LifeWiki - User contributions [en]

BTS

2023-03-12T15:18:41Z

BlinkerSpawn:

{{Stilllife
|name = BTS
|pname = bts
|c = 19
|bx = 7
|by = 8
|discoverer = Mark Niemiec
|rulemin = B/S23
|rulemax = B3678/S012345678
|rulespecial = [[Conway's Game of Life|Conway Life]], [[HighLife]]
|isorulemin = B/S2aek3nr
|isorulemax = B2in34-ainry5-jqr678/S012345678
|synthesis = 10
|plaintext = true
|rle = true
|apgcode = xs19_32qb079czw23
|pentadecathlonid = 19.28858
}}{{stub|This article can be expanded with: comparison and contrast with {{LinkCatagolue|xs18_8e13z315b8o|style=raw}} (used in places like [[p21 honey farm hassler]]) in catalysis.}}
'''BTS''', short for '''bookend-table-snake''', is a {{slcells|19|text=19-cell}} [[still life]] where a [[bookend]] is stabilized by a [[down snake on table]]. It is notable for having multiple uses as a [[catalyst]] in larger patterns.

The BTS was first officially enumerated among other still lives by [[Mark Niemiec]], but it was not until 2015 that [[Tanner Jacobi]] noticed (and somewhat popularized) its usefulness, due to its extensive appearances in results generated by [[Mike Playle]]'s [[Bellman]] program.<ref name="post18079" /> Example uses of this object as a catalyst for non-[[Spartan]] [[signal]] [[circuitry]] include the [[CC semi-cenark]], [[Jormungant's G-to-H]] and a glider-emitting [[F131]] variant.

A typical [[catalysis]] of a BTS or related still life involves the flat end of the bookend and one or both feet of the table.

{{EmbedViewer
|pname = eaterbts
|viewerconfig = #C [[ GPS 2 THUMBSIZE 2 STOP 3 ]]
|position = center
|caption = BTS as [[eater 1]] replacement when eating a [[B-heptaplet]] parent. For more examples see [[Tutorials/Catalyses#Fishhook_replacements]]
|style = width:300px;
}}

== Commonness ==
{{main|List of common still lifes}}
{{Needs occurrence info|type=still life}}

== Glider synthesis ==
On December 13, {{year|2020}}, [[MathAndCode]] found a {{gliders|10}} [[synthesis]] of this still life.<ref name="post115747" />

== References ==
<references>
<ref name="post18079">{{LinkForumThread
|format = ref
|title = Re: Catalyst improvements WIP
|p = 18079
|author = Tanner Jacobi
|date = March 19, 2015
}}</ref>
<ref name="post115747">{{LinkForumThread
|format = ref
|title = Re: Still Life Synthesis Thread
|p = 115747
|author = MathAndCode
|date = December 13, 2020
}}</ref>
</references>

== External links ==
*{{LinkLexicon|lex_b.htm#bts}}
*{{LinkCatagolue|xs19_32qb079czw23}}


__NOTOC__
{{natural}}
[[Category:Catalysts]]

BTS

2023-03-12T15:17:02Z

BlinkerSpawn:

{{Stilllife
|name = BTS
|pname = bts
|c = 19
|bx = 7
|by = 8
|discoverer = Mark Niemiec
|rulemin = B/S23
|rulemax = B3678/S012345678
|rulespecial = [[Conway's Game of Life|Conway Life]], [[HighLife]]
|isorulemin = B/S2aek3nr
|isorulemax = B2in34-ainry5-jqr678/S012345678
|synthesis = 10
|plaintext = true
|rle = true
|apgcode = xs19_32qb079czw23
|pentadecathlonid = 19.28858
}}{{stub|This article can be expanded with: comparison and contrast with {{LinkCatagolue|xs18_8e13z315b8o|style=raw}} (used in places like [[p21 honey farm hassler]]) in catalysis.}}
'''BTS''', short for '''bookend-table-snake''', is a {{slcells|19|text=19-cell}} [[still life]] where a [[bookend]] is stabilized by a [[down snake on table]]. It is notable for uses as a [[catalyst]] in a number of ways.

The BTS was first officially enumerated among other still lives by [[Mark Niemiec]], but it was not until 2015 that [[Tanner Jacobi]] noticed (and somewhat popularized) its usefulness, due to its extensive appearances in results generated by [[Mike Playle]]'s [[Bellman]] program.<ref name="post18079" /> Example uses of this object as a catalyst for non-[[Spartan]] [[signal]] [[circuitry]] include the [[CC semi-cenark]], [[Jormungant's G-to-H]] and a glider-emitting [[F131]] variant.

