LifeWiki - User contributions [en]

Queen bee

2026-07-29T12:15:32Z

Empty Emptiness: /* See also */

{{Methuselah
|name = Queen bee
|pname = queenbee
|type = Rotor
|c = 12
|bx = 7
|by = 5
|l = 191
|f = 30
|mcps = 12
|symmetry = D2_+1
|discoverer = Robert W. April
|discoveryear = 1970
|rulemin = B3/S23
|rulemax = B38/S238
|rulespecial = [[Conway's Game of Life|Conway Life]]
|isorulemin = B3-k/S23-kr
|isorulemax = B2n34cenqwyz5jkqr6-in7c8/S234cekyz5ekr6-ac7c8
|synthesis = 3
|synthesisRLE = true
|plaintext = true
|rle = true
|viewerconfig = #C [[ HEIGHT 600 WIDTH 600 THUMBSIZE 3 ZOOM 36 ]]
}}
'''Queen bee''' is a somewhat commonly arising pattern that in 15 generations develops into a [[beehive]] and a reflected copy of itself. Left alone, after repeating this process another time, it crashes into the first beehive and explodes (splitting into two [[century|centuries]], which ultimately stabilize into six [[block]]s and two [[blinker]]s at generation 191). It was originally found by [[Robert W. April]] in {{year|1970}} by evolving two parallel lines of length 15 separated by a single empty column. It is simple to stabilize into an [[oscillator]] by deleting the beehives as they are formed, as in the well-known [[queen bee shuttle]]. The term queen bee refers not just to the [[phase]] shown to the right, but also to any of the other phases of the pattern (excluding the beehives it creates) that occur before it explodes.

[[File:Queenbeegen21.png|thumb|center|Generation 21 of queen bee]]

== Turning reaction ==
One of the simplest reactions involves a queen bee involves colliding it with two [[glider]]s that come in from opposite directions in order to turn (reflect) it; this reaction was found by [[David Bell]] and was turned into a period 88 [[oscillator]] (shown below) on March 21, {{year|1996}}. The reaction itself turns the queen bee counterclockwise by 90 degrees in 22 [[generation]]s.<ref>{{CiteSummersPattern|name=jslife|accessdate=June 3, 2009}}</ref>
{{gallery top}}
{{gallery item|{{EmbedViewer
|pname = p88queenbeeturningoscillator
|viewerconfig = #C [[ HEIGHT 600 WIDTH 600 THUMBSIZE 2 ZOOM 4 GPS 11 AUTOSTART ]]
|position = center
|caption = Period 88 queen bee turning oscillator
|style = width:300px;
}}}}
{{gallery item|{{EmbedViewer
|pname = queenbeeturningreaction
|viewerconfig = #C [[ HEIGHT 600 WIDTH 600 THUMBSIZE 2 ZOOM 16 ]]
|position = center
|caption = Two-glider turning reaction
|style = width:300px;
}}}}
{{gallery bottom}}

== Use in conduits ==
The queen bee is a recognized [[conduit]] object, represented by the letter '''Q'''.

== Formation ==
{{EmbedViewer
|rle = o$o$o$b3o$b2o!
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 24 GPS 8 ]]
|position = center
|caption = Queen bees often form along with a tub (Lifespan 1874). This can be seen in both the [[R-pentomino]] sequence around generation 770 and the [[p576 R-pentomino hassler]]
|style = width:300px;
}}

== See also ==
* [[Queen bee shuttle]]
* [[Gosper glider gun]]

== References ==
<references />

== External links ==
* {{LinkForumThread|f=2|t=4752|title=Queen bee}}
* {{LinkCatagolue|xp2_7yaccy5ccya7zybccy5cczybooy5oo|patternname=Queen bee ash}}

[[Category:Gliderless methuselahs]]
[[Category:Polyominoes]]
[[Category:Factories]]
__NOTOC__

OCA:Day & Night

2025-07-07T16:38:42Z

Empty Emptiness: *

{{Rule
|name = Day & Night
|imgname = Day&night
|char = Stable
|b = 3678
|s = 34678
|reversal = [[Day & Night|B3678/S34678]]
|ruleinteger = 242120
|strobing = B01245/S0125
|checkerboard = B1e2cn3acjkr4cny5einqy6ei7c/S01e2-ei3acjkr4-ejr5einqy6-cn7c8
}}
'''Day & Night''' is a [[Life-like cellular automaton]] in which cells survive from one generation to the next if they have 3, 4, 6, 7, or 8 neighbours, and are born if they have 3, 6, 7, or 8 neighbours.

Day & Night is the most well-known [[self-complementary]] rule; that is, if all grid cells have their on/off state exchanged, the history of the pattern is the same as the history of the original.

Nathan Thompson explored the rule starting in April 1997, and [[David Bell]] discussed the rule in detail the following November.

The rule is rich in [[spaceship]]s, [[puffer]]s, and [[oscillator]]s.

On August 14, {{year|2020}}, [[Peter Naszvadi]] constructed a [[Rule 110]] [[unit cell]] in Day & Night, proving the rule [[Turing-complete]].<ref name="post102258" />

==Oscillators==
Day & Night is home to many different periods of oscillators. Here are the smallest known examples of each period up to 16:
{{EmbedViewer
|rle = x = 183, y = 12, rule = B3678/S34678
2o5bo28b2o9b2o55bo77bo$2o5b2o5b4o7bo8b4o9b2o10bobo20b2o5b2o11bob3o9bo
2bo9bobo7b2o9b3o28b2o$8bo6b2o7b3o7b6o6b5o7b6o6b5o6b3o5b3o10b5o9b3obo9b
o8b2o10b2o28b2o$15b2o8bo10b4o7b4o7b6o7b3o7b2o7b2o6b2o2b4o10b5o8bo11bo
9bo3bo7b2ob2o4b2o$15b2o18bob2o9bo9bo2b2o23bo11b9o8b5o8b2ob2o9b2o11b2o
6b4o3b4o$14b4o19b2o22b3o21b3o11b4o2b2o7b5o12bo10b2o11b2o7b9o$60b3o9bo
11b5o10b2o12b5o12bo32b4o3b4o$70b2o13b3o25bob3o11bobo31b2o4b2ob2o$72bo
13bo27bo2bo$70bo10b2o7b2o$71b2o8b3o5b3o$70bo11b2o5b2o!
|position = center}}

==Spaceships==
Many periods of c/2 spaceships are known, but different reduced speeds are common as well. The S8 transition allows many of the spaceships in Day & Night to be stable.

===Rocket===

The rocket was the first spaceship found in Day & Night, and it appears spontaneously from many reactions which have symmetry around a line. This spaceship is probably the reason that this particular Life rule was chosen for Day & Night. It is unexpectedly large and has the amazingly large period of 40.

{{EmbedViewer
|pname = rocket
|position = center
|caption = rocket
|apgcode = xq40_0sfvuvfszw1ovo1z0sgpvpgszwcvvvczookpvpkooz8hvvvvvh8z2pfvvvfp2zw37f73/b3678s34678
|style = width:400px;
}}

The rocket is easily generated from tiny predecessors.

{{EmbedViewer
|rle = x = 412, y = 102, rule = B3678/S34678
b2o$ob2o$8o$ob2o$b2o!
|position = center
|caption = rocket predecessor
|style = width:400px;
}}

===Elementary===

Unsimplified speeds are yet to be tabulated here.

Green means a spaceship has been proven to have minimal population via [[LLSSS]].
{| class="wikitable"
|-
! Speed
! Period
! Direction
! Smallest known
! Minimum # of [[cell]]s
|-
!rowspan=2| [[c/2 orthogonal|c/2]]
| 2
| orthogonal
| [https://conwaylife.com/forums/viewtopic.php?f=11&t=702&p=73855#p73855 29P2H1V0]
|style="background: #80ff80;"| {{cells|29}}
|-
| 4
| orthogonal
| {{LinkCatagolue|xq4_gkevekgzx2|b3678s34678|name=18P4H2V0|style=raw}}
|style="background: #80ff80;"| {{cells|18}}
|-
! [[3c/7 orthogonal|3c/7]]
| 7
| orthogonal
| {{LinkCatagolue|xq7_oggwdraaaardwggozdvo504sf44fs405ovdzupv80adkrrkda08vpuz0devousvvvvsuovedzwfeqctvvvvtcqefz0266ugvvvvvvgu662zwcujb73w37bjuczw1233y23321|b3678s34678|name=316P7H3V0|style=raw}}
| {{cells|316}}
|-
! [[2c/5 orthogonal|2c/5]]
| 5
| orthogonal
| [https://conwaylife.com/forums/viewtopic.php?f=11&t=702&p=73994#p73994 164P5H2V0]
| {{cells|164}}
|-
! [[c/3 orthogonal|c/3]]
| 3
| orthogonal
| {{LinkCatagolue|xq3_oq7sm9wo6335zx10eu2|b3678s34678|name=35P3H1V0|style=raw}}
|style="background: #80ff80;"| {{cells|35}}
|-
! [[2c/7 orthogonal|2c/7]]
| 7
| orthogonal
| {{LinkCatagolue|xq7_wn76oskkso67nzwgg75l55l57ggzctvvuvquuqvuvvtczw22hpffffph22zx3456w6543|b3678s34678|name=160P7H2V0|style=raw}}
| {{cells|160}}
|-
! [[c/4 orthogonal|c/4]]
| 4
| orthogonal
| [https://conwaylife.com/forums/viewtopic.php?f=11&t=702&p=73855#p73855 32P4H1V0]
| 
| {{cells|76}}
|-
! [[c/7 diagonal|c/7]]
| 7
| diagonal
| [https://conwaylife.com/forums/viewtopic.php?f=11&t=702&p=73855#p73855 48P7H1V1]
| {{cells|48}}
|-
! [[c/8 diagonal|c/8]]<ref>{{CiteDiscord|channel=naturalistic|id=1378190150135189597|author=LuveelVoom|date=May 31, 2025}}, which found the first c/8d (but laughably far from the minimal... yes indeed)</ref>
| 8
| diagonal
| {{LinkCatagolue|xq8_yhgg4esif0sczydgmqs40eun4fzy9oauvvse6s47a41zy3g0ooqipp0ec31zgooc4usvvfnff31z364iug5b23zx107|b3678s34678|name=176P8H1V1|style=raw}}
| {{cells|176}}
|}

{{EmbedViewer
|rle = x = 437, y = 103, rule = B3678/S34678
433bo$2b2ob4o5b3o9b5o4b5o13b3o10b3o12b3o11b4o6b4o7bo4bobo4bo8bo2bo5bo2bo15bo16bo5bo14b2o14b3o2b3o44bo14b3o11b3o17b3o15b2o33bo23bo35b2o$b3o3bobo3bobobo8b3obo4bob3o11b3ob3o6b3ob3o8b2ob2o12b2o3b2o3b2o8b2o3b3o3b2o8b2ob2o3b2ob2o14bobo14bobo3bobo13b2o12bob2o4b2obo40b4o13b2obo9b3obo15b5o14b3o31b3o22b3o30b2ob2o$4ob5o3b5o7bob2obo4bob2obo9b3o2b4ob2ob4o2b3o8bobobo11bo2b2o2b2o2bo9b2o2b3o2b2o8b2o4bobo4b2o13b3o14b3o3b3o26b14o39b5o10b3o2b2o11b2o15b6o12bo2b2o33bo21b4o28b4o2bo$b5o6bob3obo7b3o8b3o11b2o2b3ob4ob3o2b2o8b2o2bo13b10o12b2o3b2o10b3o2b5o2b3o13bobo33b2ob2ob2o9bo4b2o4bo39bob5o8bobo4b2o10b2o17b5o12b5o28b2o27b2o26b5ob3o$o3bo2b2o6bo11b2ob6ob2o11bob3o2bob4obo2b3obo8b4ob2o11b8o14b2ob2o12bobob5obobo31b2o5b2o9b2o2b2o2b2o8b2ob2o2b2ob2o39bob3obo7b4o2b4o10bo19b3o46bob2o22bob4o23bo3bo2b3o$14bobo9bo2b2o4b2o2bo10b3o5b6o5b3o8b2o2b2ob2o10bob2obo15b5o55b2o7b2o9b8o11bobo2bobo40bo2b5o5bo2bobo4b2o31bobo44bobobo21bo3bob2o23bo3b3o2bo$27b12o11bo7bo4bo7bo12b4o12bo2bo34bo9bo31bob2o3b2obo10b6o13b2o2b2o41b2obo9bo2b6o3bo29bobo13bo27b3obob3o17b2obo6b2o21b2o3bobobo$26bob10obo8b2o2bo6b4o6bo2b2o10bo2bo11b2o2b2o17bo41b3o15bobobobo10bob6obo10b8o39bob3obo7b3o3bobo34bo12bobo7bo21b2ob2obo17bobob2o2bob3o19b3ob2ob2obo$29b8o14bobo5bo2bo5bobo10bo15b3o4b3o57b3o15b2o3b2o12b6o13bob2obo41bo17bo2b2o47b2o7b2o16bob3ob4o18b2o2b2obo27bo2b3obo$25b2o3b6o3b2o10b2o16b2o8b4o13b3obo2bob3o54bo2bo2bo15bobo15b4o15bo2bo42bob2o17b2o45b2o9b3o15b8obo19bobo2bo24bo4bo2bo$26b2o2b6o2b2o10bo2b3o10b3o2bo7bo15b5o4b5o52bob5obo32b4o62b2o10bo6bobo47bobo6bob2o14b9o21bo2bo24b4o3b2o$26b2obob4obob2o13b2obo8bob2o9b2obo14b4o4b4o53b9o12b2obob2o13b4o14bo4bo43b2o9b3o4bo2b2o46bo2b3o2bob2o13bob5obo23b2obo20b3ob6obo$30b6o13b8o8b8o21b16o48b4ob5ob4o9b7o11b2ob2ob2o12b2o2b2o43b2o10bob2o2bo49bobobo5bo17b4o27b3o20bob6ob3o$28bo2b4o2bo12bob4o10b4obo21bob14obo47b2obob5obob2o10b5o13bob2obo12bobo2bobo41bobo9b2ob3o3bo46bo3bobo22b6o47bo2b8o$29b8o13b2ob4o8b4ob2o23b14o50b2o4bo4b2o9b3o3b3o10bo6bo9b5o2b5o39bo14bo4b3o49bo22bob2obo50b3ob3o2bo$27b12o13bo2bo10bo2bo24b2o2b8o2b2o55bo13b3o7b3o11b2o14b3o2b3o41b3o16bo2bo73b2o2bo48b2o2bo$27b12o15bo12bo31b6o75b5ob5o11b4o13b8o41b2obo15bobo74bo51bobo3b4o$28b10o18bo8bo31bo2b4o2bo75b7o14b2o11b3o3b2o3b3o38b2obo14bob2o125b6obo$30b6o19b2o8b2o29bob8obo72b11o11bo2bo11bo2bo4bo2bo34bo2bo2b2o15bo2b4o120b6obo2bo$24bob2o2b6o2b2obo14bo8bo30b2ob2o2b2ob2o76b3o15b4o11b2obob2obob2o34bob3o18bo5b2o117b8o$25b2o2bob4obo2b2o57b2o4b2o77b5o15b2o12b3ob4ob3o34b5o20bob4o117bob5o$24b5o3b2o3b5o56bo6bo78b3o14b6o12bob4obo36b3o19b3o2bobo119b7o$24b6o2b2o2b6o159bob2obo12b8o35b3obo17b4o122b9o$24b5ob6ob5o156b2o2b4o2b2o8b10o37bo19b2o2b2o115b2ob7o$22bob3o3bob2obo3b3obo153bo2b8o2bo8b8o33bob3o19bo4bo116b2o4b3o$23bo2bo3bo4bo3bo2bo154b14o6b12o31bo27bo118bobo2b3o$28bo8bo160b12o7b2ob6ob2o31b2o25b2obo115bobo3b2o$26bob3ob2ob3obo157bob10obo48bobo22b6o117bo2bobo$23b3ob2ob2o2b2ob2ob3o155b12o49b3o21bo2b4o118b4o2bo$24bo16bo156bo3bo2bo3bo11b4o32b7o16b2ob2ob2obo120bob2o$23b3o14b3o177b6o30bob4o18bo3bo4b3o117b2o$24bo16bo159b6o14b4o32b3obo20bo6bob2o118bo$23b3o4b6o4b3o157b8o11b2o4b2o30b2o22b2o3bo4bo$25bo4b2o2b2o4bo159bo2b2o2bo11bobo2bobo27b3ob3o22b2ob4o2bo$30bo4bo164bo2b2o2bo11b2ob2ob2o27bobobo22bobo2bo2b2o$30bob2obo166bo2bo48b4o25b2obo2bobo$30bob2obo185bo2bo31bo26bo2bo4b3o$221bo2bo30bo25bo2bobo4bobo$222b2o29bo2bo24b5o3b2o$254bob2o25b2obobobob2o$255b2o27b2o2bobob2o$283b2o6bo$254b3obo24b4o2b5o$255bobo27bo3b5o$253b5o25bob3ob3o$254bo27bob2o6bo$253bob2o27b2o$253b3o25b2o3bo$252b4o26bobo4b3o$251b3o29b4o3b2o$251b4o27bob2o$254bo29b3o$254b2o31b3o$254bo28bob6o$251bobo30b2obob2o$252b4o29bob2o$251b2ob2o27b2o2b4o$251b2o2bo27bo5b2o$250b3ob2o29b3ob2o$249bob3o30bob3o$251b3o32b2ob2o$248b2obo34bob2o$250b3o37b2o$248b3o2bo37bo$249b3obo35bob2o$246bo44b2o$246b2o2bo38b4o$247b2o36b6obo$245b3o34b2ob3ob2obo$244bo37b2ob3obo$244bobo36bob3obo$246b3o33bob4o$244bobob2o35bo$244b4o34b2o2bo$244b3ob2o34bo2b2o$242b2ob2ob2o35b4o$242bob3obo35b2ob2o$244bo38bo2bo$244b2o40bo$285b2o$245b2o$244b3o$244b3o$244b3o$242bob2o$242b3obo$242b4o$241bo2b2o$241bobo$242b2o$242b2o$244bo$241bo$241b2o$240bo$240bobo$238b5o$237b3o$237bob2o$235b5o$237bo$237bo!
|position = center
|viewerconfig = #C [[ ZOOM 2 WIDTH 900 ]]
|caption = A collection of these ships
|style = width:480px;
}}

