Main Page

From LifeWiki
Jump to: navigation, search
Welcome to LifeWiki,
the wiki for Conway's Game of Life.
Currently contains 1,134 articles.
Overview · How to contribute · Image gallery · Popular pages · A–Z index

This week's featured article

A one cell thick pattern is a pattern that is only one cell thick; that is, it is contained entirely within one dimension of the Life plane. Put another way, it is a pattern with bounding box of the form y×1 for some natural number y. Because of their size restriction, exhaustive computer searches have been carried out to explore one cell thick patterns up to size about 40×1. Despite their inherent limitations, one cell thick patterns can exhibit quite complex behavior, even at reasonably small sizes.

In May 1998, Stephen Silver produced a one cell thick pattern that exhibits infinite growth, following a conjecture of Nick Gotts that such patterns exist. This pattern was extremely large (12470×1 in the first version, reduced to 5447×1 the following day). In October 1998, Paul Callahan performed an exhaustive computer search to find the following pattern that exhibits infinite growth. It is probably the most well-known one cell thick pattern, and Callahan showed that it is the smallest such one cell thick pattern (in terms of its bounding box) to exhibit infinite growth. It contains 28 alive cells and has a 39×1 bounding box.

Unidimensional infinite.png

Pattern collection

The LifeWiki contains one of the most comprehensive catalogues of patterns available on the internet. Within it you will find:
Download.gif Download pattern collection
2Mb .zip archive containing the 3000+ pattern files used on the wiki

Did you know...

  • ... that any glider-constructible Life pattern can be constructed with a fixed maximum number of gliders N, probably less than 1000? It's only necessary to construct a sliding-block decoder, which self-destructs after converting the position of a far-distant block into a slow-salvo recipe that constructs the required pattern.
  • ...that the largest interesting pattern constructed, the caterpillar, contains over 11 million cells?
  • ...that the Gosper glider gun was the first pattern to be discovered that exhibits infinite growth?
  • ...that the block-laying switch engine and the glider-producing switch engine are the only two infinitely-growing patterns that are known to have ever occurred naturally from a nonsymmetric random starting configuration?
  • ...that oscillators are known that oscillate at all periods other than 19, 23, 34, 38 and 41?
  • ...that the pentadecathlon and the blinker are the only known oscillators that are polyominos in more than one phase?
  • ...that it is impossible for a period 3 oscillator to be a phoenix?
  • ...that the methuselah with the longest known lifespan, 40514M, lasts for over 40,000 generations before stabilizing? The second-place holder, Fred, runs for over 35,000 ticks.
  • ...that replicators with quadratic population growth are known to exist in Conway's Game of Life, but none have yet been found?
  • ...that the first known period 37 and 51 oscillators were found in 2009?          
Showing 10 items out of 56 More did you know...