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{{Glossary}}
{{Glossary}}
A '''methuselah''' is, roughly speaking, 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. In particular, patterns that grow forever are not methuselahs. Their exact definition is not completely agreed upon, and most definitions place restrictions on the number of [[cell]]s in the initial pattern.
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.


[[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> though some sources allow for more cells or require a longer lifespan.
[[Image:Rpentomino.png|framed|right|[[R-pentomino]]]]
[[Image:Rpent_final.png|right|thumb|Generation 1103 of R-pentomino (excluding six gliders).]]


Trivial patterns, such as a [[glider]] heading towards an arbitrarily distant [[block]], are not generally considered methuselahs.
[[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).
 
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]] 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.


==Examples==
==Examples==
The smallest 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. The [[acorn]], a pattern of seven cells developed by [[:Category:Patterns found by Charles Corderman|Charles Corderman]], takes 5206 generations to stabilize. Some other popular examples include [[B-heptomino]], [[bunnies]], [[die hard]] and [[rabbits]].
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 [[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]]).
 
{|
{|
|-
|-
|[[Image:Acorn.png|framed|Acorn]]
|[[Image:Acorn.png|framed|Acorn]]
|[[Image:Bheptomino.png|framed|B-heptomino]]
|[[Image:Bheptomino.png|framed|B-heptomino]]
|[[Image:Rpentomino.png|framed|R-pentomino]]
|[[Image:Piheptomino.png|framed|Pi-heptomino]]
|[[Image:Rabbits.png|framed|Rabbits]]
|}
|}


The longest-lived methuselah known to date, [http://www.conwaylife.com/forums/viewtopic.php?p=4610#p4610 40514M], was discovered by [[:Category:Patterns found by knightlife|knightlife]]. It has an initial population of 18, a final population of 3735, takes 40514 generations to stabilize, and fits within a 78&times;54 [[bounding box]].
===Soup searches===
{{EmbedViewer
|pname = 47575m
|caption = [[47575M]]
|viewerconfig = #C [[ WIDTH 480 HEIGHT 480 ]]
}}
[[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 non-infinitely-growing{{refn|group=note|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" /> however, this is often not counted as a methuselah.<ref name="post76185" /> Symmetric soups are also known which take up to 64,935,262 generations to "go boring".<ref name="post86214" />}} 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".
 
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==
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.
 
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.


==See also==
==See also==
*[[List of long-lived methuselahs]]
*[[List of long-lived methuselahs]]
*[[:Category:Methuselahs|List of methuselahs]]
*[[:Category:Methuselahs|List of methuselahs]]
==Notes==
<references group=note />


==References==
==References==
<references />
<references>
<ref name="thread609">{{LinkForumThread
|format = ref
|t      = 609
|f      = 7
|title  = Methuselah Definition
}}</ref>
<ref name="post65133">{{LinkForumThread
|format    = ref
|author    = Adam P. Goucher
|date      = October 28, 2018
|p          = 65133
|title      = Re: apgsearch v4.0
}}</ref>
<ref name="post76165">{{LinkForumThread
|format = ref
|title  = Re: Soup search results
|p      = 76165
|author = Oscar Cunningham
|date  = May 12, 2019
}}</ref>
<ref name="post76185">{{LinkForumThread
|format = ref
|title  = Re: Soup search results
|p      = 76185
|author = Dave Greene
|date  = May 12, 2019
}}</ref>
<ref name="post86214">{{LinkForumThread
|format = ref
|title  = Methuselah-ish Symmetric Soups
|p      = 86214
|author = Dave Greene
|date  = December 12, 2019
}}</ref>
<ref name="post70221">{{LinkForumThread
|format    = ref
|author    = Ian07
|date      = February 10, 2019
|p          = 70221
|title      = Re: Soup search results
}}</ref>
<ref name="post66402">{{LinkForumThread
|format    = ref
|author    = Ian07
|date      = December 11, 2018
|p          = 66402
|title      = Re: apgsearch v4.0
}}</ref>
<ref name="post55298">{{LinkForumThread
|format    = ref
|author    = Oscar Cunningham
|date      = January 20, 2018
|p          = 55298
|title      = Re: Largest and oldest methuselah ever found!
}}</ref>
</references>


==External links==
==External links==
[http://www.argentum.freeserve.co.uk/lex_m.htm#methuselah Methuselah] at the Life Lexicon
{{LinkWikipedia|Methuselah_(cellular_automaton)}}
{{LinkLexicon|lex_m.htm#methuselah}}

Revision as of 04:32, 30 December 2019

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] 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

#O Adam P. Goucher, February 10, 2019 #C A methuselah with a lifespan of 47575 generations, found using apgsearch. x = 16, y = 16, rule = B3/S23 5b2ob2o2bob2o$2bo2bo4b3obo$o2b2obobob2o3bo$bob2o3b2o2b3o$3o8b2o2bo$bob 3o4b3ob2o$bob4obob3o$ob2obo2bo3b3o$2b4o2b4o2bo$6b2o2bobob2o$o3bo2bo2b 5o$2b4o3b7o$o2b2o2bob2ob3o$o2bo3b2o3bobo$2ob2obob8o$6o3bobo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ WIDTH 480 HEIGHT 480 ]]
47575M
(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 2019, the longest-lasting non-infinitely-growing[note 1] methuselah found using apgsearch takes 47575 generations to stabilize and was found by Adam P. Goucher on February 10, 2019.[11] Versions v4.69 and above also report diehards lasting at least 500 generations, referring to them as "messless methuselahs".[12][note 2] 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.[note 3][note 4]

Measuring methuselahs

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,[13] resulting in the L/MCPS metric, the quotient of the methuselah's lifespan and its MCPS.

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.

See also

Notes

  1. ↑ 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;[8] however, this is often not counted as a methuselah.[9] Symmetric soups are also known which take up to 64,935,262 generations to "go boring".[10]
  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. ↑ 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. ↑ Oscar Cunningham (May 12, 2019). Re: Soup search results (discussion thread) at the ConwayLife.com forums
  9. ↑ Dave Greene (May 12, 2019). Re: Soup search results (discussion thread) at the ConwayLife.com forums
  10. ↑ Dave Greene (December 12, 2019). Methuselah-ish Symmetric Soups (discussion thread) at the ConwayLife.com forums
  11. ↑ Ian07 (February 10, 2019). Re: Soup search results (discussion thread) at the ConwayLife.com forums
  12. ↑ Ian07 (December 11, 2018). Re: apgsearch v4.0 (discussion thread) at the ConwayLife.com forums
  13. ↑ Oscar Cunningham (January 20, 2018). Re: Largest and oldest methuselah ever found! (discussion thread) at the ConwayLife.com forums

External links

Retrieved from "https://conwaylife.com/w/index.php?title=Methuselah&oldid=67505"