A typical [[catalysis]] of a BTS or related still life involves the flat end of the bookend and one or both feet of the table.

{{EmbedViewer
|pname = eaterbts
|viewerconfig = #C [[ GPS 2 THUMBSIZE 2 STOP 3 ]]
|position = center
|caption = BTS as [[eater 1]] replacement when eating a [[B-heptaplet]] parent. For more examples see [[Tutorials/Catalyses#Fishhook_replacements]]
|style = width:300px;
}}

== Commonness ==
{{main|List of common still lifes}}
{{Needs occurrence info|type=still life}}

== Glider synthesis ==
On December 13, {{year|2020}}, [[MathAndCode]] found a {{gliders|10}} [[synthesis]] of this still life.<ref name="post115747" />

== References ==
<references>
<ref name="post18079">{{LinkForumThread
|format = ref
|title = Re: Catalyst improvements WIP
|p = 18079
|author = Tanner Jacobi
|date = March 19, 2015
}}</ref>
<ref name="post115747">{{LinkForumThread
|format = ref
|title = Re: Still Life Synthesis Thread
|p = 115747
|author = MathAndCode
|date = December 13, 2020
}}</ref>
</references>

== External links ==
*{{LinkLexicon|lex_b.htm#bts}}
*{{LinkCatagolue|xs19_32qb079czw23}}


__NOTOC__
{{natural}}
[[Category:Catalysts]]

User:Bubblegum/SSLWSM

2020-07-04T13:54:27Z

BlinkerSpawn: TODO: Migrate SLs that didn't get reduced into pattern, migrate reductions into table. xs6_0ha4z1 courtesy of gooddogtyson.

This project is a spin-off from [https://conwaylife.com/forums/viewtopic.php?f=12&t=4488 this forum thread].

This is an attempt to find the smallest stabilisations of the [[still life]] constituent parts found in the [https://catagolue.appspot.com/census/bs123/C1 B/S123 census] on [[Catagolue]]. '''Edits and additions are welcome either on this table or on the thread above!'''

Still lives in [[Conway's Game of Life]] have been excluded from this table. So has the [[dot]] because it is not a still life in B/S123, and also because it is pointlessly trivial.

The metric is by [[population]], then [[bounding box]].

The corresponding project with still life [[island]]s can be found [https://conwaylife.com/w/index.php?title=User:Ian07/Still_life_islands here].

Thank you to muzikbike and gooddogtyson for [[apgsearch]]ing b3s123/C1!

The template to add rows to the table is
<nowiki>|-</nowiki>
<nowiki>| {{LinkCatagolue|CONSTITUENT APGCODE|rule=bs123|style=raw}} || {{LinkCatagolue|STABILISED APGCODE|style=raw}} || YOUR NAME</nowiki>



and please sort by constituent size, then alphanumeric order, thank you
If a still life cannot be stabilised use "none" (without the quotes) as the stabilised apgcode. An example is a 5x5 ring.

