, only a small colour-preserving reflector (Snark) is known. The smallest known 90-degree colour-changing reflector is given at the end of the reflector entry.

John Conway’s Game of Life

The Game of Life is not your typical computer game. It is a cellular automaton, and was invented by Cambridge mathematician John Conway.

This game became widely known when it was mentioned in an article published by Scientific American in 1970. It consists of a collection of cells which, based on a few mathematical rules, can live, die or multiply. Depending on the initial conditions, the cells form various patterns throughout the course of the game.


For a space that is populated:

Each cell with one or no neighbors dies, as if by solitude.

Each cell with four or more neighbors dies, as if by overpopulation.

Each cell with two or three neighbors survives.

For a space that is empty or unpopulated

Each cell with three neighbors becomes populated.

The Controls

Choose a pattern from the lexicon or make one yourself by clicking on the cells. The 'Start' button advances the game by several generations (each new generation corresponding to one iteration of the rules).

More information

In the first video, from Stephen Hawkings’ documentary The Meaning of Life, the rules are explained, in the second, John Conway himself talks about the Game of Life.

Stephen Hawkings The Meaning of Life (John Conway's Game of Life segment) Inventing Game of Life (John Conway) - Numberphile

The Guardian published a nice article about John Conway.

If you’ve been thinking “I’d like to sell my Tesla,” check out—the ultimate Tesla marketplace, and one of Game of Life’s supporters!

The Game of Life is also supported by Dotcom-Tools, Load View Testing, Driven Coffee Roasters, and Web Hosting Buddy.

Implemented by Edwin Martin <>