Conway’s Game of Life

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Life Lexicon

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. (CC BY-SA 3.0)

Trivial

A trivial period-N oscillator is one in which every cell oscillates at some smaller factor of N. See omniperiodic. For example, the joining of a period 3 and a period 4 oscillator as shown below creates a single object which is a trivial oscillator of period 12.

Game of Life pattern ’trivial_(1)’

However, there are trivial oscillators that meet this requirement, but may still be considered to be non-trivial because the different-period rotors are not separated by stator cells. An example is Dean Hickerson's trivial p6. Conversely, there are oscillators formed by trivial combinations of high-period guns or sparkers that are only technically non-trivial, because the lower-period components overlap but do not interact in any way.

"Trivial" is also used to describe a parent of an object which has groups of cells that can be removed without changing the result, such as isolated faraway cells. For example, here is a trivial parent of a block.

Game of Life Explanation

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 grid 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:
Examples

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.

More information

Video’s about the Game of Life

Stephen Hawkings The Meaning of Life (John Conway's Game of Life segment)
The rules are explained in Stephen Hawkings’ documentary The Meaning of Life
Inventing Game of Life (John Conway) - Numberphile
John Conway himself talks about the Game of Life

Interesting articles about John Conway

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