The current state of the project, represented visually:
<center>{{LV:Viewer|x = 97, y = 75, rule = LifeHistory
84.A$23.A59.A.C$22.A.C17.AC9.C8.CA9.AC7.A.C9.C$2.CA8.AC7.A.C8.AC7.A.C
8.C.A7.C9.A.C6.A.C9.C.A$2.CA8.CA8.C9.2C8.C10.C6.A.C9.2C8.C9.C.C$60.2A
31.A4$55.A$3.2A28.A20.A.A37.2A$3.A9.AC17.A.A9.A9.CA8.2A7.C9.CA8.A2.A$
4.C7.A.C7.AC7.A.C.A7.C.A6.AC9.C.A6.A.C8.C9.C.2A$3.2C6.A.C7.A2.C6.A.C.
A7.2C6.A.C9.C7.A.C7.A.C8.2C$2.C9.C9.2C8.C.C6.AC9.C9.2C8.C8.AC10.C$3.A
.A27.A6.A.A49.A$4.2A35.A50.2A4$22.2A$2.AC18.A9.AC9.C9.C7.AC12.C9.2A7.
CA$3.C9.C9.C9.C8.C.A7.C.A7.C11.C.A7.C.A7.C$2.C9.C.A7.2C8.C8.A.C8.C.A
7.C.2A8.CA8.C7.A.C$2.AC8.2C8.C9.CA8.C10.C7.AC.2A6.2C8.3C7.2C$23.A47.A
.A7.A$22.2A48.A8.2A3$34.2A49.A$15.2A7.CA8.A49.C.A$3.AC9.C.A7.C6.2A.C
9.2A18.C9.C9.CA8.CA$4.C9.C7.A.C6.A2.CA7.C.A7.2C8.C.A7.C.A6.AC9.C.A$3.
C9.2C6.A.C9.C8.C9.A.C7.A.C8.2C6.A.C9.C$2.C.C2A5.C9.C9.2C8.3C7.2C8.2C
7.AC9.C9.2C$2.A3.A6.A.A29.A24.A.A$.2A11.2A28.2A25.A4$21.2A19.AC21.A9.
A10.A$3.C9.CA6.A.C8.AC.2A6.C10.CA8.C.A7.C.A7.C2A$2.A.C8.C9.C9.C.2A6.C
.2A7.C9.C.A7.CA7.C9.2C$.A2.C9.C8.2C8.C7.A.C.2A5.C.C7.2C.A6.2C8.C.C7.C
2.A$2.2C7.A2C7.AC9.2C7.AC9.AC7.A2.C6.A.C9.AC8.2C$11.A8.A.A39.2A8.A$
21.A3$24.2A35.2A31.2A$2.A11.2A7.C.A28.2A5.A.C8.AC19.A2.A$.A.C9.C2.A6.
C10.CA.A4.AC9.C.A7.C9.C8.AC9.C.2A$.A.C9.C.2A5.AC10.C.2A5.C9.C9.CA7.C
9.C9.2C$2.C.CA6.2C8.C9.2C8.C9.2C7.AC9.AC9.C9.C$4.C8.C9.C2A6.C9.2C8.C
7.A.C10.C8.2C8.C$2.A.A6.A13.A7.A19.A7.A10.A19.2A$2.2A7.2A19.2A18.2A
18.2A2$2.2A$2.A57.2A13.CA6.AC10.C$3.C8.2A8.AC18.AC9.CA5.A.C12.C7.A.C
8.C.A$2.AC9.C9.C9.C8.C9.C.A7.C10.A.C9.C7.A.C$2.C9.C9.C6.2A.C.A8.C8.C
8.AC.2A6.A.C9.C7.A.C$3.C8.2C8.C.A5.A.C.A6.A.C5.2A.C9.C.A6.A.C9.C7.A.C
$2.CA9.C9.CA4.A2.2C7.AC6.2A.AC8.C.A7.C9.C9.C$12.A16.2A32.A18.2A$12.2A
2$16.A$4.CA9.C.A6.C10.CA7.CA6.AC9.CA.2A5.AC8.CA7.AC$4.C10.CA6.A.C8.C.
A7.C6.A2.C9.C.2A5.C9.C7.A2.C$5.C7.AC9.C.A7.C6.2A.C7.2A.C8.C9.C9.C7.AC
.A$4.CA6.A.C7.A.C2.A4.A.C6.A2.CA8.C7.A.C7.A.C7.A.C9.C$2A.C7.A.C7.A.C
2.2A3.A.C9.C7.A.C7.A.C7.A.C7.A.C7.A.C$A.CA8.C9.C9.C9.CA7.AC9.C9.C9.C
8.AC!
[[ HEIGHT 500 WIDTH 500 ZOOM 4 VIEWONLY THUMBNAIL ]]}}</center>