In February {{year|2020}}, [[AforAmpere]] found the first [[knightship]]s in D&N, of speeds (2,1)c/5<ref name="post89850" /> and (2,1)c/6<ref name="post90043" /> respectively. On October 26, 2020, [[Adam P. Goucher]] found a {{LinkCatagolue|xq5_yzy1g8ik82vcezyzy13um3zyzw8qdf5r58zyz25e9htv652zyxssssvb31zysg0k40ec3011zyrgodpzypddso135zymcnmpa8zyjgo75j1ackzyf8kvvvfvmkp32zyg9vl3ackggzyhsmr1uuaczydcktoltkionzyd25f06d601zyaggog419k7ogzy6gsvvvf60dqsi9o2zy525nvvffs9v6u6zy58umplqgd0kzy45e22gvb2rd01zx4svaf1diphkc3z0k9864ihkjjoz6vj2qo0od51zw1103733|rule=b3678s34678|patternname=second, larger (2,1)c/5 knightship|style=raw}} using [[ikpx2]],<ref name="message770287572152483841" /> and quickly found multiple [[tagalong]]s<ref name="message770293244953100318" /><ref name="message770293800652242944" /> (including a {{LinkCatagolue|xq10_8e9m2zw5dvauo8zy0efdf8gzy32j6dikzy63j7jzy526759qoqgggzybr0klgzybichlrk2zyb21vfqsn6zye137uuttq4zyi1246544kzyngnrus8zyo11evke8zyr24cm468zys7gih73nkggzyt36usvffvvm8zyugw7hlbqczyu2jn9gdtvkzyv1osaee6kf6szyy175vcb7zyykfjih108sgoggzyz2m8rnncvjvvvu8gzyzw3674u8nnvfdnzyzy1gjghmuod94zyzy11et5mvoopbmgzyzy4261pd1ghbjfsozyzy8oj3o946696czyzy914mmo64lot3zyzyb11331|rule=b3678s34678|patternname=period-10 tagalong|style=raw}}<ref name="message770294666461315082" />) and a [[wickstretcher]]<ref name="message770296523916705843" /> based on it. The same day, Goucher found a smaller and thinner (2,1)c/6 spaceship.<ref name="message770389109339324416" />

On October 27, Goucher found a "[[growing spaceship|growing knightship]]" - a pattern in which the front end moves at (2,1)c/5 while the back end moves at (2,1)c/6.<ref name="post107986" />

{{POTY|name=These knightships|year=2020|type=oca|rank=1|collective=true}}

==References==
<references>
<ref name="post102258">{{LinkForumThread
|format = ref
|title = Re: List of the Turing-complete totalistic life-like CA
|p = 102258
|author = Peter Naszvadi
|date = August 14, 2020
}}</ref>
<ref name="post89850">{{LinkForumThread
|format = ref
|title = Re: Day & Night (B3678/S34678)
|p = 89850
|author = AforAmpere
|date = February 19, 2020
}}</ref>
<ref name="post90043">{{LinkForumThread
|format = ref
|title = Re: Day & Night (B3678/S34678)
|p = 90043
|author = AforAmpere
|date = February 22, 2020
}}</ref>
<ref name="message770287572152483841">{{CiteDiscord
|author = Adam P. Goucher
|date = October 26, 2020
|channel = naturalistic
|id = 770287572152483841
}}</ref>
<ref name="message770293244953100318">{{CiteDiscord
|author = Adam P. Goucher
|date = October 26, 2020
|channel = naturalistic
|id = 770293244953100318
}}</ref>
<ref name="message770293800652242944">{{CiteDiscord
|author = Adam P. Goucher
|date = October 26, 2020
|channel = naturalistic
|id = 770293800652242944
}}</ref>
<ref name="message770294666461315082">{{CiteDiscord
|author = wwei23
|date = October 26, 2020
|channel = naturalistic
|id = 770294666461315082
}}</ref>
<ref name="message770296523916705843">{{CiteDiscord
|author = Adam P. Goucher
|date = October 26, 2020
|channel = naturalistic
|id = 770296523916705843
}}</ref>
<ref name="message770389109339324416">{{CiteDiscord
|author = Adam P. Goucher
|date = October 26, 2020
|channel = naturalistic
|id = 770389109339324416
}}</ref>
<ref name="post107986">{{LinkForumThread
|format = ref
|title = Re: Day & Night (B3678/S34678)
|p = 107986
|author = Adam P. Goucher
|date = October 27, 2020
}}</ref>
</references>

==External links==
* {{cite web
| author = David I. Bell
| year = 1997
| url = http://www.tip.net.au/~dbell/articles/DayNight.zip
| title = Day & Night - An Interesting Variant of Life
| work = See also Bell's [http://www.tip.net.au/~dbell/archive/b3678s34678.tar.gz Day & Night pattern archive]}}
* {{cite web
| author = Pete Carlton
| url = https://web.archive.org/web/20080617233100/http://www.ocf.berkeley.edu/~pcarlton/CA.html
| title = Pete's Game of Life Page: B3678 S34678}}
* {{LinkForumThread|f=11|t=702|title=Day & Night (B3678/S34678)}}
* {{LinkWikipedia|Day_and_Night_(cellular_automaton)}}
* {{LinkCatagolueRule|b3678s34678}}
* {{LinkEppsteinRule|b3678s34678}}
* {{LinkMirek|rullex_life.html#Day%20%26%20Night|title=MCell built-in Life rules: Day & Night}}
* [https://web.archive.org/web/20150422173051/http://fano.ics.uci.edu/ca/rules/b3678s34678/g15.html The Rocket (glider 19979)]

[[Category:Life-like cellular automata]]
[[Category:Self-complementary rules]]

OCA:4diagonal

2025-07-01T19:57:26Z

Empty Emptiness:

{{WIP}}{{Rule|name=4diagonal|char=Chaotic|b=34c|s=23}}
4diagonal is an [[Isotropic non-totalistic rule]] that differs from regular Life by one isotropic birth [[Transition (rule definition)|transition]].

Century

2025-06-28T18:23:37Z

Empty Emptiness:

{{Methuselah
|name = Century
|pname = century
|c = 6
|bx = 4
|by = 3
|l = 103
|f = 15
|mcps = 6
|symmetry = C1
|discoveryear = 1970
|rulemin = B3/S23
|rulemax = B38/S23
|rulespecial = [[Conway's Game of Life|Conway Life]]
|isorulemin = B3/S23
|isorulemax = B38/S236e
|synthesis2 = 3
|synthesisRLE = true
|plaintext = true
|rle = true
}}
'''Century''' is a [[hexomino]]. It is a common [[methuselah]] that evolves into three [[block]]s and a [[blinker]] after 103 generations. It produces a temporary [[toad]] at generation 59 which is destroyed at generation 79. It is a parent of the [[bookend]].

== Century hasslers ==
As the century is very common, there are many [[century hassler]]s, such as the [[74P127|p127 century hassler]] found by [[Luke Kiernan]]. As an early example, [[David Buckingham]] built a [[period-246 glider gun]] using a century as the [[engine]] in June {{year|1996}}.

== Century eaters ==
Century can be [[eater|eaten]] by a [[spartan]] configuration of three [[eater 1]]s surrounding a [[beehive]], as shown below (century is upper-right in each case). A much smaller [[century eater]] was found by [[Ivan Fomichev]] in 2013.<ref name="post8177" /> Both of them play a prominent role in the [[bistable switch]].

{| style="margin:auto; width:360px"
|{{EmbedViewer
|pname = centuryeatenbyeater1s
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 8.5 ]]
|position = center
|caption = A Spartan century eater
}}
|-
|{{EmbedViewer
|pname = centuryeater2
|viewerconfig = #C [[ THUMBSIZE 2 ]]
|position = center
|caption = Century eater 2
}}
|}

Century can also be eaten by a [[Transparent object|transparent]] [[block]] in two different ways<ref name="post6766" />, as shown below.

{| style="margin:auto; width:360px"
|{{EmbedViewer
|rle = x = 28, y = 6, rule = B3/S23
26bo$2o18b2o3b3o$2o18b2o2b2o$5bo$4b3o$3b2o!
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 10 ]]
|position = center
|caption = Century collisions with a block, where the century gets eaten.<ref name="post6766" /> Note that they are of lower clearance, so the larger century eaters generally tend to be more useful.
}}
|}

== In other rules ==
In rule B34c/S23 ([[OCA:4diagonal|4diagonal]]), the century [[Infinite growth|grows to infinity]] as it is a 46c/220 glide-symmetric dirty [[puffer]]. The back end stabilizes at tick 1543.

In rule B38/S23 ([[Pedestrian Life]]) there is a [[2-glider collision]] which produces a century from what in life is a b-heptomino synthesis - the century otherwise evolves the exact same way it does in life.

== See also ==
* [[Queen bee]]
* [[Century-to-glider converter]]

== References ==
<references>
<ref name="post6766">{{LinkForumThread
|format = ref
|title = Re: Thread For Your Accidental Discoveries
|p = 6766
|author = Tropylium
|date = July 11, 2012
}}</ref>
<ref name="post8177">{{LinkForumThread
|format = ref
|title = Re: What do you want out of (conway's) life this year?
|p = 8177
|author = Ivan Fomichev
|date = June 8, 2013
}}</ref>
</references>

== External links ==
* {{LinkLexicon|lex_c.htm#century}}
* {{LinkCatagolue|code=xp2_33z66z66yas|format=pseudo-object|patternname=Century ash}}

[[Category:Gliderless methuselahs]]
[[Category:Polyominoes]]
__NOTOC__

Period-43 glider gun

2025-06-28T18:22:34Z

Empty Emptiness:

{{Gun
|name = Period-43 glider gun
|pname = period43glidergun
|c = 66
|bx = 32
|by = 25
|p = 43
|b = 2
|discoverer = Nico Brown
|discoveryear = 2022
|rulemin = B3/S23
|rulemax = B3/S23
|rulespecial = [[Conway's Game of Life|Conway Life]]
|isorulemin = B3/S23
|isorulemax = B35c/S234ct
|synthesis = 30
|rle = true
|plaintext = true
|viewerconfig = #C [[ HEIGHT 400 THUMBSIZE 2 ZOOM 14 MAXGRIDSIZE 9 GPS 15 AUTOSTART ]]
}}
A [[true]] [[period]] 43 [[glider gun]] was discovered by [[Nico Brown]] on September 11, {{year|2022}}.<ref name="post150882" /> It uses the same [[honey farm]] + [[fishhook]] → [[glider]] reaction that many other glider guns do. It was originally found in a form using a block and eater instead of the [[shillelagh]] on [[wing]], but the block got turned into a pond rather than actually being restored, so [[Bellman]] was used to complete it.

This is the only known [[engine]]-based true period-43 gun, and oscillators based on this gun were the only known period-43 oscillators that don't use the [[Snark]] before the discovery of the [[p43 pi-heptomino hassler]] in November 2022.<ref name="post153483" /> Prior to that, the {{cells|80|text=80-cell}} form of the gun [[capped]] with fishhooks was also the smallest known period-43 oscillator by population.

When the gun was discovered, it was tied for the seventh smallest by bounding box.

