Methuselah

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, but patterns that stabilize in less than 100 generations are not generally called methuselahs.

R-pentomino

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. 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. 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.

Examples

The smallest and most well-known methuselah is the R-pentomino, a pattern of five cells first considered by John Conway 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. 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).

Acorn

B-heptomino

Pi-heptomino

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.

Versions v4.54 and above of apgsearch report soups lasting at least 25,000 generations, allowing the results to be tabulated on Catagolue. 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. Versions v4.69 and above also report diehards lasting at least 500 generations, referring to them as "messless methuselahs". After v5.03, apgsearch also reports soups with a stabilization population of above 3000 in a category of "megasized methuselae".

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

Infinite growth

Although they are often not counted as methuselahs due to not technically stabilizing, 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. Another soup, based on a crystal reaction, was found by Liston on May 29, 2020 lasting 10,514,926 generations. On February 9, 2021, another soup was found by Adam P. Goucher which continues producing novelty until generation 95,206,595. Symmetric soups are also known which take up to 225,593,194 generations to "go boring".

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. 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. 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. Later, a newcomer gravity found 20 × 20 methuselahs lasting 13,629,876 and 126,932,978 generations respectively.

On July 30, 2022, Charity Engine found a symmetric soup lasting 128,719 generations involving switch engine pairs being destroyed. 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.

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	In 2018, Oscar Cunningham suggested using the minimum covering polyplet size (MCPS) as a compromise between population and bounding box, resulting in this metric As it relies on both the initial population and bounding box of the methuselah, it is considered superior to L/I
L/I: Lifespan per Initial population	First suggested by Don Woods in 1971 under the name of evolutionary factor 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 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

• List of long-lived methuselahs
• Methuselahs (category)
• Stable

External links

• Methuselah at Wikipedia
• Methuselah at the Life Lexicon