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{{Glossary}}
{{Glossary}}
A '''methuselah''' is a [[pattern]] that takes a large number of [[generation]]s 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,<ref name="thread609" /> but patterns that stabilize in less than 100 generations are not generally called methuselahs.
A '''methuselah''' is a [[pattern]] that takes a large number of [[generation]]s 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,<ref name="thread609" /> but patterns that stabilize in less than 100 generations are not generally called methuselahs.


[[Image:Rpentomino.png|framed|right|[[R-pentomino]]]]
[[File:Rpentomino.png|thumb|right|[[R-pentomino]]]]
[[Image:Rpent_final.png|right|thumb|Generation 1103 of R-pentomino (excluding six gliders).]]
[[File :Rpent final.png|right|thumb|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.<ref>{{cite conference|author=[[Martin Gardner|Gardner, M.]]|title=The Game of Life, Part III|booktitle=Wheels, Life and Other Mathematical Amusements|year=1983|publisher=W.H. Freeman|pages=246}}</ref> 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|Measuring methuselahs]] below).
[[Martin Gardner]] defined methuselahs as patterns of fewer than ten cells that take longer than 50 generations to stabilize.<ref>{{cite conference|author=[[Martin Gardner|Gardner, M.]]|title=The Game of Life, Part III|booktitle=Wheels, Life and Other Mathematical Amusements|year=1983|publisher=W.H. Freeman|pages=246}}</ref>{{refn|group="note"|The first such use of the term methuselah thus defined is credited to Hugh W. Thompson in 1971 in [[Lifeline Volume 3]].}} 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|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 life]]s, [[oscillator]]s and escaping [[spaceship]]s, 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.<ref>{{CiteLexicon|file=lex_a.htm#ark||name=Ark|accessdate=March 14, 2016}}</ref> Most interpretations exclude such patterns.
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 life]]s, [[oscillator]]s and escaping [[spaceship]]s, 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.<ref>{{CiteLexicon|file=lex_a.htm#ark||name=Ark|accessdate=March 14, 2016}}</ref> Most interpretations exclude such patterns.


There is no limit to the lifespan of a pattern with 8 or more [[cell]]s, as a methuselah consisting of a [[glider]] heading towards an arbitrarily distant [[blinker]] can be trivially constructed. Therefore, patterns with excessively large bounding boxes are generally implicitly excluded.
There is no limit to the lifespan of a pattern with 8 or more [[cell]]s, 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 [[diehard]]s.
Methuselahs which eventually disappear are known as [[diehard]]s.


==Examples==
== Examples ==
The smallest and most well-known methuselah is the [[R-pentomino]], a pattern of five cells first considered by [[:Category:Patterns found by John Conway|John Conway]]<ref>{{cite conference|author=[[Martin Gardner|Gardner, M.]]|title=The Game of Life, Part III|booktitle=Wheels, Life and Other Mathematical Amusements|year=1983|publisher=W.H. Freeman|pages=219, 223}}</ref> 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.
The smallest and most well-known methuselah is the [[R-pentomino]], a pattern of five cells first considered by [[John Conway]]<ref>{{cite conference|author=[[Martin Gardner|Gardner, M.]]|title=The Game of Life, Part III|booktitle=Wheels, Life and Other Mathematical Amusements|year=1983|publisher=W.H. Freeman|pages=219, 223}}</ref> 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]].<ref>{{cite conference|author=[[Martin Gardner|Gardner, M.]]|title=The Game of Life, Part III|booktitle=Wheels, Life and Other Mathematical Amusements|year=1983|publisher=W.H. Freeman|pages=246}}</ref> The [[acorn]], a pattern of seven cells developed by [[:Category:Patterns found by Charles Corderman|Charles Corderman]], takes 5206 generations to stabilize.
[[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]].<ref>{{cite conference|author=[[Martin Gardner|Gardner, M.]]|title=The Game of Life, Part III|booktitle=Wheels, Life and Other Mathematical Amusements|year=1983|publisher=W.H. Freeman|pages=246}}</ref> 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]]).
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]]).