A {{gliders|30}} [[synthesis]] of the gun was found early the next day.<ref name="post150896"/>

== In other rules ==
The specific honey farm predecessor triggered in the gun evolves differently under the isotropic transition B4c (as in 4diagonal, B34c/S23) to advance 2 generations faster, rephasing the gun to p41.<ref name="post156100" />

{{EmbedViewer
|rle = x = 72, y = 25, rule = Rainbow1TFL
20.2A7.A30.2V7.V$16.2A.A.A5.3A26.2V.V.V5.3V$7.A7.A.A.A6.A20.V7.V.V.V6.
V$6.A.A5.A2.A2.A5.2A18.V.V5.V2.V2.V5.2V$7.A7.2A2.2A26.V7.2V2.2V3$30.2A
38.2V$30.A39.V$28.A.A37.V.V$8.2A12.A5.2A18.2V12.V5.2V$8.A.A10.A.A24.V
.V10.V.V$7.A16.A22.V16.V$8.A.A10.A.A24.V.V10.V.V$2.2A5.A12.2A18.2V5.V
12.2V$.A.A37.V.V$.A39.V$2A38.2V3$11.2A2.2A7.A26.2V2.2V7.V$3.A7.A2.A2.
A5.A.A17.V7.V2.V2.V5.V.V$3.A.A6.A.A.A7.A18.V.V6.V.V.V7.V$3.2A5.A.A.2A
27.2V5.V.V.2V$10.2A38.2V!
|viewerconfig = #C [[ MAXGRIDSIZE 9 THUMBSIZE 2 ZOOM 6 GPS 1 HEIGHT 600 WIDTH 600 GRID OFF ]]
|position = center
|caption = Depiction of the phase where the evolution of the honey farm predecessor differs between Life (B3/S23, left) and 4diagonal (B34c/S23, right). Advance the pattern 1 generation to see the difference between the honey farm predecessors.
|style = width:300px;
}}

Due to this rephasing, the discovery of [[cribbage]] provided [[OCA:4diagonal|4diagonal]] (B34c/S23) with proof of being [[omniperiodic]] one week before regular Life (B3/S23).<ref name="post165056" />

==References==
<references>
<ref name="post150882">{{LinkForumThread
|format = ref
|p = 150882
|title = Re: Gun Discussion Thread
|author = Nico Brown
|date = September 11, 2022
}}</ref>
<ref name="post150896">{{LinkForumThread
|format = ref
|p = 150896
|title = Re: Synthesising Oscillators
|author = Carson Cheng
|date = September 12, 2022
}}</ref>
<ref name="post153483">{{LinkForumThread
|format = ref
|p = 153483
|title = Re: Oscillator Discussion Thread
|author = Nico Brown
|date = November 13, 2022
}}</ref>
<ref name="post156100">{{LinkForumThread
|format = ref
|p = 156100
|title = Re: Oscillator Discussion Thread (1-transition)
|author = Period1GliderGun
|date = January 17, 2023
}}</ref>
<ref name="post165056">{{LinkForumThread
|format = ref
|p = 165056
|title = Re: Rules 1 transition from Life
|author = Period1GliderGun
|date = August 13, 2023
}}</ref>
</references>

==External links==
* {{LinkCatagolue|code=xp43_ybca23y0ca23zx4a4y1swkozy0gyc6ikl3zwml4jyb3421z032011y1ckwsy1g8gzw8oy28oy61z311y1311|patternname=Capped period-43 glider gun}}

{{Symmetry|180degree}}

Herschel

2025-06-28T18:21:58Z

Empty Emptiness:

{{Methuselah
|name = Herschel
|pname = herschel
|c = 7
|bx = 3
|by = 4
|l = 128
|f = 24
|mcps = 7
|symmetry = C1
|discoverer = John Conway
|discoveryear = 1970
|rulemin = B3/S23
|rulemax = B38/S23
|rulespecial = [[Conway's Game of Life|Conway Life]]
|isorulemin = B3/S23
|isorulemax = B38/S23
|synthesis = 3
|synthesisRLE = true
|plaintext = true
|rle = true
|viewerconfig = #C [[ THUMBSIZE 3 ZOOM 42 HEIGHT 500 ]]
}}
The '''Herschel''' (or, much less commonly, '''D-heptomino'''<ref>{{CiteLexicon|file=lex_d.htm#dheptomino|name=D|accessdate=March 25, 2009}}</ref><ref>{{citeLifeline|vol=1}}</ref> or '''J-heptomino'''<ref>{{CiteLexicon|file=lex_j.htm#jheptomino|name=J-heptomino|accessdate=June 13, 2009}}</ref>) is a [[heptomino]] shaped like the lowercase letter ''h'', which occurs at generation 20 of the [[B-heptomino]]. It evolves into two [[block]]s, two [[glider]]s and a [[ship]] after 128 [[generation]]s, and also produces a [[phi spark]].

== Common uses ==
Herschels are a recognizable "bottleneck" stage of a very common progression of three small active objects, frequently seen during the evolution of chaotic patterns. An [[R-pentomino]] evolves after 28 ticks into a [[B-heptomino]] a dozen cells away from the starting point, plus some active trailing junk; the B-heptomino then evolves into a Herschel in another 20 ticks, while traveling another 8 cells in the same direction. 22 ticks and 5 cells later yet the Herschel evolves into a backwards escaping glider (known as the [[first natural glider]], FNG), and a [[Herschel descendant]] that evolves into a larger explosion before settling down.

The unusual distance that R-pentominoes and B-heptominoes travel during their evolution into Herschels has allowed for the development of a growing collection of [[Herschel conduit]]s, which use [[catalyst]]s to modify the 128-step reaction. Instead of producing the still lifes and gliders described above, an input Herschel "bounces off" a series of eaters and other catalysts and produces a new output Herschel some distance away. In some cases, the active reaction travels directly "through" one or more [[transparent catalyst]]s, destroying an object completely and re-creating it in the same location several ticks later. The output Herschel can then become the input for another conduit, which may continue in the same direction or turn left or right. If it eventually forms a closed loop, the result is a Herschel-based [[oscillator]] or [[gun]].

Most (but not all) conduits only engage the Herschel after its splitting into its final offspring and the FNG. Dealing with the latter is crucial in assembling a track from separate conduits: it is fired in a direction where it would commonly collide with a previous conduit's catalysts. [[Eater 5]] is one of the most convenient solutions for this task.

== Etymology ==
The term "Herschel" is attributed to '''John Conway''', who very early in the history of Life investigated the fates of all '''polyominoes''' up to at least 7 bits <ref>{{cite web|url=http://www.ibiblio.org/lifepatterns/october1970.html |title=Mathematical Games: The fantastic combinations of John Conway's new solitaire game "life" |author=Martin Gardner |date=October, 1970 |accessdate=August 2, 2009}}</ref>. The name is commonly ascribed to the Herschel heptomino's similarity to a planetary symbol ♄ erroneously attributed to Uranus (discovered by William Herschel in 1781.) However, in point of fact a Herschel closely resembles the symbol for ''Saturn'', but bears no particular resemblance to either of the symbols used for Uranus. So the appropriate name might actually be "Huygens" -- but "Herschel" is now universally used by tradition.

== Ancestor gallery ==
{| style="margin:auto; width:300px"
|{{EmbedViewer
|pname = herschelparent
|viewerconfig = #C [[ THUMBSIZE 4 ZOOM 40 HEIGHT 500 ]]
|position = center
|caption = [[Parent]]
}}
|{{EmbedViewer
|pname = herschelgrandparent
|viewerconfig = #C [[ THUMBSIZE 4 ZOOM 40 HEIGHT 500 ]]
|position = center
|caption = [[Grandparent]]
}}
|{{EmbedViewer
|pname = herschelgreatgrandparent
|viewerconfig = #C [[ THUMBSIZE 4 ZOOM 40 HEIGHT 500 ]]
|position = center
|caption = Great-grandparent
}}
|}

The right-hand domino of the '''Herschel parent''' can be removed, producing a 6 cell parent. The form shown is the parent produced by the B-heptomino.

The '''Herschel great-grandparent''' is a specific three-[[tick]] [[predecessor]] of the Herschel, commonly seen in [[Herschel conduit]] collections that contain [[dependent conduit]]s. In some situations it is helpful to display the input reaction in this form instead of the standard Herschel form. Dependent conduit inputs are catalyzed by a [[Transparent object|transparent]] [[block]] before the Herschel's standard form can appear, and before the Herschel's [[first natural glider]] is produced. This means that these conduits will fail if an actual Herschel is placed in the "correct" input location for a dependent conduit. Refer to [[F166]] or [[Lx200]] to see the correct relative placement of the standard transparent block catalyst. Almost all known Herschel conduits produce a Herschel great-grandparent near the end of their [[evolution]]ary sequence. In the original [[universal]] set of Herschel conduits, [[Fx158]] is the only exception.

== Gallery ==
{|
|[[File:HerschelFinal.png|thumb|left|Generation 128 of a Herschel]]
|}

== In other rules ==
In both [[HoneyLife]] (B38/S238) and [[OCA:4diagonal|4diagonal]] (B34c/S23), the Herschel is a failed reflectorless rotating oscillator/gun (p430 in HoneyLife and p288 in 4diagonal) which fails due to extraneous debris which inhibits further unassisted evolution. However, there are known completions in both rules which allow for oscillators and guns to be constructed. <ref name="post108467" /> <ref name="post196720" />

== See also ==
* [[B-heptomino]]
* [[Conduit 1]]

== References ==
<ref name="post108467">{{LinkForumThread
|format = ref
|p = 108467
|author = FWKnightship
|title = Re: Miscellaneous Discoveries in Other Cellular Automata
|date = October 30, 2020
}}</ref>
<ref name="post196720">{{LinkForumThread
|format = ref
|p = 196720
|author = EvinZL
|title = Re: Rules 1 transition from Life
|date = October 27, 2024
}}</ref>
<references />

== External links ==
* {{LinkLexicon|lex_h.htm#herschel}}
* {{LinkLexicon|lex_h.htm#herschelgreatgrandparent|name=Herschel great-grandparent}}

[[Category:Polyominoes]]

Period-43 glider gun

2025-06-28T18:20:40Z

Empty Emptiness: there is now a page for that

{{Gun
|name = Period-43 glider gun
|pname = period43glidergun
|c = 66
|bx = 32
|by = 25
|p = 43
|b = 2
|discoverer = Nico Brown
|discoveryear = 2022
|rulemin = B3/S23
|rulemax = B3/S23
|rulespecial = [[Conway's Game of Life|Conway Life]]
|isorulemin = B3/S23
|isorulemax = B35c/S234ct
|synthesis = 30
|rle = true
|plaintext = true
|viewerconfig = #C [[ HEIGHT 400 THUMBSIZE 2 ZOOM 14 MAXGRIDSIZE 9 GPS 15 AUTOSTART ]]
}}
A [[true]] [[period]] 43 [[glider gun]] was discovered by [[Nico Brown]] on September 11, {{year|2022}}.<ref name="post150882" /> It uses the same [[honey farm]] + [[fishhook]] → [[glider]] reaction that many other glider guns do. It was originally found in a form using a block and eater instead of the [[shillelagh]] on [[wing]], but the block got turned into a pond rather than actually being restored, so [[Bellman]] was used to complete it.

This is the only known [[engine]]-based true period-43 gun, and oscillators based on this gun were the only known period-43 oscillators that don't use the [[Snark]] before the discovery of the [[p43 pi-heptomino hassler]] in November 2022.<ref name="post153483" /> Prior to that, the {{cells|80|text=80-cell}} form of the gun [[capped]] with fishhooks was also the smallest known period-43 oscillator by population.

When the gun was discovered, it was tied for the seventh smallest by bounding box.

A {{gliders|30}} [[synthesis]] of the gun was found early the next day.<ref name="post150896"/>

== In other rules ==
The specific honey farm predecessor triggered in the gun evolves differently under the isotropic transition B4c (as in 4diagonal, B34c/S23) to advance 2 generations faster, rephasing the gun to p41.<ref name="post156100" />

{{EmbedViewer
|rle = x = 72, y = 25, rule = Rainbow1TFL
20.2A7.A30.2V7.V$16.2A.A.A5.3A26.2V.V.V5.3V$7.A7.A.A.A6.A20.V7.V.V.V6.
V$6.A.A5.A2.A2.A5.2A18.V.V5.V2.V2.V5.2V$7.A7.2A2.2A26.V7.2V2.2V3$30.2A
38.2V$30.A39.V$28.A.A37.V.V$8.2A12.A5.2A18.2V12.V5.2V$8.A.A10.A.A24.V
.V10.V.V$7.A16.A22.V16.V$8.A.A10.A.A24.V.V10.V.V$2.2A5.A12.2A18.2V5.V
12.2V$.A.A37.V.V$.A39.V$2A38.2V3$11.2A2.2A7.A26.2V2.2V7.V$3.A7.A2.A2.
A5.A.A17.V7.V2.V2.V5.V.V$3.A.A6.A.A.A7.A18.V.V6.V.V.V7.V$3.2A5.A.A.2A
27.2V5.V.V.2V$10.2A38.2V!
|viewerconfig = #C [[ MAXGRIDSIZE 9 THUMBSIZE 2 ZOOM 6 GPS 1 HEIGHT 600 WIDTH 600 GRID OFF ]]
|position = center
|caption = Depiction of the phase where the evolution of the honey farm predecessor differs between Life (B3/S23, left) and 4diagonal (B34c/S23, right). Advance the pattern 1 generation to see the difference between the honey farm predecessors.
|style = width:300px;
}}

Due to this rephasing, the discovery of [[cribbage]] provided [[OCA:4diagonal]] (B34c/S23) with proof of being [[omniperiodic]] one week before regular Life (B3/S23).<ref name="post165056" />

==References==
<references>
<ref name="post150882">{{LinkForumThread
|format = ref
|p = 150882
|title = Re: Gun Discussion Thread
|author = Nico Brown
|date = September 11, 2022
}}</ref>
<ref name="post150896">{{LinkForumThread
|format = ref
|p = 150896
|title = Re: Synthesising Oscillators
|author = Carson Cheng
|date = September 12, 2022
}}</ref>
<ref name="post153483">{{LinkForumThread
|format = ref
|p = 153483
|title = Re: Oscillator Discussion Thread
|author = Nico Brown
|date = November 13, 2022
}}</ref>
<ref name="post156100">{{LinkForumThread
|format = ref
|p = 156100
|title = Re: Oscillator Discussion Thread (1-transition)
|author = Period1GliderGun
|date = January 17, 2023
}}</ref>
<ref name="post165056">{{LinkForumThread
|format = ref
|p = 165056
|title = Re: Rules 1 transition from Life
|author = Period1GliderGun
|date = August 13, 2023
}}</ref>
</references>

==External links==
* {{LinkCatagolue|code=xp43_ybca23y0ca23zx4a4y1swkozy0gyc6ikl3zwml4jyb3421z032011y1ckwsy1g8gzw8oy28oy61z311y1311|patternname=Capped period-43 glider gun}}

{{Symmetry|180degree}}

OCA:4diagonal

2025-06-28T18:07:38Z

Empty Emptiness:

{{WIP}}{{Rule|name=4diagnol|char=Chaotic|b=34c|s=23}}
4diagonal is an [[Isotropic non-totalistic rule]] that differs from regular Life by one isotropic birth [[Transition (rule definition)|transition]].

4diagonal

2025-06-28T17:50:51Z

Empty Emptiness: Redirected page to OCA:4diagonal

#REDIRECT [[OCA:4diagonal]]

OCA:4diagonal

2025-06-28T17:20:13Z

Empty Emptiness: Created page with "{{WIP}}{{Rule|name=4diagnol|char=Chaotic|b=34c|s=23}} 4diagnol is an Isotropic non-totalistic rule that differs from regular Life by one isotropic birth transition."

{{WIP}}{{Rule|name=4diagnol|char=Chaotic|b=34c|s=23}}
4diagnol is an [[Isotropic non-totalistic rule]] that differs from regular Life by one isotropic birth [[Transition (rule definition)|transition]].

Agar

2025-06-08T22:58:29Z

Empty Emptiness: this is not an agar

{{Glossary}}
An '''agar''' is any pattern covering the whole plane that is periodic in both space and time. In other words, they are the shift periodic configurations contemplated by symbolic dynamical systems theory, although this characterization is not always followed rigorously. Low entropy and a semblance of order is the real criterion; there are several possibilities:

* strict periodicity according to a compatible lattice group,
* degenerate one dimensional periodicity
* symmetry arising from a second stage de Bruijn diagram,
* color symmetry following a Shubnikov group,
* irregular with the symmetry of a superlattice,
* fractal symmetry described by a Lindenmayer system, or
* they just look pretty.

Any set of bounded patterns may be laid side by side, provided that they are sufficiently separated, and still not be seen as an agar. For example, that is the difference between still lifes and pseudo still lifes. As a restricted class of Life patterns, agars often subject to mathematical or computational analysis. If they were much more arbitrary, they would be called [[soup|soups]] or [[ash]].

The following tables show examples of linear and tiling agars. Refer to each link for building methods and more variations than may be shown here.