{| class="wikitable sortable"
! Constituent [[apgcode]] !! Stabilised apgcode !! Found by
|-
| {{LinkCatagolue|xs2_3|rule=bs123|style=raw}} ([[Domino]]) || {{LinkCatagolue|xs4_33|style=raw}} ([[Block]]) || bubblegum
|-
| {{LinkCatagolue|xs2_12|rule=bs123|style=raw}} ([[Duoplet]]) || {{LinkCatagolue|xs4_33|style=raw}} (Block) || bubblegum
|-
| {{LinkCatagolue|xs3_124|rule=bs123|style=raw}} || {{LinkCatagolue|xs6_25a4|style=raw}} ([[Barge]]) || bubblegum
|-
| {{LinkCatagolue|xs3_13|rule=bs123|style=raw}} ([[Pre-block]]) || {{LinkCatagolue|xs4_33|style=raw}} (Block) || bubblegum
|-
| {{LinkCatagolue|xs3_16|rule=bs123|style=raw}} ([[Banana spark]]) || {{LinkCatagolue|xs5_253|style=raw}} ([[Boat]]) || bubblegum
|-
| {{LinkCatagolue|xs3_25|rule=bs123|style=raw}} ([[V spark]]) || {{LinkCatagolue|xs4_252|style=raw}} ([[Tub]]) || Saka
|-
| {{LinkCatagolue|xs3_7|rule=bs123|style=raw}} ([[Blinker]]) || {{LinkCatagolue|xs7_178c|style=raw}} ([[Eater 1]]) || bubblegum
|-
| {{LinkCatagolue|xs4_116|rule=bs123|style=raw}} || {{LinkCatagolue|xs6_356|style=raw}} ([[Ship]]) || bubblegum
|-
| {{LinkCatagolue|xs4_1248|rule=bs123|style=raw}} || {{LinkCatagolue|xs8_25ak8|style=raw}} ([[Long barge]]) || bubblegum
|-
| {{LinkCatagolue|xs4_125|rule=bs123|style=raw}} || {{LinkCatagolue|xs6_25a4|style=raw}} (Barge) || bubblegum
|-
| {{LinkCatagolue|xs4_126|rule=bs123|style=raw}} || {{LinkCatagolue|xs11_3586246|style=raw}} ([[Snake with feather]]) || BlinkerSpawn
|-
| {{LinkCatagolue|xs4_12c|rule=bs123|style=raw}} || {{LinkCatagolue|xs7_3lo|style=raw}} ([[Long snake]]) || bubblegum
|-
| {{LinkCatagolue|xs4_152|rule=bs123|style=raw}} || {{LinkCatagolue|xs5_253|style=raw}} (Boat) || bubblegum
|-
| {{LinkCatagolue|xs4_161|rule=bs123|style=raw}} || {{LinkCatagolue|xs12_4alla4|style=raw}} ([[Honeycomb]]) || bubblegum
|-
| {{LinkCatagolue|xs4_162|rule=bs123|style=raw}} ([[Prepond]]) || {{LinkCatagolue|xs15_ci5diczw11|style=raw}} || bubblegum
|-
| {{LinkCatagolue|xs4_168|rule=bs123|style=raw}} || {{LinkCatagolue|xs12_4alla4|style=raw}} (Honeycomb) || bubblegum
|-
| {{LinkCatagolue|xs4_17|rule=bs123|style=raw}} ([[Tail]]) || {{LinkCatagolue|xs7_178c|style=raw}} (Eater 1) || bubblegum
|-
| {{LinkCatagolue|xs4_1a4|rule=bs123|style=raw}} || {{LinkCatagolue|xs6_25a4|style=raw}} (Barge) || bubblegum
|-
| {{LinkCatagolue|xs4_1e|rule=bs123|style=raw}} || {{LinkCatagolue|xs7_178c|style=raw}} (Eater 1) || bubblegum
|-
| {{LinkCatagolue|xs4_27|rule=bs123|style=raw}} ([[T-tetromino]]) || {{LinkCatagolue|xs13_j5c4goz11|style=raw}} || Saka
|-
| {{LinkCatagolue|xs4_2d|rule=bs123|style=raw}} || {{LinkCatagolue|xs6_bd|style=raw}} ([[Snake]]) || bubblegum
|-
| {{LinkCatagolue|xs4_35|rule=bs123|style=raw}} ([[Hook]]) || {{LinkCatagolue|xs5_253|style=raw}} (Boat) || bubblegum
|-
| {{LinkCatagolue|xs4_36|rule=bs123|style=raw}} ([[Z-tetromino]]) || {{LinkCatagolue|xs10_drz32|style=raw}} ([[Snake siamese snake]]) || bubblegum
|-
| {{LinkCatagolue|xs4_3c|rule=bs123|style=raw}} || {{LinkCatagolue|xs6_bd|style=raw}} (Snake) || bubblegum
|-
| {{LinkCatagolue|xs4_5a|rule=bs123|style=raw}} || {{LinkCatagolue|xs6_bd|style=raw}} (Snake) || bubblegum
|-
