From LifeWiki
(Redirected from F/L)
Jump to navigation Jump to search

A methuselah is a pattern that takes a large number of generations in order to stabilize (known as its lifespan) and becomes much larger than its initial configuration at some point during its evolution. There is no consensus on the exact definition,[1] but patterns that stabilize in less than 100 generations are not generally called methuselahs.

Generation 1103 of R-pentomino (excluding six gliders).

Martin Gardner defined methuselahs as patterns of fewer than ten cells that take longer than 50 generations to stabilize.[2][note 1] Some other interpretations allow for more cells while requiring a longer lifespan, or characterize the size of an initial configuration by the size of its bounding box instead of the number of cells. Others use more complex metrics to measure the "quality" of methuselahs (see Measuring methuselahs below).

The time when a pattern is considered to have stabilized is commonly agreed upon to be the first generation such that the pattern can be resolved into still lifes, oscillators and escaping spaceships, provided such a generation exists. For infinitely growing patterns, no agreed-upon definition is known, although the Life Lexicon describes a particular ark as stabilizing at generation 736692.[3] Most interpretations exclude such patterns.

There is no limit to the lifespan of a pattern with 8 or more cells, as a methuselah consisting of a glider heading towards an arbitrarily distant blinker or pre-block can be trivially constructed. Therefore, patterns with excessively large bounding boxes are generally implicitly excluded.

Methuselahs which eventually disappear are known as diehards.


The smallest and most well-known methuselah is the R-pentomino, a pattern of five cells first considered by John Conway[4] that takes 1103 generations before stabilizing as a pattern of eight blocks, six gliders, four beehives, four blinkers, one boat, one loaf, and one ship. This methuselah is particularly notable since almost all other patterns of similar size stabilize within 10 generations.

Martin Gardner gave the first well-known definition of a methuselah along with some examples. Among the examples are pi-heptomino, thunderbird, B-heptomino and acorn.[5] The acorn, a pattern of seven cells developed by Charles Corderman, takes 5206 generations to stabilize.

Because they are very active, frequently-appearing methuselahs can be used as conduit objects. Known methuselahs of this type include B-heptomino, century, Herschel, pi-heptomino, queen bee, R-pentomino, and wing (also known as Block and glider).


Soup searches

x = 16, y = 16, rule = B3/S23 3o2b2obob2ob3o$2obob3o4bobo$bo2bo2bobob3obo$2bo2b2o3bo2bo$2bo5bobo3b2o $o4b2o3b3obo$3b2o2bo2bobo2bo$2b4obo2bob2o$2ob2o2b2o5b2o$ob4obo4b3o$o3b 4o2b3o$b10o2b3o$2o3bob3obob3o$b2ob6o3bobo$obo5b4obo$3obobob2o5bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ WIDTH 600 HEIGHT 600 ]]
52513M, a methuselah found using apgsearch
(click above to open LifeViewer)
RLE: here Plaintext: here

Soup searching is a popular method of finding methuselahs fitting within a given bounding box. The Online Life-Like CA Soup Search, for example, collected the longest-lasting soups found using Nathaniel Johnston's search script. The longest-lasting soup found in this census was Fred, which takes 35426 generations to stabilize and was found by Schneelocke on May 15, 2010.[6]

Versions v4.54 and above of apgsearch report soups lasting at least 25,000 generations, allowing the results to be tabulated on Catagolue.[7] As of early 2021, the longest-lasting non-infinitely-growing methuselah found using apgsearch takes 52513 generations to stabilize and was found by Dylan Chen on January 16, 2021.[8] Versions v4.69 and above also report diehards lasting at least 500 generations, referring to them as "messless methuselahs".[9][note 2] After v5.03, apgsearch also reports soups with a stabilization population of above 3000 in a category of "megasized methuselae".[10]

Due to the difficulty of testing a soup's ash for stability, both of these censuses estimate the lifespan of methuselahs found.[note 3][note 4]

Infinite growth

Although they are often not counted as methuselahs due to not technically stabilizing,[11] infinitely growing soups can potentially take hundreds of thousands or even millions of generations to "go boring", i.e. to stop producing novelty. An infinitely growing soup which "goes boring" after 133100 generations due to a backwards-firing stream of gliders was found by Rob Liston on May 12, 2019.[12] Another soup, based on a crystal reaction, was found by Liston on May 29, 2020 lasting 10,514,926 generations.[13] On February 9, 2021, another soup was found by Adam P. Goucher which continues producing novelty until generation 95,206,595.[14] Symmetric soups are also known which take up to 225,593,194 generations to "go boring".[15]

However, switch engine-based patterns can still qualify as methuselahs if the switch engines are destroyed, specifically by forward-facing gliders catching up to them. On December 16, 2019, Paul Callahan found a 30 × 16 methuselah involving a period-96 puffer which is destroyed after approximately 1.3 million generations, before the pattern as a whole finally stabilizes at generation 1,730,304.[16] On July 2, 2022, yaochen2 found another pattern using this same puffer but fitting within a 15 × 16 bounding box and lasting 71,093 generations.[17] This was the first time since 2018 that the record for the longest-lasting known methuselah within 16 × 16 was not held by an apgsearch soup (or derivative thereof). Further searching of similar patterns by dani led to the discovery of a 16 × 16 methuselah lasting 4,764,364 generations.[18] Later, a newcomer gravity found 20 × 20 methuselahs lasting 13,629,876[19] and 126,932,978[20] generations respectively.