== Line agars ==
{| class="wikitable" style="margin-left:auto;margin-right:auto;"
!Agar !! [[density]] !! [[period]] !! stable !!notes !! image
|-
|[[Zebra stripes]] || 1/2 || 1 || B (1)||Alternating bands of live and unoccupied [[cell]]s (ripples(2)) ||[[Image:LINEZB.GIF]]
|-
|[[Venetian blinds]] || 1/2 || 2 || B ||[[Phoenix]] made of fat ripples, varying only longitudinally (2) ||[[Image:LINEVB.GIF]]
|-
|[[Chicken wire]] || 1/2 || 1 || B ||''Wires'' have a uniform height of 2 but with gaps at least 2 cells wide||[[Image:LINECW.GIF]]
|-
|Phoenix || - || 2 || ||The avatar filaments can be separated, and possibly terminated as [[barberpole]]s ||[[Image:LINEPH.GIF]]
|}

# S, stable ; B, must be bound on two or four sides ; for common bounds see [[Dean Hickerson]]'s list.<ref>{{CiteHickersonOscillators}}</ref>
# Cross sections following [[Stephen Wolfram|Wolfram]]'s (2,1) [[Rule 22]].
# Cross sections following [[Stephen Wolfram|Wolfram]]'s (2,2) Rule 01140238X

== Tile agars ==
{| class="wikitable" style="margin-left:auto;margin-right:auto;"
!Agar !! tile size !! [[bounding box]] !! density !! period !! stable !! notes !! Image showing unit cell and {{times|2|2}} cell
|-
|[[Onion rings]] || 72 || {{times|12|12}} || 1/2 || 1 || B ||Unit cell composed of nested squares (4n×4n) ; static on a color lattice (complementary sublattices alternate checkerboardwise)||[[Image:TILEOR.GIF]]
|-
|[[Marshland agar]] || 4 || {{times|3|3}} || 4/9 || 1 || S ||Consists of [[pond]]s and [[lake]]s, that is, [[domino]]es ; of many possible combinations, only basic ones go squared ||[[Image:TILEML.GIF]]
|-
|[[Houndstooth agar]] || 8 || {{times|4|4}} || 1/2 || 2 || B ||Really the pattern of a known checquered twill ||[[Image:TILEHO.GIF]]
|-
|Herparian agar || 12 || {{times|6|6}} || 1/3 || 1 || S ||[[Lake]]s made of [[snake]]s acting like dominoes ; only the most basic give a ''square'' tiling ||[[Image:TILEHA.GIF]]
|-
|Herparian agar || 12 || {{times|6|6}} || 1/3 || 1 || S ||Snakes polymerize in three ways; the unit cell of this agar is oblong ||[[Image:TILEHB.GIF]]
|-
|[[Squaredance]] || 8 || {{times|6|6}} || 2/9 || 2 || B ||[[Period]] 2 diagonal agar and [[phoenix]], low density domino pattern ||[[Image:TILESD.GIF]]
|-
|Scrubber/Piston || 16 || {{times|7|7}} || 16/49 || 2 || B ||Period 2; odd generations = [[piston]] (or [[spark coil]]), even generations = [[scrubber]] ||[[Image:TILEPS.GIF]]
|-
|Reciprocating agar || || || || 2 || B ||Period 2; [[Test tube baby]] / [[Spark coil]] can be elongated, rotated, stabilized, to get numerous tiles. Packable regularly or irregularly into the cartesian plane, none is necessarily a unit cell. || [[Image:RCPAAGR.GIF]]

|}

==References==
<references/>

==See also==
* {{CategoryLink|Agars}}

==External links==
* {{LinkLexicon|lex_a.htm#agar}}
* {{LinkGoLNews|2006/07/period_16284_agar.html|title=Period 16284 Agar|date=July 15, 2006|author=Heinrich Koenig}}

; Forum threads
* {{LinkForumThread|f=2|t=4795|title=Agar discussion thread}}
* {{LinkForumThread|f=7|t=5858|title=Agars and other infinite patterns}}
* {{LinkForumThread|f=11|t=4503|title=Agar in Other Cellular Automata}}

Seed

2024-08-23T19:47:23Z

Empty Emptiness: /* Common one-glider seeds */

{{About|a constellation that can be triggered to form a target object|the rule B2/S|OCA:Seeds}}

A [[seed]] is a [[constellation]] that when triggered (normally hit by a [[glider]]) evolves into a target object, possibly with some extra junk.

Seed constellations are commonly used in [[self-constructing circuitry]]. For example, to create a faraway target object to start construction of a new copy of a [[construction arm]] at a safe distance, it is often useful to use a seed for a complex spaceship or [[wickstretcher]] -- something that can be stopped when it reaches its destination by following it with a faster spaceship or [[wick]] [[burn]]ing reaction.

[[One-glider seed]]s, or "1G seeds", are particularly useful in [[slow salvo]] construction because the constellation can be built up incrementally, with changes made one glider at a time. When it is complete it can be [[trigger]]ed by the final glider in the recipe. Triggering a seed will usually create several precisely synchronized gliders that then [[Collision|collide]] to construct the target object via a [[glider synthesis]].<ref name="post100181" />

'''Seed''' is also sometimes used in a more general way, to mean any initial configuration -- i.e., a [[predecessor]] of the target state of the pattern.

==Common one-glider seeds==
{{related|List of one-glider seeds|Collisions of a glider with common objects}}
Many [[common evolutionary sequence]]s have common objects that are one-glider seeds. Here is a list:
* [[Traffic light]] (can be triggered from a [[blinker]], [[beehive]], [[loaf]], [[long boat]], or [[toad]]);
* [[Honey farm]] (can be triggered from a [[block]], beehive, loaf, [[boat]], or toad);
* [[Pi-heptomino|Pi-sequence]] (can be triggered from a block, blinker, beehive, boat, [[ship]], [[pond]], toad, [[beacon]], or [[fishhook]]);
* [[R-pentomino|R-sequence]] (can be triggered from a beehive, loaf, or toad);
* [[B-heptomino|B-sequence]] (can be triggered from a boat, toad, or beacon);
* [[Century|Century sequence]] (can be triggered from a boat, toad, or beacon);
* [[Block and glider|Wing sequence]] (can be triggered from a boat, ship, or beacon);
* [[Lumps of muck]] (can be triggered from a beehive);
* [[Queen bee]] (can be triggered from a ship);
* [[E-heptomino|E-sequence]] (can be triggered from a boat);
* [[Blonk-tie|Blonk-tie sequence]] (can be triggered from a blinker or fishhook)
* [[Phi spark]] (can be triggered from a blinker or a boat)

{{EmbedViewer
|pname = stilllifepiseeds
|position = right
|viewerconfig = #C [[ AUTOSTART GPS 5 LOOP 17 T 0 PAUSE 0.6 T 4 PAUSE 0.4 T 6 PAUSE 0.7 T 12 PAUSE 0.2 ]]
}}

The reason that so many objects are one-glider seeds for a pi-sequence is because when a glider hits a line of two cells in a still life in a certain way, the way that the glider reacts almost always produces a pentaplet grandparent of the pi-heptomino after four generations, as well as some cells behind it.<ref name="p105552" /> For a block, beehive, boat (in one orientation), ship (in one orientation), and pond, the excess cells turn out to be sparks, so a clean pi-sequence is produced. The only common one-glider seed for a pi-sequence that does not produce the pi-this way is a blinker, which does not actually produce a pi-heptomino but instead produces a twelve-cell cluster with the same great-grandchild (hence the term pi-''sequence'' rather than pi-''heptomino'').

==Splitter-based==
Many spaceships and some other difficult-to-construct objects have activation stages that require many gliders coming at once from multiple directions. For uses in self-constructing circuitry, simply firing all of the gliders at once in a synchronized manner is impractical. For this reason, the activation stage uses a series of [[turner|turners and splitters]] that create all of the necessary synchronized gliders from only one initial glider that requires no synchronization.

==See also==
* [[Tutorials/Seed building]]

==References==
<references>
<ref name="post100181">{{LinkForumThread
|format = ref
|title = One Glider Seeds
|p = 100181
|author = Goldtiger997
|date = July 7, 2020
}}</ref>
<ref name="p105552">{{LinkForumThread
|format = ref
|title = One Glider Seeds
|p = 105552
|author = Entity Valkyrie 2
|date = October 4, 2020
}}</ref>
</references>

==External links==
* {{LinkLexicon|lex_s.htm#seed}}

__NOTOC__

{{Glossary}}

OCA talk:Tlife

2024-07-13T14:38:07Z

Empty Emptiness: /* it doesn't show us the "ant" spaceship. */ new section

== Catagolue links ==

I noticed that all three links at the bottom of the page are for "Tlife", even though they link to the tlife, tHighLife, and tDryLife pages. Is there any way around that? The LinkCatagolueRule template seems to be reading the page name, which obviously doesn't work here. [[User:A for awesome|A for awesome]] ([[User talk:A for awesome|talk]]) 16:33, 19 June 2017 (UTC)

:Yeah, the template supports a <tt>rulename=</tt> parameter and only defaults to the pagename if no name is explicitely specified using that. I've edited the article to use this parameter. [[User:Apple Bottom|Apple Bottom]] ([[User talk:Apple Bottom|talk]]) 12:05, 20 June 2017 (UTC)

::Thanks! [[User:A for awesome|A for awesome]] ([[User talk:A for awesome|talk]]) 02:56, 21 June 2017 (UTC)

== My thoughts ==

I think can briefly describe they here, and create a new articles to key describe they ([[User talk:Spaceship|talk]]).

== condition vs transition ==

Re: [https://conwaylife.com/w/index.php?diff=141326&oldid=141321 "... it also stomped on a valid improvement, "condition" -> "transition"."] -- that is an incorrect summary of what happened. Instead, [https://conwaylife.com/w/index.php?diff=141270&oldid=140860 my initial edit] changed "transition" to "condition" since that is more correct (see for example [https://conwaylife.com/forums/viewtopic.php?f=11&t=732 thread732]). A transition is an event that can happen with a cell (e.g. birth is a transition from "dead" to "alive"). A condition is a part of a rule definition, e.g. specific neighbourhood ("B6" = "birth when there are 6 alive neighbours" is a condition). Then my edit was [https://conwaylife.com/w/index.php?diff=141307&oldid=141270 reverted] without any explanation, which included both restoring alternative name for a rule that is not found on the forum, and revert of my change of "transition" to "condition". The revert was not a valid improvement. [[User:Confocal|Confocal]] ([[User talk:Confocal|talk]]) 15:26, 20 November 2023 (UTC)
: I'm not too surprised that I didn't get the summary exactly correct, but I do still object to the edit warring, which is what these undo-redo-undo sequences amount to. The original source of that "condition" wording makes things all the more interesting, I suppose. I don't immediately agree with the use of "condition" in that context. Before you edited it again just now, the entire article contained similar phrases, like "differing by only two transitions" in the first paragraph.

: That's a very common usage, and it looks like you must have noticed that adding one inconsistent use of "condition" lower down in the article was not actually an improvement.

: The link to thread 732 is an appeal to an authority from way back in 2011 -- a post by Tropylium. I haven't seen that usage of "condition" getting picked up very much for use in situations like this, though it's certainly used sometimes, like in [[Life-like cellular automaton]] and [[Strobing rule]].

: This "condition" vs. "transition" might be a good new topic for the LifeWiki Discussion board. I'm a bit surprised that you decided to unilaterally go ahead and change all existing uses of "transition" to "condition" in the article, as you have just done -- especially immediately after a moderator made an edit to try to settle an edit war. You've been asked very recently to avoid second-guessing moderator edits in this way.

: There are quite a lot of other LifeWiki articles where "transition" is used in the exact sense that you've now edited out of the tlife article. There seems to be some disagreement on this condition-vs.-transition point, so some discussion definitely needs to happen before any more such changes are made. [[User:Dvgrn|Dvgrn]] ([[User talk:Dvgrn|talk]]) 16:32, 20 November 2023 (UTC)

:: I did say "for example" when linking to the thread. More recent examples are easy to find via forum search: [https://conwaylife.com/forums/search.php?keywords=birth+condition "birth condition"], [https://conwaylife.com/forums/search.php?keywords=survival+condition "survival condition"], [https://conwaylife.com/forums/search.php?keywords=death+condition "death condition"]. Re: "unilaterally go ahead" -- I don't think that is valid either. My edit is an attempt to improve the content (by switching to clearer wording), per point #1 in [[LW:DR]]. [[User:Confocal|Confocal]] ([[User talk:Confocal|talk]]) 16:56, 20 November 2023 (UTC)

::: The action that I described as "unilaterally going ahead" happened immediately after I changed the wording back. In making that change I was attempting to recognize an edit war that seemed to be beginning. Please be careful to avoid immediately reverting moderators' actions, as you did here (you changed "transition" back to "condition", which I had just changed back.) When a moderator gets involved, you're no longer on step 1 of [[LW:DR]] -- and you had skipped the "discussion" part of step 1, anyway.

::: You've been making enough of these impressively confident but misguided "re-undo" types of edits, that moderators have had to invent a whole new system to try and deal with them. Please do your best from now on to disengage and de-escalate in these kinds of situations, rather than doubling down and making four of the same edit that just got undone. Whenever you can do so, please feel free to skip down the [[LW:DR]] list to the "wait a week" parts; this will be a big help to me and other people who are trying to reduce unnecessary edit-war unpleasantness. [[User:Dvgrn|Dvgrn]] ([[User talk:Dvgrn|talk]]) 18:11, 20 November 2023 (UTC)

:::: Of course I did not 'skipped the "discussion" part'. I am participating in discussion on this right here and now, once it is more or less clear what should be discussed. (And with an unexplained undo [https://conwaylife.com/w/index.php?diff=141307&oldid=141270 like this], there was nothing to discuss, because there was no explanation for the undo.) [[User:Confocal|Confocal]] ([[User talk:Confocal|talk]]) 18:29, 20 November 2023 (UTC)

::::: Okay. We've established that I get details wrong fairly regularly. I don't perfectly correctly describe everything that you did, in every case ... at least in your opinion. This is very, very likely to continue to happen -- I will happily acknowledge that it has happened and will (probably) happen in the future, but I don't feel much need to apologize for it. Moderators quite simply are not always going to have time to double-check every nuance of every past edit, before figuring out a reasonable thing to try, to avoid LifeWiki edit wars and move forward. Moderators expect you to cooperate with efforts to reduce future edit wars, even in the absence of perfect communications.

::::: Here I'm pointing out something that I'd really like you, specifically, to avoid doing so much in the future. You're still doing far too many repeated edits, changing something back after another editor just made it clear that they objected to the change. Maybe the reasons for the objection aren't always as clear as you'd like, but the existence of the objection is perfectly clear.

::::: Now, sometimes you're going to be right about the issue in question, sometimes you're not going to be right. But no matter whether you're right or not, a re-undo is in general ''no longer an appropriate thing for you to do'' in advance of good-faith attempts to discuss in other ways.

::::: You say you 'did not skip the "discussion" part'. What good-faith attempt to discuss this issue did I miss in this case, before you changed the four instances of "transition" back to "condition"? [[User:Dvgrn|Dvgrn]] ([[User talk:Dvgrn|talk]]) 18:59, 20 November 2023 (UTC)

:::::: My [https://conwaylife.com/w/index.php?diff=141328&oldid=141136 first reply] on this talk page was such an attempt. After that, I [https://conwaylife.com/w/index.php?diff=141329&oldid=141326 edited] the article accordingly. Directly making the suggested changes is easier/more straightforward than trying to describe the same suggested changes on the talk page, and it is easier to understand what are the changes if they can be viewed directly as a diff. [[User:Confocal|Confocal]] ([[User talk:Confocal|talk]]) 19:09, 20 November 2023 (UTC)

::::::: I understand the theory of making the edits directly as part of a discussion. That's great when the issue in question is not too controversial -- i.e., when people haven't already made the mistake of escalating with repeated undo-redo-undo cycles, to the point where a moderator gets involved.