{|
{|
|-
|[[File:Acorn.png|thumb|Acorn]]
|[[Image:Acorn.png|framed|Acorn]]
|[[File:Bheptomino.png|thumb|B-heptomino]]
|[[Image:Bheptomino.png|framed|B-heptomino]]
|[[File:Piheptomino.png|thumb|Pi-heptomino]]
|[[Image:Piheptomino.png|framed|Pi-heptomino]]
|}
|}


===Soup searches===
=== Soup searches ===
{{EmbedViewer
{| style="margin-left:16px; margin-bottom:8px; width:300px; float:right"
|pname = 47575m
|{{EmbedViewer
|caption = [[47575M]]
|pname       = 52513m
|viewerconfig = #C [[ WIDTH 480 HEIGHT 480 ]]
|viewerconfig = #C [[ WIDTH 600 HEIGHT 600 ]]
|position    = center
|caption      = [[52513M]], a methuselah found using [[apgsearch]]
}}
}}
|}
[[Soup search]]ing 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 [[soup]]s 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, {{year|2010}}.<ref>{{Cite web|url=https://web.archive.org/web/20101203183556/http://www.conwaylife.com/soup/methuselahs.asp?rule=B3/S23|title=Long-Lived Patterns in Conway's Life|work=Online Life-Like CA Soup Search|accessdate=March 2, 2019}} (archived from the original)</ref>
[[Soup search]]ing 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 [[soup]]s 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, {{year|2010}}.<ref>{{Cite web|url=https://web.archive.org/web/20101203183556/http://www.conwaylife.com/soup/methuselahs.asp?rule=B3/S23|title=Long-Lived Patterns in Conway's Life|work=Online Life-Like CA Soup Search|accessdate=March 2, 2019}} (archived from the original)</ref>


Versions v4.54 and above of [[apgsearch]] report soups lasting at least 25,000 generations, allowing the results to be tabulated on [[Catagolue]].<ref name="post65133" /> As of early 2019, the longest-lasting methuselah found using apgsearch takes 47575 generations to stabilize and was found by [[Adam P. Goucher]] on February 10, {{year|2019}}.<ref name="post70221" /> Versions v4.69 and above also report [[diehard]]s lasting at least 500 generations, referring to them as "messless methuselahs".<ref name="post66402" />{{refn|group=note|Methuselahs and diehards are only reported by apgsearch in symmetries of [[Conway's Game of Life]].}} After v5.03, apgsearch also reports soups with a stabilization population of above 3000 in a category of "megasized methuselae".
Versions v4.54 and above of [[apgsearch]] report soups lasting at least 25,000 generations, allowing the results to be tabulated on [[Catagolue]].<ref name="post65133" /> {{AS OF|early 2021}}, the longest-lasting non-infinitely-growing methuselah found using apgsearch takes [[52513M|52513 generations to stabilize]] and was found by [[Dylan Chen]] on January 16, {{year|2021}}.<ref name="post119406" /> Versions v4.69 and above also report [[diehard]]s lasting at least 500 generations, referring to them as "messless methuselahs".<ref name="post66402" />{{refn|group=note|Methuselahs and diehards are only reported by apgsearch in symmetries of [[Conway's Game of Life]].}} After v5.03, apgsearch also reports soups with a stabilization population of above 3000 in a category of "megasized methuselae".<ref name="post73826" />


Due to the difficulty of testing a soup's [[ash]] for stability, both of these censuses estimate the lifespan of methuselahs found.{{refn|group=note|Long-lived soups found as part of TOLLCASS had their exact lifespan verified manually.}}{{refn|group=note|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.}}
Due to the difficulty of testing a soup's [[ash]] for stability, both of these censuses estimate the lifespan of methuselahs found.{{refn|group=note|Long-lived soups found as part of TOLLCASS had their exact lifespan verified manually.}}{{refn|group=note|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.}}


==Measuring methuselahs==
==== Infinite growth ====
Various metrics have been proposed to measure 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. [[Oscar Cunningham]] suggested using the [[minimum covering polyplet size]] (MCPS) for this as a compromise between population and [[bounding box]],<ref name="post55298" /> resulting in the [[L/MCPS]] metric, the quotient of the methuselah's lifespan and its MCPS.
Although they are often not counted as methuselahs due to not technically stabilizing,<ref name="post76185" /> 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.<ref name="post76165" /> Another soup, based on a [[crystal]] reaction, was found by Liston on May 29, 2020 lasting 10,514,926 generations.<ref name="post99036" /> On February 9, {{year|2021}}, another soup was found by Adam P. Goucher which continues producing novelty until generation 95,206,595.<ref name="post122507" /> Symmetric soups are also known which take up to 225,593,194 generations to "go boring".<ref name="post144121" />
 
However, [[switch engine]]-based patterns can still [[List of long-lived methuselahs#Puffer-based methuselahs|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 {{times|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.<ref name="post86308" /> On July 2, {{year|2022}}, [[yaochen2]] found another pattern using this same puffer but fitting within a {{times|15|16}} bounding box and lasting 71,093 generations.<ref name="post147829" /> This was the first time since 2018 that the record for the longest-lasting known methuselah within {{times|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 {{times|16|16}} methuselah lasting 4,764,364 generations.<ref name="post147834" /> Later, a newcomer [[gravity]] found {{times|20|20}} methuselahs lasting 13,629,876<ref name="post152437" /> and 126,932,978<ref name="post153956" /> generations respectively.