| {{LinkCatagolue|xs4_69|rule=bs123|style=raw}} ([[Moon]]) || {{LinkCatagolue|xs6_696|style=raw}} ([[Beehive]]) || bubblegum
|-
| {{LinkCatagolue|xs4_f|rule=bs123|style=raw}} || {{LinkCatagolue|xs10_32qr|style=raw}} ([[Block on table]]) || bubblegum
|-
| {{LinkCatagolue|xs5_1168|rule=bs123|style=raw}} || {{LinkCatagolue|xs7_178c|style=raw}} (Eater 1) || Hunting
|-
| {{LinkCatagolue|xs5_117|rule=bs123|style=raw}} || {{LinkCatagolue|xs11_g0s453z11|style=raw}} ([[Elevener]]) || Hunting
|-
| {{LinkCatagolue|xs5_11e|rule=bs123|style=raw}} || {{LinkCatagolue|xs7_178c|style=raw}} (Eater 1) || Hunting
|-
| {{LinkCatagolue|xs5_12d|rule=bs123|style=raw}} || {{LinkCatagolue|xs12_642tic|style=raw}} ([[R-bee with feather]]) || Lewis
|-
| {{LinkCatagolue|xs5_12e|rule=bs123|style=raw}} || {{LinkCatagolue|xs12_354cga6|style=raw}} || Saka
|-
| {{LinkCatagolue|xs5_12s|rule=bs123|style=raw}} || {{LinkCatagolue|xs8_178k8|style=raw}} ([[Tub with tail]]) || Saka
|-
| {{LinkCatagolue|xs5_13c|rule=bs123|style=raw}} || {{LinkCatagolue|xs12_32qj4c|style=raw}} ([[Carrier bridge table]]) || Lewis
|-
| {{LinkCatagolue|xs5_153|rule=bs123|style=raw}} ([[Glider]]) || {{LinkCatagolue|xs11_31e853|style=raw}} ([[Eater with cape]]) || Saka
|-
| {{LinkCatagolue|xs5_156|rule=bs123|style=raw}} || {{LinkCatagolue|xs6_356|style=raw}} (Ship) || GUYTU6J
|-
| {{LinkCatagolue|xs5_15a|rule=bs123|style=raw}} || {{LinkCatagolue|xs7_25ac|style=raw}} ([[Long boat]]) || Hunting
|-
| {{LinkCatagolue|xs5_16a|rule=bs123|style=raw}} || {{LinkCatagolue|xs10_g8o652z01|style=raw}} ([[Boat-tie]]) || Hunting
|-
| {{LinkCatagolue|xs5_16o|rule=bs123|style=raw}} || {{LinkCatagolue|xs14_1no3tg|style=raw}} ([[Sidewalk]]) || Hunting
|-
| {{LinkCatagolue|xs5_178|rule=bs123|style=raw}} || {{LinkCatagolue|xs7_178c|style=raw}} (Eater 1) || Hunting
|-
| {{LinkCatagolue|xs5_196|rule=bs123|style=raw}} || {{LinkCatagolue|xs7_2596|style=raw}} ([[Loaf]]) || GUYTU6J
|-
| {{LinkCatagolue|xs5_1d2|rule=bs123|style=raw}} || {{LinkCatagolue|xs10_69ar|style=raw}} ([[Loop]]) || Hunting
|-
| {{LinkCatagolue|xs5_1e2|rule=bs123|style=raw}} || {{LinkCatagolue|xs12_256o8a6|style=raw}} ([[Boat tie eater tail]]) || Lewis
|-
| {{LinkCatagolue|xs5_1f|rule=bs123|style=raw}} || {{LinkCatagolue|xs10_32qr|style=raw}} (Block on table) || Hunting
|-
| {{LinkCatagolue|xs5_1u|rule=bs123|style=raw}} || {{LinkCatagolue|xs12_330fho|style=raw}} ([[Trans-block on long hook]]) || Hunting
|-
| {{LinkCatagolue|xs5_21e|rule=bs123|style=raw}} || {{LinkCatagolue|xs7_178c|style=raw}} (Eater 1) || Hunting
|-
| {{LinkCatagolue|xs5_22d|rule=bs123|style=raw}} || {{LinkCatagolue|xs12_o4q552z01|style=raw}} ([[Beehive at beehive]]) || GUYTU6J
|-
| {{LinkCatagolue|xs5_23c|rule=bs123|style=raw}} || {{LinkCatagolue|xs11_08o652z32|style=raw}} ([[Carrier tie boat]]) || Hunting
|-
| {{LinkCatagolue|xs5_24b|rule=bs123|style=raw}} || {{LinkCatagolue|xs12_4alla4|style=raw}} (Honeycomb) || Hunting
|-
| {{LinkCatagolue|xs5_255|rule=bs123|style=raw}} || {{LinkCatagolue|xs6_696|style=raw}} (Beehive) || GUYTU6J
|-
| {{LinkCatagolue|xs5_2c3|rule=bs123|style=raw}} || {{LinkCatagolue|xs12_354qic|style=raw}} || Saka
|-
