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.
An interesting question is: What is the minimum population of a pattern that exhibits infinite growth? In 1971 Charles Corderman found that a switch engine could be stabilized by a pre-block in a number of different ways, giving 11-cell patterns with infinite growth. This record stood for more than quarter of a century until Paul Callahan found, in November 1997, two 10-cell patterns with infinite growth. The following month he found the one shown below, which is much neater, being a single cluster. This produces a stabilized switch engine of the block-laying type.
.png)
In October 2014, Michael Simkin discovered a three-glider collision that produces a glider-producing stabilized switch engine and thus produces infinite growth from the smallest possible number of gliders (since all 71 2-glider collisions have a finite limit population).
Also of interest is the following pattern (again found by Callahan), which is the only 5×5 pattern with infinite growth. This too emits a block-laying switch engine.
.png)
Following a conjecture of Nick Gotts, Stephen Silver produced, in May 1998, a pattern of width 1 which exhibits infinite growth. This pattern was very large (12470×1 in the first version, reduced to 5447×1 the following day). In October 1998 Paul Callahan did an exhaustive search, finding the smallest example, the 39×1 pattern shown below. This produces two block-laying switch engines, stability being achieved at generation 1483. Larger patterns have since been constructed that display quadratic growth.
Although the simplest infinite growth patterns grow at a rate that is (asymptotically) linear, many other types of growth rate are possible, quadratic growth (see also breeder) being the fastest. Dean Hickerson has found many patterns with unusual growth rates, such as sawtooths and a caber tosser. Another pattern with superlinear but non-quadratic growth is Gotts dots.
See also Fermat prime calculator.
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.
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.
Each cell with three neighbors becomes populated.
Video’s about the Game of Life
Interesting articles about John Conway
These are services I personally use and trust every day. These links are affiliate links, which means I may earn a commission if you choose to make a purchase—at no extra cost to you. This helps support this site and allows me to continue improving it. Thank you for your support!
This site is made by Edwin Martin <edwin@playgameoflife.com>