Other quotient-based metrics include [[F/I]], [[F/L]], and [[L/I]], with ''F'', ''I'', and ''L'' standing for final population, initial population, and lifespan respectively.
On July 30, 2022, [[Charity Engine]] found a symmetric soup lasting 128,719 generations involving switch engine pairs being destroyed.<ref name="post148949" /> 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.<ref name="post149071" />


==See also==
== Measuring methuselahs ==
*[[List of long-lived 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.
*[[:Category:Methuselahs|List of methuselahs]]


==Notes==
{| class="wikitable"
! 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]],<ref name="post55298" /> 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''<ref>{{CiteLifeline|vol=1|pages=page 6}}</ref>
* 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<ref>{{CiteLifeline|vol=3|pages=page 8}}</ref>
* 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]]
* {{CategoryLink|Methuselahs}}
* [[Stable]]
 
== Notes ==
<references group=note />
<references group=note />


==References==
== References ==
<references>
<references>
<ref name="thread609">{{LinkForumThread
<ref name="thread609">{{LinkForumThread
Line 58: Line 91:
|f      = 7
|f      = 7
|title  = Methuselah Definition
|title  = Methuselah Definition
|author = lifespeed
|date  = February 6, 2011
}}</ref>
<ref name="post55298">{{LinkForumThread
|format = ref
|p      = 55298
|title  = Re: Largest and oldest methuselah ever found!
|author = Oscar Cunningham
|date  = January 20, 2018
}}</ref>
}}</ref>
<ref name="post65133">{{LinkForumThread
<ref name="post65133">{{LinkForumThread
|format     = ref
|format = ref
|author     = Adam P. Goucher
|p      = 65133
|date       = October 28, 2018
|title  = Re: apgsearch v4.0
|p         = 65133
|author = Adam P. Goucher
|title      = Re: apgsearch v4.0
|date   = October 28, 2018
}}</ref>
<ref name="post66402">{{LinkForumThread
|format = ref
|p     = 66402
|title = Re: apgsearch v4.0
|author = Ian07
|date  = December 11, 2018
}}</ref>
<ref name="post73826">{{LinkForumThread
|format = ref
|p     = 73826
|title  = Re: apgsearch v5.0
|author = Adam P. Goucher
|date  = March 24, 2019
}}</ref>
<ref name="post76165">{{LinkForumThread
|format = ref
|p      = 76165
|title  = Re: Soup search results
|author = Oscar Cunningham
|date  = May 12, 2019
}}</ref>
<ref name="post76185">{{LinkForumThread
|format = ref
|p      = 76185
|title  = Re: Soup search results
|author = Dave Greene
|date  = May 12, 2019
}}</ref>
<ref name="post86308">{{LinkForumThread
|format = ref
|p      = 86308
|title  = Re: Methuselah-ish Symmetric Soups
|author = Paul Callahan
|date  = December 16, 2019
}}</ref>
<ref name="post99036">{{LinkForumThread
|format = ref
|p      = 99036
|title  = Re: Soup search results
|author = Adam P. Goucher
|date  = June 17, 2020
}}</ref>
<ref name="post119406">{{LinkForumThread
|format = ref
|p      = 119406
|title  = Re: Soup search results
|author = creeperman7002
|date  = January 16, 2021
}}</ref>
<ref name="post122507">{{LinkForumThread
|format = ref
|p      = 122507
|title  = Re: Soup search results
|author = Ian07
|date  = February 11, 2021
}}</ref>
<ref name="post144121">{{LinkForumThread
|format = ref
|p      = 144121
|title  = Re: Soup search results
|author = dani
|date  = April 11, 2022
}}</ref>
<ref name="post147829">{{LinkForumThread
|format = ref
|p      = 147829
|title  = Re: Thread For Your Useless Discoveries
|author = yaochen2
|date  = July 2, 2022
}}</ref>
<ref name="post147834">{{LinkForumThread
|format = ref
|p      = 147834
|title  = Re: Thread for your unsure discoveries
|author = dani
|date  = July 3, 2022
}}</ref>
}}</ref>
<ref name="post70221">{{LinkForumThread
<ref name="post148949">{{LinkForumThread
|format     = ref
|format = ref
|author    = Ian07
|p     = 148949
|date      = February 10, 2019
|title = Re: Soup search results
|p         = 70221
|author = dani
|title     = Re: Soup search results
|date  = July 30, 2022
}}</ref>
}}</ref>
<ref name="post66402">{{LinkForumThread
<ref name="post149071">{{LinkForumThread
|format     = ref
|format = ref
|author     = Ian07
|p      = 149071
|date       = December 11, 2018
|title  = Re: Soup search results
|p         = 66402
|author = dani
|title     = Re: apgsearch v4.0
|date   = August 2, 2022
}}</ref>
<ref name="post152437">{{LinkForumThread
|format = ref
|p     = 152437
|title = Re: Thread for your unsure discoveries
|author = gravity
|date  = October 20, 2022
}}</ref>
}}</ref>
<ref name="post55298">{{LinkForumThread
<ref name="post153956">{{LinkForumThread
|format     = ref
|format = ref
|author    = Oscar Cunningham
|p      = 153956
|date      = January 20, 2018
|title  = Re: Thread for your unsure discoveries
|p          = 55298
|author = gravity
|title      = Re: Largest and oldest methuselah ever found!
|date  = November 21, 2022
}}</ref>
}}</ref>
</references>
</references>


