Play John Conway’s Game of Life

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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.

Puffer

:puffer An object that moves like a spaceship, except that it leaves debris behind. The first known puffers were found by Bill Gosper and travelled at c/2 orthogonally (see diagram below for the very first one, found in 1971).

Game of Life pattern ’puffer’

Not long afterwards c/12 diagonal puffers were found (see switch engine). Discounting wickstretchers, which are not puffers in the conventional sense, no new velocity was obtained after this until David Bell found the first c/3 orthogonal puffer in April 1996. Other new puffer speeds followed over the next several years.

Many spaceships that travel orthogonally at a speed less than c/2 have useful side or back sparks. These can be used to perturb standard spaceships that approach from behind. A common technique for creating puffers for a new speed uses a convoy of the new spaceships to create debris from an approaching standard spaceship such that a new standard spaceship is recreated on the same path as the original one. This forms a closed loop, resulting in a high-period puffer for the new speed.

As of June 2018, puffers have been found matching every known velocity of elementary spaceship, except for c/6 and c/7 diagonal and (2,1)c/6. It is also generally easy to create puffers based on macro-spaceships, simply by removing some part of the trailing cleanup mechanism.

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.

Rules

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.


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