| {{LinkCatagolue|xs5_2f|rule=bs123|style=raw}} || {{LinkCatagolue|xs15_39c8a6z033|style=raw}} || Hunting
|-
| {{LinkCatagolue|xs5_2t|rule=bs123|style=raw}} || {{LinkCatagolue|xs11_32132ac|style=raw}} || Saka
|-
| {{LinkCatagolue|xs5_32c|rule=bs123|style=raw}} || {{LinkCatagolue|xs12_641j4czx11|style=raw}} ([[Carrier bridge carrier]]) || GUYTU6J
|-
| {{LinkCatagolue|xs5_3d|rule=bs123|style=raw}} || {{LinkCatagolue|xs14_1no3tg|style=raw}} (Sidewalk) || Hunting
|-
| {{LinkCatagolue|xs5_3e|rule=bs123|style=raw}} || {{LinkCatagolue|xs11_354c826|style=raw}} ([[Carrier siamese eater tail]]) || Hunting
|-
| {{LinkCatagolue|xs5_3s|rule=bs123|style=raw}} || {{LinkCatagolue|xs14_1no3tg|style=raw}} (Sidewalk) || Hunting
|-
| {{LinkCatagolue|xs5_4r|rule=bs123|style=raw}} || {{LinkCatagolue|xs10_drz32|style=raw}} || Saka
|-
| {{LinkCatagolue|xs5_5b|rule=bs123|style=raw}} || {{LinkCatagolue|xs6_bd|style=raw}} (Snake) || Hunting
|-
| {{LinkCatagolue|xs5_5e|rule=bs123|style=raw}} || {{LinkCatagolue|xs16_0bt0uiz32|style=raw}} || GUYTU6J
|-
| {{LinkCatagolue|xs5_5q|rule=bs123|style=raw}} || {{LinkCatagolue|xs10_drz32|style=raw}} || Saka
|-
| {{LinkCatagolue|xs5_6b|rule=bs123|style=raw}} || {{LinkCatagolue|xs10_0drz32|style=raw}} ([[Broken snake]]) || Hunting
|-
| {{LinkCatagolue|xs5_6p|rule=bs123|style=raw}} || {{LinkCatagolue|xs8_3pm|style=raw}} ([[Shillelagh]]) || Hunting
|-
| {{LinkCatagolue|xs5_79|rule=bs123|style=raw}} || {{LinkCatagolue|xs10_32qr|style=raw}} (Block on table) || Hunting
|-
| {{LinkCatagolue|xs5_9m|rule=bs123|style=raw}} || {{LinkCatagolue|xs8_3pm|style=raw}} (Shillelagh) || Hunting
|-
| {{LinkCatagolue|xs5_eh|rule=bs123|style=raw}} || {{LinkCatagolue|xs12_330fho|style=raw}} (Trans-block on long hook) || Hunting
|-
| {{LinkCatagolue|xs5_v|rule=bs123|style=raw}} || {{LinkCatagolue|xs14_09v04a4z32|style=raw}} || Hunting
|-
| {{LinkCatagolue|xs6_0g87z1|rule=bs123|style=raw}} || {{LinkCatagolue|xs16_ra9jzw1252|style=raw}} || bubblegum
|-
| {{LinkCatagolue|xs6_0g96z1|rule=bs123|style=raw}} || {{LinkCatagolue|xs16_ra9jzw1252|style=raw}} || bubblegum
|-
| {{LinkCatagolue|xs6_0ga5z1|rule=bs123|style=raw}} || {{LinkCatagolue|xs10_g8ka52z01|style=raw}} ([[Very long barge]]) || bubblegum
|-
| {{LinkCatagolue|xs6_0gb4z1|rule=bs123|style=raw}} || {{LinkCatagolue|xs12_ck3123z11|style=raw}} || Saka
|-
| {{LinkCatagolue|xs6_0gc3z1|rule=bs123|style=raw}} || {{LinkCatagolue|xs12_25a8og8o|style=raw}} || Saka
|-
| {{LinkCatagolue|xs6_0gd2z1|rule=bs123|style=raw}} || {{LinkCatagolue|xs17_25a8k8zbd11|style=raw}} || bubblegum
|-
| {{LinkCatagolue|xs6_0ge1z1|rule=bs123|style=raw}} || {{LinkCatagolue|xs10_g0s252z11|style=raw}} ([[Integral with tub]]) || bubblegum
|-
| {{LinkCatagolue|xs6_0gfz1|rule=bs123|style=raw}} || {{LinkCatagolue|xs13_0gbb8oz121|style=raw}} || bubblegum
|-
| {{LinkCatagolue|xs6_0ha4z1|rule=bs123|style=raw}} || {{LinkCatagolue|xs17_312kozw122qm|style=raw}} || bubblegum
|-
| {{LinkCatagolue|xs6_0hez1|rule=bs123|style=raw}} || {{LinkCatagolue|xs8_178k8|style=raw}} ([[Tub with tail]]) || bubblegum
|-
| {{LinkCatagolue|xs6_0idz1|rule=bs123|style=raw}} || {{LinkCatagolue|xs17_25a8k8zbd11|style=raw}} || bubblegum
|}