==External links==
== External links ==
{{LinkWikipedia|Methuselah_(cellular_automaton)}}
* {{LinkWikipedia|Methuselah_(cellular_automaton)}}
{{LinkLexicon|lex_m.htm#methuselah}}
* {{LinkLexicon|lex_m.htm#methuselah}}

Latest revision as of 22:08, 13 September 2025

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.

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.[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.

Examples

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).

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.[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

Notes

  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.

References

  1. ↑ lifespeed (February 6, 2011). Methuselah Definition (discussion thread) at the ConwayLife.com 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 ConwayLife.com forums
  8. ↑ creeperman7002 (January 16, 2021). Re: Soup search results (discussion thread) at the ConwayLife.com forums
  9. ↑ Ian07 (December 11, 2018). Re: apgsearch v4.0 (discussion thread) at the ConwayLife.com forums
  10. ↑ Adam P. Goucher (March 24, 2019). Re: apgsearch v5.0 (discussion thread) at the ConwayLife.com forums
  11. ↑ Dave Greene (May 12, 2019). Re: Soup search results (discussion thread) at the ConwayLife.com forums
  12. ↑ Oscar Cunningham (May 12, 2019). Re: Soup search results (discussion thread) at the ConwayLife.com forums
  13. ↑ Adam P. Goucher (June 17, 2020). Re: Soup search results (discussion thread) at the ConwayLife.com forums
  14. ↑ Ian07 (February 11, 2021). Re: Soup search results (discussion thread) at the ConwayLife.com forums
  15. ↑ dani (April 11, 2022). Re: Soup search results (discussion thread) at the ConwayLife.com forums
  16. ↑ Paul Callahan (December 16, 2019). Re: Methuselah-ish Symmetric Soups (discussion thread) at the ConwayLife.com forums
  17. ↑ yaochen2 (July 2, 2022). Re: Thread For Your Useless Discoveries (discussion thread) at the ConwayLife.com forums
  18. ↑ dani (July 3, 2022). Re: Thread for your unsure discoveries (discussion thread) at the ConwayLife.com forums
  19. ↑ gravity (October 20, 2022). Re: Thread for your unsure discoveries (discussion thread) at the ConwayLife.com forums
  20. ↑ gravity (November 21, 2022). Re: Thread for your unsure discoveries (discussion thread) at the ConwayLife.com forums
  21. ↑ dani (July 30, 2022). Re: Soup search results (discussion thread) at the ConwayLife.com forums
  22. ↑ dani (August 2, 2022). Re: Soup search results (discussion thread) at the ConwayLife.com forums
  23. ↑ Oscar Cunningham (January 20, 2018). Re: Largest and oldest methuselah ever found! (discussion thread) at the ConwayLife.com forums
  24. ↑ Robert Wainwright (March 1971). Lifeline, vol 1, page 6.
  25. ↑ Robert Wainwright (September 1971). Lifeline, vol 3, page 8.
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