::::::: Once a moderator is involved, the situation has generally moved on to the "disengage and wait a week" stage. It doesn't work very well to pretend the issue is still in the non-controversial stage at that point -- it just makes it look like you're absolutely certain that your point of view is the correct one.

::::::: If you want to make proposed edits of this kind without giving that impression of over-confidence in your own opinion, I'd suggest that you start being more careful to include polite wording in your edit summaries, such as "this is a proposed edit only; please feel free to undo if this is controversial". Neither your first reply nor your edit summary seem to give any sign that you are considering the possibility that you might be wrong about which term is "more correct" -- or, leaving right vs. wrong aside, whether there might be significant objections from the community about you making that change.

::::::: Since the change you made was just a "suggested change", I'll go ahead and undo it for now, since it will still be visible as a diff. Would you care to open a new thread on LifeWiki discussion about "condition" vs. "transition", with a link to that diff -- and then we'll see how things go from there? [[User:Dvgrn|Dvgrn]] ([[User talk:Dvgrn|talk]]) 19:32, 20 November 2023 (UTC)

:::::::: I already [https://conwaylife.com/forums/viewtopic.php?f=16&t=6235 started a thread] on the slightly wider question of CA rule definition terminology. [[User:Confocal|Confocal]] ([[User talk:Confocal|talk]]) 19:37, 20 November 2023 (UTC)

::::::::: Okay, I've added a post there. I guess the other idea that I'd like to get across is this: you characterized your first reply on the talk page as an attempt at discussion. But it's just plain not a discussion until somebody responds. I'm going to be taking a dim view of edits that undo other edits in the future, until enough time has passed that a discussion could reasonably happen. (Whether it actually happens or not is a different question, of course!) [[User:Dvgrn|Dvgrn]] ([[User talk:Dvgrn|talk]]) 20:20, 20 November 2023 (UTC)

:::::: Re: "the existence of the objection is perfectly clear." -- even the existence of some specific objection was not clear in this case. https://conwaylife.com/w/index.php?diff=141307&oldid=141270 That is an undo without any explanation at all reverting two unrelated changes at once, and not a valid objection. Re: "condition" vs. "transition" -- I posted several quotes, both [https://conwaylife.com/forums/viewtopic.php?p=171596#p171596 from forum posts] and [https://conwaylife.com/forums/viewtopic.php?p=171595#p171595 from other CA-related sources outside this website]. These quotes show that the proper common term for something like B3j or S8 is 'condition'. [[User:Confocal|Confocal]] ([[User talk:Confocal|talk]]) 21:44, 20 November 2023 (UTC)

::::::: I would say that those quotes show 'condition' is '''a''' proper common term for something like B3j or S8. I don't see that those links give any evidence at all that 'condition' is '''the''' proper term -- and it doesn't look like it's nearly as common as 'transition'. You've labeled 'transition' as jargon, which seems like something of a death sentence in your mind for LifeWiki usage -- but that's just another premise that I haven't been convinced of yet.

::::::: 'Transition' has been plenty precise enough to be used without any controversy in dozens of LifeWiki articles, up to now. It matches common usage. It's clear from context what it means. 'Condition' doesn't sound right to me in some of these cases, because it doesn't match common usage. Some of those proposed and implied changes look like they will cause more confusion than they solve (since I don't think the current uses of 'transition' are actually causing any real confusion). [[User:Dvgrn|Dvgrn]] ([[User talk:Dvgrn|talk]]) 23:36, 20 November 2023 (UTC)

:::::::: Replied in https://conwaylife.com/forums/viewtopic.php?p=171629#p171629 [[User:Confocal|Confocal]] ([[User talk:Confocal|talk]]) 00:12, 21 November 2023 (UTC)

: I don't remember ever seeing "condition" in this context. These things are generally called "transitions" in my experience. Although usually it refers to an INT transition, not an OT transition, especially in the context of an INT rule, so maybe "B6 transition'''s'''" is more appropriate. --[[User:Galoomba|Galoomba]] ([[User talk:Galoomba|talk]]) 01:01, 21 November 2023 (UTC)

:: I posted several quotes in the forum thread ( https://conwaylife.com/forums/viewtopic.php?f=16&t=6235 ) and more examples can be found via search. In this case, {{rl|tlife}} is non-totalistic, and it is fairly clear that both S2i and S4q are isotropic non-totalistic conditions. (It would be even more clear that these conditions are expressed in Hensel notation, if [https://conwaylife.com/w/index.php?diff=141329&oldid=141326 my edit] was not reverted by [[User:Dvgrn]].) When the context is a discussion of Life-like cellular automata, there are just 9 birth conditions and 9 survival conditions (from 0 to 8 alive neighbours in each case). In general the set of distinguishable conditions depends on the specific way to define/specify a rule from some rulespace. [[User:Confocal|Confocal]] ([[User talk:Confocal|talk]]) 01:09, 21 November 2023 (UTC)

::: Just for the record: @confocaloid, I reverted your latest attempt to continue your extremely ill-advised edit war with a moderator. This time the revert wasn't accidental, and I don't think any apology from me is needed.

::: I've tried to lay out my reasons again very carefully [https://conwaylife.com/forums/viewtopic.php?p=171738#p171738 on the relevant forum thread]. If there's something you don't understand, please ask questions. If there's something you disagree with, please follow the [[LW:DR]] guidelines and involve another moderator -- after at least a week has passed. However, I'd advise that you review my explanation very thoroughly a time or two, and think about the whole issue very carefully, before you involve anyone else. Other moderators aren't necessarily nearly as patient as I am. [[User:Dvgrn|Dvgrn]] ([[User talk:Dvgrn|talk]]) 14:51, 22 November 2023 (UTC)

:::: It is one thing when one actually directly states their objections (i.e. explains why some changes are not considered improvements). It is another thing when one is merely asserting "I object" without explaining why. That is not a valid objection. (Otherwise any edit in any article could be arbitrarily reverted with summary as illuminating as "There's no need to change this." or "I've reverted that change for now, mostly to register a clear objection.") Unfortunately this is the first post that actually contained a direct explanation. And it only appeared after some attempts to invoke "slippery slope" or otherwise blame me. Re: "moderator hat", if you blame people instead of/before trying to actually understand the issue, then it shouldn't come as a great surprise when those people find it harder and harder to take your words seriously / trust you in that you will not mishandle future situations like this again and again. This is my feedback anyway. [[User:Confocal|Confocal]] ([[User talk:Confocal|talk]]) 16:00, 22 November 2023 (UTC)

::::: Please remember that in this case you're dealing with a moderator on a limited time budget who is trying to stop unpleasant edit wars. You're perfectly correct that just "I object" by itself would be a lousy edit summary, if it was not followed by good-faith attempts to discuss and explain the objection elsewhere. However, I made several such good-faith attempts -- I've spent quite a lot of time on this issue this week. It's not actually a requirement to explain an objection to your perfect satisfaction on the first try, especially when you don't ask any actual clarifying questions.

::::: Coming from a moderator, an even a minimal registered objection is intended to be a clear signal that the edit under discussion is in fact controversial -- and that it has moved to a later stage of the [[LW:DR]] dispute resolution list. It's just plain not ever going to work to ignore a moderator objection on the grounds that it's "not a valid objection". The objection might not be clear to you yet, but that's because the topic is a work in progress.

::::: Again because my time for doing moderator stuff is somewhat limited, in this case I was looking for help from other members of the community in explaining the objection to you -- so my immediate initial response post included this text:
I'd like to hear what other people think about this. Should we leave the four uses of "transition" in the OCA:Tlife article the way they currently are, or would it be better to change them to "condition"?
::::: Any responses from other members of the community would have been fine by me. Your charge that, if someone else showed up who also wanted to change 'transition' to 'condition', I would be likely to mistreat them somehow ... well, honestly, it looks to me like you're making mountains out of molehills. I wouldn't necessarily agree with them, of course, and I wouldn't necessarily do what they say, but I wouldn't accuse them of malfeasance or anything.

::::: In this case, I expected that the moderator objection would have temporarily stopped you from attempting to re-make the objectionable edits, until you had made some good-faith efforts of your own to understand the objection, and you honestly believed that the edits in question were no longer controversial. Moderators won't always have time to explain everything instantly -- they might incorrectly think that their explanation is clear, as in this case. It's going to be up to you to ask questions if an objection is not in fact clear to you.

::::: Now, I don't mind explaining all of these edit-war-related expectations to you several times, if necessary, until you understand them. Some of these rules that I'm laying out here are pretty new, because we've never had a need for them before... because we've never had this many pointless LifeWiki edit wars before.

::::: I don't particularly want you to feel "blamed" or "picked on", though I certainly do want you to reduce how often you quickly undo controversial LifeWiki edits, going forward. Please do try to understand that the rules I'm describing are going to be the rules going forward, until and unless they have to change again. [[User:Dvgrn|Dvgrn]] ([[User talk:Dvgrn|talk]]) 01:41, 23 November 2023 (UTC)

== Regarding "It is likely one of the best-studied non-totalistic rules in existence" ==

Does that statement still hold true? I noticed that the LeapLife thread has double the number of posts than the tlife thread.
(Of course, many posts in the LeapLife thread doesn't include discoveries.)

P.S. Why is tDryLeapLife listed on the LeapLife page but not on tlife page?
[[User:Iddi01|Iddi01]] ([[User talk:Iddi01|talk]]) 10:25, 25 April 2024 (UTC)

== it doesn't show us the "ant" spaceship. ==

[[User:Empty Emptiness|Empty Emptiness]] ([[User talk:Empty Emptiness|talk]]) 14:38, 13 July 2024 (UTC)

Polyomino

2024-07-13T10:44:37Z

Empty Emptiness: /* Tetrominoes */

{{Glossary}}
A '''polyomino''' (or simply '''omino''') is a finite collection of orthogonally connected [[cell]]s. The mathematical study of polyominoes was initiated by Solomon W. Golomb in 1953.<ref>Golomb, Solomon W. (1994). ''Polyominoes'' (2nd ed.). Princeton, New Jersey: Princeton University Press. ISBN 978-0-691-02444-8.</ref> Conway's early investigations of [[Conway's Game of Life|Life]] and other [[cellular automaton|cellular automata]] involved tracking the histories of small polyominoes, this being a reasonable way to ascertain the typical behaviour of different cellular automata when the patterns had to be evolved by hand rather than by computer. Polyominoes have no special significance in Life, but their extensive study during the early years lead to a number of important discoveries and has influenced the terminology of Life.

[[Image:Cross_small.png|framed|right|A cross]]During the course of its evolution a polyomino could regain its original form, thereby constituting one phase of an [[oscillator]], as seen in the (infinite) [[cross]] family. The only other known examples are the [[block]] (which has [[period]] 1), the [[blinker]], the [[toad]], the [[star]] (and its hybrid with cross that gives another [[extensible]] family of period-3 oscillators<ref name="post155104" />) and (in two different phases) the [[pentadecathlon]]. Were a recurring polyomino displaced, it would be participating in a spaceship, though the only known examples are the [[lightweight spaceship]], the [[middleweight spaceship]], and the [[heavyweight spaceship]]. Of course, its evolution could follow other trajectories, possibly very long lived.

== Sizes of polyominoes ==
Polyominoes of with n cells for n = 1, 2, 3, 4, ... are called haplominoes, dominoes, triominoes, tetrominoes, pentominoes, hexominoes, heptominoes, octominoes, and n-ominoes in general. The number of distinct polyominoes with n cells for n = 1, 2, 3, ... is given by the sequence 1, 1, 2, 5, 12, 35, 108, 369, 1285, ... (<tt>{{OEIS|A000105|tt=tt}}</tt> on the OEIS).

=== Haplominoes ===
There is only [[dot|one]] '''haplomino''' (also called '''monomino''' or '''dot''') and by itself it dies after one [[generation]]. Several objects, such as the [[middleweight spaceship]], produce dot [[spark]]s.

It can be stabilised into [[lone dot agar]] and the [[barberpole]] family, the [[rotor]]s of which are [[phoenician]].

=== Dominoes ===
There is also only [[domino|one]] '''domino''' and by itself it too dies after one generation. A number of objects, such as the [[heavyweight spaceship]] and the [[pentadecathlon]], produce domino sparks.

Based upon that instant dying property of the domino, [[Squaredance]] is a low density domino-based [[agar]] and [[phoenix]].

=== Triominoes ===
There are exactly two distinct '''triominoes'''. The term is rarely used in Life, because the two objects in question are simply the [[blinker]] and the [[pre-block]].

=== Tetrominoes ===
There are five distinct '''tetrominoes''', each of which is shown below. The first is the [[block]], the second is the [[T-tetromino]] (a traffic lights predecessor), and the remaining three rapidly evolve into [[beehive]]s. The fourth is commonly referred to as a [[tail]] and is often attached to small [[still life]]s, for example combining with [[tub]] to form [[tub with tail]].

<center>
{{EmbedViewer
|pname = tetrominoes
|position = center
|viewerconfig = #C [[ THUMBSIZE 2 ]]
|caption = The five distinct tetrominoes, from left to right: {{nowrap|O, T, I, J, Z}}
|style = width:360px;
}}
</center>

=== Pentominoes ===
There are 12 distinct '''pentominoes'''. [[John Conway]] assigned them all letters in the range O to Z, loosely based on their shapes, and they are all shown below in order.
Unlike triominoes and tetrominoes, it has been proven that none of the pentominoes can work as [[induction coil]]s.

{| style="margin-left: auto; margin-right: auto"
| [[File:Opentomino small.png|thumb|center|O]]
| [[File:Ppentomino small.png|thumb|center|P]]
| [[File:Qpentomino small.png|thumb|center|Q]]
| [[File:Rpentomino small.png|thumb|center|R]]
| [[File:Spentomino small.png|thumb|center|S]]
| [[File:Tpentomino small.png|thumb|center|T]]
|-
| [[File:Upentomino small.png|thumb|center|U]]
| [[File:Vpentomino small.png|thumb|center|V]]
| [[File:Wpentomino small.png|thumb|center|W]]
| [[File:Xpentomino small.png|thumb|center|X]]
| [[File:Ypentomino small.png|thumb|center|Y]]
| [[File:Zpentomino small.png|thumb|center|Z]]
|}

* The O-pentomino is a [[traffic light]] [[predecessor]]. Its most common grandparent is 3o$3o$bo$2bo$2bo!.
* The P-pentomino or [[crotchet]] dies in [[generation]] 4.
* The Q-pentomino is a traffic light predecessor.
* The [[R-pentomino]] is a [[methuselah]] and by far the most well-known pentomino.
* The S-pentomino dies in generation 5.
* The T-pentomino is a common [[parent]] of the [[T-tetromino]].
* The U-pentomino or [[short table]] dies in generation 4.
* The V-pentomino evolves into a [[loaf]] in generation 3.
* The W-pentomino is a common loaf grandparent.
* The X-pentomino is a traffic light predecessor.
* The Y-pentomino dies in generation 3, creating [[obo spark]]s along the way.
* The Z-pentomino dies in generation 3.

