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.

Sliding block memory

:sliding block memory A memory register whose value is stored as the position of a block. The block can be moved by means of glider collisions. See block pusher for an example.

In Conway's original formulation (as part of his proof of the existence of a universal computer in Life) two gliders were used to pull the block inwards by three diagonal spaces, as shown below, and thirty gliders were used to push it out by the same amount.

Game of Life pattern ’sliding_block_memory’

Dean Hickerson later greatly improved on this, finding a way to pull a block inwards by one diagonal space using 2 gliders, and push it out the same distance using 3 gliders. In order for the memory to be of any use there also has to be a way to read the value held. It suffices to be able to check whether the value is zero (as Conway did), or to be able to detect the transition from one to zero (as Hickerson did).

Dean Hickerson's sliding block memory is used in Paul Chapman's URM, and the key salvos from it are used in several other complex constructions, such as David Bell's Collatz 5N+1 simulator and Adam P. Goucher's pi calculator and Spartan universal computer-constructor.

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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