User:BlinkerSpawn

2020-02-10T00:11:42Z

BlinkerSpawn: Initial table

== Minimal Matching Patterns ==
This project is a parallel project to [[User:Ian07/Still life islands|this one]], except with less restrictions: the matched patterns are not required to remain islands, so stabilizing cells can be adjacent to the base pattern. This project uses the [https://catagolue.appspot.com/census/bs123/C1 bs123 census], starting at 4 cells, since all smaller patterns are matched by patterns with at most 7 cells.

{| class="wikitable sortable"
! Base pattern !! Stabilization !! Size !! Created by
|-
| {{LinkCatagolue|xs4_f|rule=bs123|style=raw}} (I-tetromino) || block-on-table || 10 ||
|-
| {{LinkCatagolue|xs4_1e|rule=bs123|style=raw}} || eater 1 || 7 ||
|-
| {{LinkCatagolue|xs4_17|rule=bs123|style=raw}} (L-tetromino) || eater 1 || 7 ||
|-
| {{LinkCatagolue|xs4_35|rule=bs123|style=raw}} || boat || 5 ||
|-
| {{LinkCatagolue|xs4_116|rule=bs123|style=raw}} || ship || 6 ||
|-
| {{LinkCatagolue|xs4_2d|rule=bs123|style=raw}} || snake || 6 ||
|-
| {{LinkCatagolue|xs4_3c|rule=bs123|style=raw}} || snake || 6 ||
|-
| {{LinkCatagolue|xs4_152|rule=bs123|style=raw}} || boat || 5 ||
|-
| {{LinkCatagolue|xs4_126|rule=bs123|style=raw}} || snake with feather || 11 ||
|-
| {{LinkCatagolue|xs4_12c|rule=bs123|style=raw}} || long boat || 7 ||
|-
| {{LinkCatagolue|xs4_69|rule=bs123|style=raw}} || beehive || 6 ||
|-
| {{LinkCatagolue|xs4_27|rule=bs123|style=raw}} (T-tetromino) || xs13_j5c48cz11 || 13 ||
|-
| {{LinkCatagolue|xs4_36|rule=bs123|style=raw}} (Z-tetromino) || snake siamese snake || 10 ||
|-
| {{LinkCatagolue|xs4_161|rule=bs123|style=raw}} || beehive at beehive || 12 ||
|-
| {{LinkCatagolue|xs4_5a|rule=bs123|style=raw}} || snake || 6 ||
|-
| {{LinkCatagolue|xs4_162|rule=bs123|style=raw}} || boat-tie || 10 ||
|-
| {{LinkCatagolue|xs4_168|rule=bs123|style=raw}} || eater 1 || 7 ||
|-
| {{LinkCatagolue|xs4_125|rule=bs123|style=raw}} || barge || 6 ||
|-
| {{LinkCatagolue|xs4_33|rule=bs123|style=raw}} (block) || block || 4 ||
|-
| {{LinkCatagolue|xs4_1a4|rule=bs123|style=raw}} || barge || 6 ||
|-
| {{LinkCatagolue|xs4_252|rule=bs123|style=raw}} (tub) || tub || 4 ||
|-
| {{LinkCatagolue|xs4_1248|rule=bs123|style=raw}} || canoe || 8 ||
|}

Pre-pulsar shuttle

2019-01-23T23:15:25Z

BlinkerSpawn: Pre-pulsar shuttle 26 has period 26, not 25

A [[pre-pulsar]] shuttle is a [[shuttle]] that hassles a predecessor of the [[pulsar]].
The captions are:
p(period), left: (step),(displacement), right: (step),(displacement)