On July 30, 2022, Charity Engine found a symmetric soup lasting 128,719 generations involving switch engine pairs being destroyed.[21] On August 2, it found a second soup lasting 132,364 generations, making it the longest-lasting methuselah to be classified as such in an official Catagolue census.[22]

Measuring methuselahs

Various metrics have been proposed to measure the quality of methuselahs so as to reward patterns such as the R-pentomino and acorn while penalizing trivial examples such as the glider-and-blinker construction mentioned above.

metric comments
L/MCPS: Lifespan per MCPS
L/I: Lifespan per Initial population
  • First suggested by Don Woods in 1971 under the name of evolutionary factor[24]
  • For example, R-pentomino has an L/I of 220.6
F/I: Final population per Initial population
  • Benchmarks the growth of a methuselah, i.e. the number of new cells born
  • First suggested in 1971[25]
  • Used to track the quality of mega-sized soups in apgsearch, and is censused in non-vanilla apgsearch versions such as 10x10
  • The most superior methuselah in this respect is 24827M
F/L: Final population per Lifespan

See also


  1. The first such use of the term methuselah thus defined is credited to Hugh W. Thompson in 1971 in Lifeline Volume 3.
  2. Methuselahs and diehards are only reported by apgsearch in symmetries of Conway's Game of Life.
  3. Long-lived soups found as part of TOLLCASS had their exact lifespan verified manually.
  4. apgsearch automatically tests the lifespan of a soup more precisely if its estimated lifespan is sufficiently high, but is not guaranteed to detect all methuselahs with a lifespan of less than 26,000 generations.


  1. lifespeed (February 6, 2011). Methuselah Definition (discussion thread) at the forums
  2. Gardner, M. (1983). "The Game of Life, Part III". Wheels, Life and Other Mathematical Amusements: 246, W.H. Freeman. 
  3. "Ark". The Life Lexicon. Stephen Silver. Retrieved on March 14, 2016.
  4. Gardner, M. (1983). "The Game of Life, Part III". Wheels, Life and Other Mathematical Amusements: 219, 223, W.H. Freeman. 
  5. Gardner, M. (1983). "The Game of Life, Part III". Wheels, Life and Other Mathematical Amusements: 246, W.H. Freeman. 
  6. "Long-Lived Patterns in Conway's Life". Online Life-Like CA Soup Search. Retrieved on March 2, 2019. (archived from the original)
  7. Adam P. Goucher (October 28, 2018). Re: apgsearch v4.0 (discussion thread) at the forums
  8. creeperman7002 (January 16, 2021). Re: Soup search results (discussion thread) at the forums
  9. Ian07 (December 11, 2018). Re: apgsearch v4.0 (discussion thread) at the forums
  10. Adam P. Goucher (March 24, 2019). Re: apgsearch v5.0 (discussion thread) at the forums
  11. Dave Greene (May 12, 2019). Re: Soup search results (discussion thread) at the forums
  12. Oscar Cunningham (May 12, 2019). Re: Soup search results (discussion thread) at the forums
  13. Adam P. Goucher (June 17, 2020). Re: Soup search results (discussion thread) at the forums
  14. Ian07 (February 11, 2021). Re: Soup search results (discussion thread) at the forums
  15. dani (April 11, 2022). Re: Soup search results (discussion thread) at the forums
  16. Paul Callahan (December 16, 2019). Re: Methuselah-ish Symmetric Soups (discussion thread) at the forums
  17. yaochen2 (July 2, 2022). Re: Thread For Your Useless Discoveries (discussion thread) at the forums
  18. dani (July 3, 2022). Re: Thread for your unsure discoveries (discussion thread) at the forums
  19. gravity (October 20, 2022). Re: Thread for your unsure discoveries (discussion thread) at the forums
  20. gravity (November 21, 2022). Re: Thread for your unsure discoveries (discussion thread) at the forums
  21. dani (July 30, 2022). Re: Soup search results (discussion thread) at the forums
  22. dani (August 2, 2022). Re: Soup search results (discussion thread) at the forums
  23. Oscar Cunningham (January 20, 2018). Re: Largest and oldest methuselah ever found! (discussion thread) at the forums
  24. Robert Wainwright (March 1971). Lifeline, vol 1, page 6.
  25. Robert Wainwright (September 1971). Lifeline, vol 3, page 8.

External links