=== Hexominoes ===
There are 35 distinct '''hexominoes''', the majority of which behave uninterestingly. The most interesting and well-known examples are [[century]], [[line-of-six spark]], [[stairstep hexomino]], [[table]], [[toad]], [[Pre-beehive]] and [[Z-hexomino]].

<center>
{{EmbedViewer
|pname = hexominoes
|position = center
|viewerconfig = #C [[ THUMBSIZE 2 WIDTH 1200 HEIGHT 700 ZOOM 12 ]]
|caption = The 35 distinct hexominoes
|style = width:360px;
}}
</center>

* The 1st hexomino is the [[line-of-six spark]], which dies in generation 12.
* The 2nd hexomino stabilizes into two blinkers at generation 40.<ref group="note">Four copies of this hexomino arranged in a certain way can make a [[Kok%27s galaxy]] [[predecessor]].</ref><ref name="xp2_111zy2s"/>
* The 3rd hexomino evolves into a [[block]] in generation 4.
* The 4th hexomino evolves into a [[traffic light]] in generation 9.
* The 5th hexomino dies in generation 4.
* The 6th hexomino evolves into a block in generation 4.
* The 7th hexomino is a [[grandparent]] of the [[boat]].
* The 8th hexomino evolves into a block in generation 4.
* The 9th hexomino is the [[table]], which becomes the line-of-six spark in 3 generations and therefore dies in generation 15.
* The 10th hexomino is the [[Z-hexomino]], which dies in generation 45.
* The 11th hexomino dies in generation 5.
* The 12th hexomino dies in generation 7 via the P-pentomino.
* The 13th hexomino converges to the same evolutionary sequence as the [[pi-heptomino]] and stabilizes at generation 176, leaving behind 6 blocks, 5 blinkers, and two [[pond]]s.
* The 14th hexomino dies in generation 5 via the P-pentomino.
* The 15th hexomino evolves into a block in generation 3.
* The 16th hexomino is a parent of the [[aircraft carrier]].
* The 17th hexomino dies in generation 5.
* The 18th hexomino is a parent of the [[stairstep hexomino]].
* The 19th hexomino converges to the same evolutionary sequence as the stairstep hexomino.
* The 20th hexomino also converges to the same evolutionary sequence as the stairstep hexomino.
* The 21st hexomino is the period-2 oscillator [[toad]].
* The 22nd hexomino evolves into a boat in generation 4.
* The 23rd hexomino dies in generation 6.
* The 24th hexomino is the century and stabilizes at generation 103, leaving behind 3 blocks and a blinker.
* The 25th hexomino is the [[ghost Herschel]] and dies in generation 6.
* The 26th hexomino is generation 1 of the R-pentomino and stabilizes at generation 1,102, leaving behind 8 blocks, 4 blinkers, 4 beehives, two boats, a ship, and a loaf and having created six escaping gliders.
* The 27th hexomino is a parent of the loaf.
* The 28th hexomino dies in generation 4.
* The 29th hexomino is a [[pre-beehive|parent of the beehive]].
* The 30th hexomino dies in generation 4.
* The 31st hexomino is a great grandparent of the pond.
* The 32nd hexomino dies in generation 3.
* The 33rd hexomino dies in generation 9.
* The 34th hexomino is a parent of the [[pi-heptomino]].
* The 35th hexomino is the stairstep hexomino and lasts 63 generations, leaving a [[blockade]].

=== Heptominoes ===
There are 108 distinct '''heptominoes'''. Those with names in common use are the [[B-heptomino]], the [[bullet heptomino]], the [[C-heptomino]], the [[E-heptomino]], the [[F-heptomino]],the [[H-heptomino]], the [[I-heptomino]], the [[Herschel]], and the [[pi-heptomino]].

Of the 108 heptominoes:
* 26 die completely.
* 16 become [[beehive]]s.
* 10 become [[block]]s.
* 10 become [[honey farm]]s.
* 6 become [[loaf|loaves]].
* 6 follow the [[pi-heptomino]] sequence.
* 5 become [[traffic light]]s.
* 4 become [[lumps of muck]].
* 3 become [[blinker]]s.
* 3 follow the [[butterfly]] sequence.
* 3 become [[glider]]s.
* 1 becomes a [[boat]].
* 1 follows the [[century]] sequence.
* 1 becomes a [[pulsar]].
* 1 becomes an [[R-pentomino]].
* 2 become two blocks: one with spacing [[Half-blockade|(4,1)]] and another with offset (5,0).
* 1 becomes two blinkers.
* 1 becomes two loaves.
* 1 becomes 2 traffic lights plus 2 blocks.

The remaining 7 have their own names due to being common methuselah sequences: the B, C, E, F, H, and I heptominoes and the Herschel.

All 108 heptominoes were either analyzed in 1970 or classified as "unknown so far" in [[Lifeline Volume 1]].

=== Octominoes ===
There are 369 distinct '''octominoes'''. Despite the abundance of octominoes, [[two-glider octomino|the following fairly common octomino]] (which evolves into a different octomino after two generations), which stabilizes after 386 generations into two [[traffic light]]s and four [[beehive]]s, is often referred to as simply ''the'' octomino:
[[File:Octomino.png|thumb|center|The octomino and its two-generation successor.]]
This leaves a [[toad]] at gen 21, but it does not survive after gen 153.

== Switch engine ==
[[Charles Corderman]] discovered the [[switch engine]] by running an exhaustive computer search on all decominoes and lower polyominoes. The machine that discovered the nonomino seed was unique, possessing an unusual architecture.

== Larger polyominoes ==
In April {{year|2023}}, yushimitsu announced completion of a Catagolue census of all polyominoes with {{nowrap|population ≤ 18}}.<ref name="post160531" /> Some of the results are 18-ominoes that produce a [[jam]], a [[mazing]], and a [[cis-queen bee shuttle]]; 17-omino predecessors for [[mold]] and [[blocker]]; a 14-omino that produces a [[block-laying switch engine]] and a 16-omino that produces a [[glider-producing switch engine]]; several [[Methuselah|long-lasting patterns]].

=== Enumeration ===
<tt>{{OEIS|A000105|tt=tt}}</tt> contains counts of polyominoes up to 50 cells. It has been shown that there exists a constant <tt>{{lim|n->∞|{{sqrt|a(n)|n}}}} = {{lim|n->∞|{{frac|a(n)|a(n-1)}}}} = λ</tt>, where <tt>4.00253<ref>Gill Barequet, Günter Rote, Mira Shalah (November 12, 2015). [https://link.springer.com/chapter/10.1007/978-3-662-48350-3_8 ''λ > 4''].</ref> < λ ≤ 4.5252<ref>Gill Barequet, Mira Shalah (June 28, 2019). [https://arxiv.org/abs/1906.11447 ''Improved Upper Bounds on the Growth Constants of Polyominoes and Polycubes''].</ref></tt> is Klarner's constant. Additionally, it appears the sequence <tt>{{frac|a(n)|a(n-1)}}</tt> is strictly increasing (converging to <tt>λ</tt>) with strictly decreasing first differences for all <tt>n > 13</tt>.

== Nomenclature ==
The name is a back-formation from 'domino', which explicitly refers to a pair of orthogonally connected live cells. According to the Life Lexicon, the pluralised name can be spelt two different ways: 'polyominos' and 'polyominoes' are both acceptable; the Life Lexicon follows Golomb in using the longer form. The same applies to the systematic names of each of the polyomino sizes.

== See also ==
* [[Polyplet]]
* {{CategoryLink|Polyominoes}}

== Notes ==
<references group="note"/>

== References ==
<references>
<ref name="xp2_111zy2s">[[Ash]] on {{LinkCatagolue|xp2_111zy2s|style=brief}}</ref>
<ref name="post155104">{{LinkForumThread
|format = ref
|p = 155104
|title = Re: Oscillator Discussion Thread
|author = Matthias Merzenich
|date = December 22, 2022
}}</ref>
<ref name="post160531">{{LinkForumThread
|format = ref
|p = 160531
|title = Re: Thread for your unsure discoveries
|author = yushimitsu
|date = April 16, 2023
}}</ref>
</references>

== External links ==
* {{LinkLexicon|lex_p.htm#polyomino}}
* {{LinkForumThread|f=12|t=3978|title=Polyominoes beyond CA}}
* {{LinkForumThread|f=12|t=3036|title=Polyomino tilings}}
* {{LinkForumThread|f=2|t=5888|title=UC-based polyomino oscillators and spaceships}}
* {{cite web|url=https://press.princeton.edu/books/paperback/9780691024448/polyominoes|title=Polyominoes: Puzzles, Patterns, Problems, and Packings|publisher=Princeton University Press|author=Solomon W. Golomb}} Revised and expanded second edition.

[[Category:Polyominoes| ]]
[[Category:Mathematical miscellany]]

Fleet

2024-07-12T17:15:54Z

Empty Emptiness: Undo revision 150316 by HotdogPi (talk) not like THAT. what I am talking about is literally in the evolutionary sequence of a ship with that dot on its tip.

{{Stilllife
|name = Fleet
|pname = fleet
|type = constellation
|c = 24
|bx = 10
|by = 10
|rulemin = B/S23
|rulemax = B3578/S012345678
|rulespecial = [[Conway's Game of Life|Conway Life]]
|isorulemin = B/S2e3kn
|isorulemax = B1e2-ae34-w56-n78/S012345678
|synthesis = 3
|synthesisRLE = true
|plaintext = true
|rle = true
|apgcode = xs24_g8o653wggz11wokc321
}}
'''Fleet''' is a fairly common [[constellation]] made up of two [[ship-tie]]s and is one of the [[familiar fours]]. It is frequently created via a pond with cells on two opposing corners.

Drawing a [[block]] between the two ship-ties will result in the block being eaten and the fleet being inverted in 27 generations. A 4 cell long diagonal line running parallel through the centre will do the same in just 4 [[generation]]s.

The minimum number of cells required to form a fleet is 7; there are several ways to do this.

{{EmbedViewer
|pname = blinkermovingfleet
|viewerconfig = #C [[ GPS 10 THUMBSIZE 2 AUTOSTART LOOP 60 PAUSE 3 ]]
|position = center
|caption = A blinker next to a fleet will move the fleet
|style = width:300px;
}}

==See also==
* [[Harbor]]
* [[Ship]]
* [[Bakery]]

==External links==
* {{LinkLexicon|lex_f.htm#fleet}}
* {{LinkCatagolue|xs24_g8o653wggz11wokc321|format=pseudo-object}}
* {{LinkNiemiec|cons.htm#cons-24|title=4 easily-constructible 24-bit constellations}}

{{Symmetry|diagonal4}}

Still life

2024-07-11T23:27:50Z

Empty Emptiness: /* Quasi still lifes */

{{Glossary}}
[[File:Still life classification.png|thumb|right|Classification of still lifes (stable patterns). Click to enlarge.|link=https://conwaylife.com/w/images/7/73/Still_life_classification.png]]
A '''still life'''{{refn|group=note|For the plural form, both "still lifes" and "still lives" are in common use.}} (or '''stable''' pattern) is a [[pattern]] that does not change from one generation to the next, and thus may be thought of as an [[oscillator]] with [[period]] 1. Still lifes are sometimes assumed to be finite and non-empty. The two main subgroups of still lifes are [[#Strict still lifes|strict still lifes]] and [[#Pseudo still lifes|pseudo still lifes]]. In some contexts, the term "still life" may refer to stable objects rather than stable patterns in general, or strict still lifes rather than stable objects in general.

== Strict still lifes ==
A '''strict still life''' is a still life that is either connected (i.e., has only one [[island]]), or is such that removing one or more its islands destroys the stability of the pattern. For example, [[beehive with tail]] is a strict still life because it is connected, and [[mirrored table]] is a strict still life because neither of the [[table]]s are stable by themselves.

<gallery widths="240px" style="text-align:center;">
Image:Beehive.png|[[Beehive]] is a strict still life because it is connected
Image:Beehivewithtail.png|Beehive with tail is a strict still life because it is connected, even though it contains a smaller still life
Image:Mirroredtable.png|Mirrored table is a strict still life because neither [[table]] is stable without the other
</gallery>

== Pseudo still lifes ==
A '''pseudo still life''' consists of two or more [[island]]s which can be partitioned (either individually or as sets) into non-interacting subpatterns which are by themselves each still lifes. Furthermore, there must be at least one dead cell that has more than three alive neighbours in the overall pattern but has less than three alive neighbours in the subpatterns. This final restriction removes patterns such as [[bakery]], [[blockade]] and [[fleet]] from consideration, as the islands are not "almost touching".

Note that a pattern may have multiple disconnected components and still be a strict (as opposed to pseudo) still life if the disconnected components are dependent on each other for stability (for example, [[mirrored table]] above). Some pseudo still lifes have also been found by [[Gabriel Nivasch]] that can be partitioned into a minimum of three and four stable subpatterns, respectively, as in the second and third images below.<ref name="gn_stilllife">{{cite web|url=http://www.gabrielnivasch.org/fun/life/still-lifes |title=Still lifes |author=Nivasch, Gabriel|date=July, 2001|accessdate=March 23, 2016}}</ref> The stable subpatterns themselves may be either strict or pseudo still lifes. It is not possible to construct a pseudo still life that can be partitioned into a minimum of greater than four stable subpatterns because of the four-color theorem.<ref name="gn_stilllife" />

<gallery widths="240px" style="text-align:center;">
Image:Biblock.png|[[Bi-block]] is a pseudo still life because each [[block]] is stable by itself
Image:triplepseudostilllife.png|[[triple pseudo still life]]
Image:quadpseudostilllife.png|[[quad pseudo still life]]
</gallery>

It has been shown that it is possible to determine whether a still life pattern is a strict still life or a pseudo still life in polynomial time by searching for cycles in an associated skew-symmetric graph.<ref>{{cite web|url=https://academic.oup.com/book/40819/chapter-abstract/348790306?redirectedFrom=fulltext |year=2003|title=New Constructions in Cellular Automata: Still life theory, pages 93–118|publisher=Santa Fe Institute Studies in the Sciences of Complexity, Oxford University Press |author=Cook, Matthew|authorlink=Matthew Cook}}</ref><ref name="cook">{{cite web|url=http://msri.org/publications/ln/msri/2000/gametheory/cook/1/index.html |title=Still Life |author=Cook, Matthew |publisher=Mathematical Sciences Research Institute}}</ref>

== Constellations ==
A (stable) '''[[constellation]]''' is a still life that is composed of two or more non-interacting objects. This contrasts with pseudo and quasi still lifes, in which the objects in question must interact. Compare for instance the bi-block and blockade:

<gallery widths="240px" style="text-align:center;">
Image:Biblock.png|Bi-block is a pseudo still life because the two [[block]]s interact: the two dead cells between them (highlighted in red) are influenced by both
Image:Blockade.png|Blockade is a constellation because the four blocks do not interact in any way
</gallery>

Certain unstable (e.g. oscillating) patterns are sometimes also referred to as [[constellation]]s. The term "stable constellation" is used to refer specifically to still life constellations.

== Quasi still lifes ==
A stable constellation in which the constituent objects share dead cells, but where all cells that used to remain dead from under-population in the overall pattern still do so in the constituent objects, is called a '''quasi still life'''. In [[Conway's Game of Life|Conway's Life]], this occurs when objects are diagonally adjacent (e.g. two [[block]]s sharing a single diagonal neighbor), or when single protruding cells in two objects such as [[tub]]s share multiple neighbors.

<gallery widths="240px" style="text-align:center;">
Image:Quasistilllife.png|Two [[block]]s sharing a single diagonal neighbor, marked in yellow; this cell is dead from underpopulation and remains so after separation
</gallery>

The term "quasi still life" was coined by Mark Niemiec.

== Enumerating still lifes ==
The number of strict and pseudo still lifes that exist for a given number of cells has been enumerated up to 34, and the number of quasi still lifes for a given number of cells up to 22.
* The values in the strict still life table below were originally computed by [[John Conway]] (4-7 cells), [[Robert Wainwright]] (8-10 cells), [[David Buckingham]] (11-13 cells), [[Peter Raynham]] (14 cells), [[Mark Niemiec]] (15-24 cells), [[Simon Ekström]] (25-28 cells),<ref name="post38931" /><ref name="post38965" /><ref name="post39082" /> Simon Ekström and "Apple Bottom" (29-30 cells),<ref name="post39322" /> and [[Nathaniel Johnston]] (31-34 cells).<ref name="post42106" /><ref name="post43762" /><ref name="post74524" /><ref name="post87225" />
* The values in the pseudo still life table were enumerated by Mark Niemiec (1-24 cells), Simon Ekström (25-28 cells),<ref name="post38931" /><ref name="post38965" /><ref name="post39082" /> Simon Ekström and "Apple Bottom" (29-30 cells),<ref name="post39322" /> and Nathaniel Johnston (31-34 cells).<ref name="post42106" /><ref name="post43762" /><ref name="post74524" /><ref name="post87225" />
* The values in the quasi still life table below were originally computed by [[Mark Niemiec]] (8-20 cells) and Simon Ekström (21-22 cells).<ref name="post39372" />

{| class="wikitable" style="text-align:center"
! rowspan="2" | Live cells
! colspan="3" | Strict still lifes
! colspan="3" | Pseudo still lifes
! colspan="3" | Quasi still lifes
|-
! Count ({{OEIS|A019473}})
! Examples
! List
! Count ({{OEIS|A056613}})
! Examples
! List
! Count ({{OEIS|A330283}})
! Examples
! List
|-
|1|| {{A019473|1}} || || || {{A056613|1}} || || || {{A330283|1}} || ||
|-
|2|| {{A019473|2}} || || || {{A056613|2}} || || || {{A330283|2}} || ||
|-
|3|| {{A019473|3}} || || || {{A056613|3}} || || || {{A330283|3}} || ||
|-
|4|| {{A019473|4}} || [[block]], [[tub]] || [[:Category:Strict still lifes with 4 cells|Full list]] || {{A056613|4}} || || || {{A330283|4}} || ||
|-
|5|| {{A019473|5}} || [[boat]] || [[:Category:Strict still lifes with 5 cells|Full list]] || {{A056613|5}} || || || {{A330283|5}} || ||
|-
|6|| {{A019473|6}} || [[beehive]], [[ship]] || [[:Category:Strict still lifes with 6 cells|Full list]] || {{A056613|6}} || || || {{A330283|6}} || ||
|-
|7|| {{A019473|7}} || [[eater 1]], [[loaf]] || [[:Category:Strict still lifes with 7 cells|Full list]] || {{A056613|7}} || || || {{A330283|7}} || ||
|-
|8|| {{A019473|8}} || [[canoe]], [[pond]] || [[:Category:Strict still lifes with 8 cells|Full list]] || {{A056613|8}} || [[bi-block]] || [[Small pseudo still lifes#8 cells|Full list]] || {{A330283|8}} || {{LinkCatagolue|code=xs8_g8g252z01|style=raw}} ||
|-
|9|| {{A019473|9}} || [[hat]], [[integral sign]] || [[:Category:Strict still lifes with 9 cells|Full list]] || {{A056613|9}} || [[block on boat]] || [[Small pseudo still lifes#9 cells|Full list]] || {{A330283|9}} || {{LinkCatagolue|code=xs9_g8o033z01|style=raw}} ||
|-
|10|| {{A019473|10}} || [[boat-tie]], [[loop]] || [[:Category:Strict still lifes with 10 cells|Full list]] || {{A056613|10}} || [[cis-bi-boat]] || [[Small pseudo still lifes#10 cells|Full list]] || {{A330283|10}} || {{LinkCatagolue|code=xs10_0gg0652z121|style=raw}} ||
|-
|11|| {{A019473|11}} || [[elevener]] || [[:Category:Strict still lifes with 11 cells|Full list]] || {{A056613|11}} || [[Small pseudo still lifes#11 cells|block on loaf]]
|| [[Small pseudo still lifes#11 cells|Full list]] || {{A330283|11}} || {{LinkCatagolue|code=xs11_0gg0652z321|style=raw}} ||
|-
|12|| {{A019473|12}} || [[honeycomb]], [[mirrored table]] || [[:Category:Strict still lifes with 12 cells|Full list]] || {{A056613|12}} || {{LinkCatagolue|code=xs12_6606996|style=raw}} || || {{A330283|12}} || {{LinkCatagolue|code=xs12_0gg0653z321|style=raw}} ||
|-
|13|| {{A019473|13}} || [[sesquihat]] || [[:Category:Strict still lifes with 13 cells|Partial list]] || {{A056613|13}} || {{LinkCatagolue|code=xs13_253035ac|style=raw}} || || {{A330283|13}} || {{LinkCatagolue|code=xs13_x6952z653|style=raw}} ||
|-
|14|| {{A019473|14}} || [[fourteener]], [[paperclip]] || [[:Category:Strict still lifes with 14 cells|Partial list]] || {{A056613|14}} || {{LinkCatagolue|code=xs14_ca23z3lo|style=raw}} || || {{A330283|14}} || {{LinkCatagolue|code=xs14_2596zw69a4|style=raw}} ||
|-
|15|| {{A019473|15}} || [[moose antlers]] || [[:Category:Strict still lifes with 15 cells|Partial list]] || {{A056613|15}} || {{LinkCatagolue|code=xs15_2lmzold|style=raw}} || || {{A330283|15}} || {{LinkCatagolue|code=xs15_dbwkcz6421|style=raw}} ||
|-
|16|| {{A019473|16}} || [[mirrored cap]], [[scorpion]] || [[:Category:Strict still lifes with 16 cells|Partial list]] || {{A056613|16}} || [[pond on pond]] || || {{A330283|16}} || {{LinkCatagolue|code=xs16_2l20kq23z121|style=raw}} ||
|-
|17|| {{A019473|17}} || [[twin hat]] || [[:Category:Strict still lifes with 17 cells|Partial list]] || {{A056613|17}} || {{LinkCatagolue|code=xs17_4aar0rr|style=raw}} || || {{A330283|17}} || ||
|-
|18|| {{A019473|18}} || [[dead spark coil]] || [[:Category:Strict still lifes with 18 cells|Partial list]] || {{A056613|18}} || {{LinkCatagolue|code=xs18_8e12kmz31243|style=raw}} || || {{A330283|18}} || ||
|-
|19|| {{A019473|19}} || [[eater 2]] || [[:Category:Strict still lifes with 19 cells|Partial list]] || {{A056613|19}} || {{LinkCatagolue|code=xs19_4aar0ra96|style=raw}} || || {{A330283|19}} || ||
|-
|20|| {{A019473|20}} || [[spiral]] || [[:Category:Strict still lifes with 20 cells|Partial list]] || {{A056613|20}} || {{LinkCatagolue|code=xs20_0ml3z0ddz653|style=raw}} || || {{A330283|20}} || ||
|-
|21|| {{A019473|21}} || [[tri-loaf 2]] || [[:Category:Strict still lifes with 21 cells|Partial list]] || {{A056613|21}} || {{LinkCatagolue|code=xs21_4aar0rahr|style=raw}} || || {{A330283|21}} || ||
|-
|22|| {{A019473|22}} || [[cis-mirrored worm]] || [[:Category:Strict still lifes with 22 cells|Partial list]] || {{A056613|22}} || {{LinkCatagolue|code=xs22_2lm0mmz343056|style=raw}} || || {{A330283|22}} || ||
|-
|23|| {{A019473|23}} || [[Large natural still lifes|xs23_259e0ehu0ui]] || || {{A056613|23}} || {{LinkCatagolue|code=xs23_bd0mkk8z178l8|style=raw}} || || {{A330283|23}} || ||
|-
|24|| {{A019473|24}} || [[lake 2]] || [[:Category:Strict still lifes with 24 cells|Partial list]] || {{A056613|24}} || {{LinkCatagolue|xs24_gg0gbbg0ggz1101qq1011|style=raw}} || || {{A330283|24}} || ||
|-
|25|| {{A019473|25}} || [[squid]] || [[:Category:Strict still lifes with 25 cells|Partial list]] || {{A056613|25}} || {{LinkCatagolue|xs25_3lkkl3zrag023z01|style=raw}} || || {{A330283|25}} || ||
|-
|26|| {{A019473|26}} || [[Mickey Mouse]] || [[:Category:Strict still lifes with 26 cells|Partial list]] || {{A056613|26}} || {{LinkCatagolue|xs26_rhe0ehr0rr|style=raw}} || || {{A330283|26}} || ||
|-
|27|| {{A019473|27}} || [[hat siamese vase]] || [[:Category:Strict still lifes with 27 cells|Partial list]] || {{A056613|27}} || {{LinkCatagolue|xs27_ciqb96z4aicggzx1221|style=raw}} || || {{A330283|27}} || ||
|-
|28|| {{A019473|28}} || [[O quad-loaf]] || [[:Category:Strict still lifes with 28 cells|Partial list]] || {{A056613|28}} || {{LinkCatagolue|xs28_69bqic0ciqb96|style=raw}} || || {{A330283|28}} || ||
|-
|29|| {{A019473|29}} || [[xs29_cc0s2ticz330fgkc]] || [[:Category:Strict still lifes with 29 cells|Partial list]] || {{A056613|29}} || {{LinkCatagolue|xs29_0g8ow31e8gz2fgkc0c871|style=raw}} || || {{A330283|29}} || ||
|-
|30|| {{A019473|30}} || [[Clips]] || [[:Category:Strict still lifes with 30 cells|Partial list]] || {{A056613|30}} || {{LinkCatagolue|xs30_03lkl3zgbq0qbgz11x11|style=raw}} || || {{A330283|30}} || ||
|-
|31|| {{A019473|31}} || [[Aries betwixt two blocks]] || [[:Category:Strict still lifes with 31 cells|Partial list]] || {{A056613|31}} || {{LinkCatagolue|xs32_bd0mk2sgz1785d0mq|style=raw}} || || {{A330283|31}} || ||
|-
|32|| {{A019473|32}} || [[Inflected 30-great sym]] || [[:Category:Strict still lifes with 32 cells|Partial list]] || {{A056613|32}} || [[triple pseudo still life]] || [[:Category:Pseudo still lifes with 32 cells|Partial list]] || {{A330283|32}} || ||
|-
|33|| {{A019473|33}} || {{LinkCatagolue|code=xs33_69b8bb88gz69d1dd11|style=raw}} || || {{A056613|33}} || {{LinkCatagolue|xs33_321fgkcz6a88a6z651156|style=raw}} || || {{A330283|33}} || ||
|-
|34|| {{A019473|34}} || [[Cis-mirrored elf-shoe]] || [[:Category:Strict still lifes with 34 cells|Partial list]] || {{A056613|34}} || [[quad pseudo still life]] || [[:Category:Pseudo still lifes with 34 cells|Partial list]] || {{A330283|34}} || ||
|}

As the number of bits increases, these counts increase exponentially; the rate for strict still lifes is about O(2.46n), while for pseudo still lifes it is around O(2.56n), and approximately O(3.04n) for quasi still lifes.

== See also ==
* [[List of common still lifes]]
* {{CategoryLink|Pseudo still lifes}}
* {{CategoryLink|Still lifes}}
* {{CategoryLink|Strict still lifes}}
* [[Object]]

==Notes==
<references group=note />

== References ==
<references>
<ref name="post38931">{{LinkForumThread
|format = ref
|title = Re: Enumerating Still Lifes (in C)
|p = 38931
|author = Simon Ekström
|date = January 2, 2017
}}</ref>
<ref name="post38965">{{LinkForumThread
|format = ref
|title = Re: Enumerating Still Lifes (in C)
|p = 38965
|author = Simon Ekström
|date = January 3, 2017
}}</ref>
<ref name="post39082">{{LinkForumThread
|format = ref
|title = Re: Enumerating Still Lifes (in C)
|p = 39082
|author = Simon Ekström
|date = January 7, 2017
}}</ref>
<ref name="post39322">{{LinkForumThread
|format = ref
|title = Re: Enumerating Still Lifes (in C)
|p = 39322
|author = Simon Ekström
|date = January 14, 2017
}}</ref>
<ref name="post42106">{{LinkForumThread
|format = ref
|title = Re: Enumerating Still Lifes (in C)
|p = 42106
|author = Nathaniel Johnston
|date = March 27, 2017
}}</ref>
<ref name="post43762">{{LinkForumThread
|p = 43762
|title = Re: Enumerating Still Lifes (in C)
|author = Nathaniel Johnston
|format = ref
|date = May 25, 2017
}}</ref>
<ref name="post74524">{{LinkForumThread
|format = ref
|title = Re: Enumerating Still Lifes (in C)
|p = 74524
|author = Nathaniel Johnston
|date = April 5, 2019
}}</ref>
<ref name="post87225">{{LinkForumThread
|format = ref
|title = Re: Enumerating Still Lifes (in C)
|p = 87225
|author = Nathaniel Johnston
|date = January 9, 2020
}}</ref>
<ref name="post39372">{{LinkForumThread
|author = Mark Niemiec
|title = Re: Enumerating Still Lifes (in C)
|format = ref
|p = 39372
|date = January 15, 2017
}}</ref>
</references>

== External links ==
* {{LinkWikipedia|Still_life_(cellular_automaton)}}
* {{LinkLexicon|lex_s.htm#stilllife|name=Still life}}
* {{LinkLexicon|lex_p.htm#pseudostilllife|name=Pseudo still life}}
* {{LinkLexicon|lex_q.htm#quasistilllife|name=Quasi still life}}
* {{LinkNiemiec|objcount.htm|patternname=Life Object Counts}}

Fleet

2024-07-03T16:18:19Z

Empty Emptiness:

Block

2024-07-03T13:53:51Z

Empty Emptiness: /* Use in higher still lifes */

{{Stilllife
|name = Block
|pname = block
|c = 4
|bx = 2
|by = 2
|fc = 0.0
|discoverer = John Conway
|discoveryear = 1969
|rulemin = B/S3
|rulemax = B345678/S012345678
|isorulemin = B/S3a
|isorulemax = B1e2-a345678/S012345678
|synthesis = 2
|synthesisRLE = true
|plaintext = true
|rle = true
|apgcode = xs4_33
|pentadecathlonid = 4.1
|viewerconfig = #C [[ ZOOM 60 ]]
}}
'''Block''' is an extremely well-known and common [[still life]] that was found by [[John Conway]] in {{year|1970}}.<ref>{{CiteHickersonOscillators|accessdate=March 14, 2020}}</ref> In terms of its {{slcells|4|text=4 cells}} it is tied with [[tub]] as the smallest still life, and in terms of its {{times|2|2}} [[bounding box]] it is the outright smallest. It is also the only known still life that is a [[polyomino]], and the only finite [[strict still life]] where all living cells have three neighbors{{refn|group=note|Any such still life would remain a still life in B3/S3. A proof that there are no finite strict still lifes other than the block in B3/S3 was cross-posted from Discord in August 2023,<ref name="post164841" /> settling an open problem.}}. Its small size, [[#Uses in catalysis|ability to act as a catalyst]], and simple [[glider syntheses]] make it extremely useful in the construction of larger patterns.

The block was one of the patterns described in the original 1970 article by [[Martin Gardner]] that introduced the [[Game of Life]] to the world.

== Use in higher still lifes ==
Blocks serve useful in the construction of larger still lifes. Due to its high density, orthogonal and diagonal connections (like those seen in [[ship-tie]]) would overpopulate any present cells, preventing any patterns with this arrangement from being useful in a still life (this reaction can instead be used for oscillators such as [[beacon]] and variants of [[star]]). As such, its uses are limited to acting as an [[induction coil]].

Given the high symmetry of the block (the highest a pattern can have on the [[square grid]]), cis-, trans- and other isomeric variants only arise if the object stabilised by the block is itself of a sufficiently low symmetry.

Examples of known still lifes which use the block as an induction coil are as follows:
* [[Block on table]] (10)
* [[Block on cap]] (12)
* [[Block on cover]] (12)
* [[Cis-block on long bookend]] (12)
* [[Trans-block on long bookend]] (12)
* [[Block on dock]] (14)
* [[Eater 2]] (19)
* [[Mango with block on dock]] (19)

Blocks can also be used to stabilise certain oscillators in a [[Catalysis|non-catalytic]] fashion, with examples as follows:
* [[Block on griddle]] (p2)
* [[Blocks on griddle]] (p2)
* [[Cis-block on candlefrobra]] (p3)
* [[Trans-block on candlefrobra]] (p3)
* [[101]] (p5)

== Uses in catalysis ==
{{main|Tutorials/Catalyses#Block}}

The block sees a diverse array of uses in larger patterns. For example, [[glider-block cycle|it can work]] as a [[reflector]] for two gliders via the [[interchange]] synthesis, as can be seen in [[106P135]].

There are multiple ways in which the block may act as a [[catalyst]]. These fall into roughly two camps, according to how the block will be regenerated (since the block's cells already have three neighbors, it cannot act as a [[rock]], except through induction, such as the [[p47 pre-pulsar shuttle]] or [[84P199]]). Oscillators such as [[blocker]], [[p56 B-heptomino shuttle]], [[queen bee shuttle]], [[twin bees shuttle]] and [[unix]] showcase mechanisms which leave a [[pre-block]] or a [[hook]], while the mechanisms seen in [[Coe's p8]], [[eater 5]] and [[octagon 4]] leave a [[grin]]. A different mechanism yet, where only a single cell of the original block survives the whole ordeal, appears in [[37P7.1]]. It has been seen [[Eater|eating]] [[mango]]s, [[boat]]s, [[loaf|loaves]], and [[beehive]]s.

Some more complex eaters can be based on the block as well. [[Eater 2]] is a construction allowing a block to [[Glider eater|eat gliders]]: while the collision would normally destroy both, the addition of further still life(s) or [[inductee]]s allows the remaining three-cell [[spark]] to regenerate into a block.

Since the block is the most common object to emerge from soups, it is also the most common object to show [[transparent debris effect]], as described above. Several larger oscillators including [[p54 shuttle]], [[78P70]], [[two blockers hassling R-pentomino]] and [[Achim's p144]] are examples. A particular reaction with a [[B-heptomino]] is commonly used in the construction of [[Herschel track]]s.

== Blockic constellations ==
{{main|Blockic}}
A blockic constellation is a [[constellation]] consisting entirely of blocks. It's possible to arrange blocks in [[seed|a way]] that can be [[trigger]]ed by a single glider to produce any glider-constructible pattern.<ref>{{citeCGoLMC|section=5.7.3|page=140-143}}</ref>

== Block agar and block arrays ==
{{main|Block agar}}
The block agar is an agar consisting of blocks arranged periodically in rows and columns, with distance of 1 cell between any two adjacent rows or columns.
Sometimes, more sparse arrangements of blocks are also described as block agars.

[[Pseudo still life]]s consisting of an arbitrary array of blocks may be referred to as [[block array]]s. There are known methods of [[Glider synthesis|constructing]] block arrays of sizes {{times|2|''n''}}, {{times|3|''n''}}, {{times|4|''n''}}; the general problem is still open.

== Occurrence ==
The block is the most common object, and thus the most common still life, that occurs as a result of [[soup|random starting patterns]]. As such, it is the reference element for calculating [[frequency class]].

In the [[Catagolue]] [[census]], the block comprises 30.9% of all object occurrences.
In [[Achim Flammenkamp's census]] it occurred almost twice as often as [[beehive]], the next most common still life. However, the blinker is slightly more common than the block in Achim's census, unlike on Catagolue. This can be explained by [[Herschel]]s, which have a lot of empty space to evolve in {{times|16|16}} soups but not on a [[torus]], leaving two blocks behind.<ref>{{citeAchim|accessdate=January 15, 2009}}</ref>

The chance of a block in a specific location in an infinite random soup is approximately 1 in 473. This number is the frequency of on cells (0.0287) divided by the average object size (4.388) times the chance that a particular object will be a block (0.323). As blocks have 8-way symmetry, there is no symmetry factor to take into account. This number is helpful in determining how often transparent blocks occur; transparent blocks are twice as common as transparent blinkers, almost four times as common as transparent beehives, and more than twenty times as common as anything else.

== Glider synthesis ==
The block is the most common object produced by [[2-glider collision]]s; three head-on instances and three perpendicular ones create a clean block, and there are also other examples that produce solely blocks (in the form of bi-block, half-blockade, four skewed blocks or blockade).

== Notes ==
<references group=note>
</references>

== See also ==
* [[Bi-block]]
* [[Blockade]]
* [[Bricklayer]]
* [[Blockstacker]]
* [[List of common catalysts]]
* [[Block fuse]]

== References ==
<references>
<ref name="post164841">{{LinkForumThread|p = 164841|author = LaundryPizza03 (original by rachel)|date = August 10, 2023|title = Re: Speed limits and theorems about the existence of periodic objects|format = ref}}</ref>
</references>

== External links ==
* {{LinkLexicon|lex_b.htm#block}}
* {{LinkCatagolue|xs4_33}}
* {{LinkNiemiec|p1.htm#p1-4|The 2 four-bit still-lifes|rle=0/4bk.rle}}
* {{LinkPentadecathlonObject|id=4.1|archivedate=20221101214854|patternname=Block}}
* [http://www.ibiblio.org/lifepatterns/october1970.html The fantastic combinations of John Conway's new solitaire game "life"] by Martin Gardner

[[Category:Catalysts]]
[[Category:Eaters]]
[[Category:Polyominoes]]

{{Symmetry|full}}

Switch engine

2024-07-02T18:51:11Z

Empty Emptiness:

{{Methuselah
|name = Switch engine
|pname = switchengine
|c = 8
|bx = 6
|by = 4
|l = 3911
|f = 842
|mcps = 10
|discoverer = Charles Corderman
|discoveryear = 1971
|rulemin = B3/S23
|rulemax = B3/S23
|isorulemin = B3/S23
|isorulemax = B3/S23 
|synthesis = 3
|synthesisRLE = true
|plaintext = true
|rle = true
|viewerconfig = #C [[ HEIGHT 600 WIDTH 600 THUMBSIZE 3 ZOOM 60 ]]
}}
A '''switch engine''' (or '''Corder engine'''<ref>{{CiteLexicon|file=lex_c.htm#corderengine|name=Corder engine|accessdate=June 10, 2009}}</ref>) is a [[methuselah]] that was found by [[Charles Corderman]] in {{year|1971}}.<ref>{{CiteLifeline|vol=4|pages=page 2}}</ref> It produces a copy of itself after 48 generations, glide-reflected 4 cells northwest (starting in the form to the right), along with some active [[junk]]. If left unattended, the accumulating exhaust overtakes and destroys the engine after 24 cycles, but it can be stabilized to make [[c/12 diagonal]] [[puffer]]s and [[spaceship]]s.

==History==
In {{year|1971}}, Charles Corderman investigated the [[fate]] of all the small [[polyomino]]es exhaustively. Records indicate that he found the switch engine while investigating the [[decomino]]es (polyominoes having 10 cells). However, record of the decomino switch engine [[predecessor]] seems to have been lost.<ref name="post21235" /> There is, however, a unique [[nonomino]] switch engine predecessor whose 2-tick descendant matches that of a switch engine:<ref name="post21249" />

{{EmbedViewer
|pname = nonominoswitchenginepredecessor
|viewerconfig = #C [[ THUMBSIZE 4 ZOOM 32 HEIGHT 480 GPS 2 THEME Book AUTOSTART T 0 PAUSE 2 T 2 PAUSE 1 LOOP 3 ]]
|position = center
|caption = Nonomino switch engine predecessor
|style = width:300px;
}}

It is the smallest known polyomino to do so. If Corderman was examining polyominoes in order of size, then this smaller predecessor should have been found first in any case.

==Stabilization==

The movement of a switch engine can be sustained in several different types of patterns.

===Infinite growth===

There are two basic types of stabilized switch engine [[orbit]]s, both of which were also found by Charles Corderman: the [[period]]-288 [[block-laying switch engine]] (the more common of the two), stabilizing in an orbit of six cycles (with additional glide symmetry) and period-384 [[glider-producing switch engine]], stabilizing in an asymmetric orbit of eight cycles. These two puffers are the most natural [[infinite growth]] patterns in [[Conway's Game of Life]], being by far the most common ones to occur from non-symmetric [[soup|random starting patterns]].<ref name="statistics">{{citeCatagolueStats}}</ref> Switch engine-based puffers and combinations thereof, such as [[pony express]] and [[birthday puffer]], are also the only infinite growth patterns observed to have emerged from asymmetric soups on [[Catagolue]].

Because the switch engine lends itself so naturally to infinitely-growing patterns, it appears in many of the smallest known superlinear growth patterns, including the [[mosquito]]es, [[catacryst]], [[metacatacryst]], [[Gotts dots]], and [[20-cell quadratic growth]].

In addition to the puffers based on a single switch engine, puffers such as [[Noah's ark]] can be created by combining two switch engines. Such puffers are generally quite [[dirty]].

There are also patterns such as [[conga line switch engine extender]] which produces an extending line of switch engines. It is based on [[Ian07]]'s discovery earlier that month that a single switch engine could be stabilized by another switch engine following closely behind it.

===Spaceship===
{{main|Cordership}}

it is also possible to create spaceships made of switch engines that interact to remove their combined exhaust. They are named "Cordership" in honor of Charles Corderman. These spaceships move at [[c/12 diagonal]]ly and are thus the slowest known non-[[adjustable spaceship]]s in Life. Such spaceships can be constructed by combining as few as [[2-engine Cordership|two]] switch engines.

==='Swimmer' tracks===
{{main|Switch engine channel}}

Like [[Herschel]]s, switch engines can be supported by [[conduit]]s made out of well-separated still lifes. These 'swimmer tracks' were first constructed by [[David Bell]] in 2005. Stable [[converter]]s have since been constructed that convert Herschels or gliders to switch engines and back.

==Final pattern==
[[File:Switchengine_final.png|300px|thumb|Generation 3911]]
The final pattern that results from a lone switch engine has 842 [[cell]]s. It consists of 60 [[block]]s, 33 [[beehive]]s (including one [[honey farm]]), 50 [[blinker]]s (including eight [[traffic light]]s), 12 [[glider]]s, 11 [[boat]]s, 11 [[loaf|loaves]], four [[ship]]s, two [[long boat]]s, two [[pond]]s, and two [[tub]]s.

==Synthesis==

In {{year|1973}}, [[Douglas G. Petrie]] employed a {{gliders|4}} recipe of a switch engine in his [[synthesis]] for a block-laying switch engine.<ref>{{CiteLifeline|vol=10|pages=page 5}}</ref> Decades later, [[Luka Okanishi]] discovered a surprisingly small {{gliders|3}} synthesis for a clean switch engine on March 12, {{year|2017}}.<ref name="post41557" />

==Other rules==
The only [[Hensel notation|two-state isotropic]] alien rule where the main mechanism of the switch engine still works is {{rl|B3/S236e}}. No single-engine orbits are known in that rule despite searches being done<ref name="post153290" /><ref name="post107613" />, but there are known Corderships that work.<ref name="post107613" />

== Gallery ==
{{EmbedViewer
|pname = 8and9cellswitchenginepredecessors
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 8 HEIGHT 600 ]]
|position = center
|caption = 8-cell 0, 1, 2 and 9-cell 3, 4, 5-generation switch engine predecessors<ref name="post143047" />
|style = width:300px;
}}

==References==
<references>
<ref name="post21235">{{LinkForumThread
|format = ref
|p = 21235
|title = Re: CMD shape switch engine
|author = Dave Greene
|date = July 17, 2015
}}</ref>
<ref name="post21249">{{LinkForumThread
|format = ref
|p = 21249
|title = Re: CMD shape switch engine
|author = Dave Greene
|date = July 18, 2015
}}</ref>
<ref name="post41557">{{LinkForumThread
|format = ref
|p = 41557
|title = Re: Thread For Your Accidental Discoveries
|author = Luka Okanishi
|date = March 12, 2017
}}</ref>
<ref name="post107613">{{LinkForumThread
|format = ref
|p = 107613
|title = Re: Thread for basic non-CGOL questions
|author = Schiaparelliorbust
|date = October 23, 2020
}}</ref>
<ref name="post143047">{{LinkForumThread
|format = ref
|p = 143047
|title = Re: Thread for your unsure discoveries
|author = dani
|date = March 17, 2022
}}</ref>
<ref name="post153290">{{LinkForumThread
|format = ref
|p = 153290
|title = Re: Thread for basic questions
|author = dani
|date = November 8, 2022
}}</ref>
</references>

==External links==
* {{LinkLexicon|lex_s.htm#switchengine}}

* {{LinkLexicon|filename=lex_n.htm#nonominoswitchenginepredecessor|patternname=Nonomino switch engine predecessor}}
* {{cite web
|url = https://web.archive.org/web/20200728034553/http://www.pentadecathlon.com/objects/class4/typeB/SwitchEngine1/switchEngine1.php
|title = Single Switch Engine
|work = [[Game of Life News|Game of Life Information]], Class 4 Objects Catalog, Type B -- Puffer Trains
}}
* {{cite web
|url = https://web.archive.org/web/20200509142738/http://www.pentadecathlon.com/objects/class4/typeB/switchEngine2/switchEngine2.php
|title = Double Switch Engine
|work = [[Game of Life News|Game of Life Information]], Class 4 Objects Catalog, Type B -- Puffer Trains
}}
* {{cite web
|url = https://web.archive.org/web/20200508230804/http://www.pentadecathlon.com/objects/class4/typeB/switchEngineN/switchEngineN.php
|title = Multiple Switch Engines
|work = [[Game of Life News|Game of Life Information]], Class 4 Objects Catalog, Type B -- Puffer Trains
}}

[[Category:Puffer engines]]
[[Category:Patterns involving switch engines| ]]

Island

2024-07-02T18:46:25Z

Empty Emptiness: this would be easier if my mouse wasn't out of battery

{{Glossary}}
[[Image:Aircraftcarrier.png|framed|right|An aircraft carrier has two islands]]An '''island''' is an individual [[polyplet]] of a larger (usually [[still life|stable]]) [[pattern]]. For example, a [[boat]] has only one island, an [[aircraft carrier]] has two islands, a [[honey farm]] has four islands, and [[eater 3]] has five islands.

Each island may or may not interact with one another. For example, the islands in [[dead spark coil]] interact via [[induction coil|induction]], while the islands in [[blockade]] do not interact at all.

==See also==
*[[Still_life#Pseudo still lifes|Pseudo still life]]

==External links==
{{LinkLexicon|lex_i.htm#island}}