{{EmbedViewer
|viewerconfig = #C [[ AUTOSTART GPS 50 THUMBLAUNCH THUMBSIZE 2 THEME 6 ZOOM 12 HEIGHT 600 WIDTH 600 ]]
|pname = prepulsarshuttle22
|caption = p22, left: (11,3), right: (11,3)
|position = center
}}
{{EmbedViewer
|viewerconfig = #C [[ AUTOSTART GPS 50 THUMBLAUNCH THUMBSIZE 2 THEME 6 ZOOM 12 HEIGHT 600 WIDTH 600 ]]
|pname = prepulsarshuttle25
|caption = p25, left: (14,3), right: (11,3)
|position = center
}}
{{EmbedViewer
|viewerconfig = #C [[ AUTOSTART GPS 50 THUMBLAUNCH THUMBSIZE 2 THEME 6 ZOOM 12 HEIGHT 600 WIDTH 600 ]]
|pname = prepulsarshuttle26
|caption = p26, edge: (14,3), centre: (12,3)
|position = center
}}
{{EmbedViewer
|viewerconfig = #C [[ AUTOSTART GPS 50 THUMBLAUNCH THUMBSIZE 2 THEME 6 ZOOM 12 HEIGHT 600 WIDTH 600 ]]
|pname = prepulsarshuttle28
|caption = p28, left: (14,3), right: (14,3)
|position = center
}}
{{EmbedViewer
|viewerconfig = #C [[ AUTOSTART GPS 50 THUMBLAUNCH THUMBSIZE 2 THEME 6 ZOOM 12 HEIGHT 600 WIDTH 600 ]]
|pname = prepulsarshuttle29
|caption = p29, left: (15,3), right: (14,3)
|position = center
}}
{{EmbedViewer
|viewerconfig = #C [[ AUTOSTART GPS 50 THUMBLAUNCH THUMBSIZE 2 THEME 6 ZOOM 12 HEIGHT 600 WIDTH 600 ]]
|pname = prepulsarshuttle30
|caption = p30, left: (15,3), right: (15,3)
|position = center
}}
{{EmbedViewer
|viewerconfig = #C [[ AUTOSTART GPS 50 THUMBLAUNCH THUMBSIZE 2 THEME 6 ZOOM 12 HEIGHT 600 WIDTH 600 ]]
|pname = prepulsarshuttle32
|caption = p32, left: (16,5), right: (16,5)
|position = center
}}
{{EmbedViewer
|viewerconfig = #C [[ AUTOSTART GPS 50 THUMBLAUNCH THUMBSIZE 2 THEME 6 ZOOM 8 HEIGHT 600 WIDTH 600 ]]
|pname = prepulsarshuttle36
|caption = p36, left: (20,5), right: (16,5)
|position = center
}}
{{EmbedViewer
|viewerconfig = #C [[ AUTOSTART GPS 50 THUMBLAUNCH THUMBSIZE 2 THEME 6 ZOOM 12 HEIGHT 600 WIDTH 600 ]]
|pname = prepulsarshuttle40
|caption = p40, left: (20,5), right: (20,5)
|position = center
}}
{{EmbedViewer
|viewerconfig = #C [[ AUTOSTART GPS 50 THUMBLAUNCH THUMBSIZE 2 THEME 6 ZOOM 12 HEIGHT 600 WIDTH 600 ]]
|pname = prepulsarshuttle42
|caption = p42, edge: (20,5), centre: (22,5)
|position = center
}}
{{EmbedViewer
|viewerconfig = #C [[ AUTOSTART GPS 50 THUMBLAUNCH THUMBSIZE 2 THEME 6 ZOOM 12 HEIGHT 600 WIDTH 600 ]]
|pname = prepulsarshuttle44
|caption = p44
|position = center
}}
{{EmbedViewer
|viewerconfig = #C [[ AUTOSTART GPS 50 THUMBLAUNCH THUMBSIZE 2 THEME 6 ZOOM 12 HEIGHT 600 WIDTH 600 ]]
|pname = prepulsarshuttle47
|caption = p47, edge: (25,5), centre: (22,5)
|position = center
}}
{{EmbedViewer
|viewerconfig = #C [[ AUTOSTART GPS 50 THUMBLAUNCH THUMBSIZE 2 THEME 6 ZOOM 12 HEIGHT 600 WIDTH 600 ]]
|pname = prepulsarshuttle55
|caption = p55, right: (40,3), left: (15,3)
|position = center
}}
{{EmbedViewer
|viewerconfig = #C [[ AUTOSTART GPS 50 THUMBLAUNCH THUMBSIZE 2 THEME 6 ZOOM 12 HEIGHT 600 WIDTH 600 ]]
|pname = prepulsarshuttle58
|caption = p58, left: (29,6), right: (29,6)
|position = center
}}
{{EmbedViewer
|viewerconfig = #C [[ AUTOSTART GPS 50 THUMBLAUNCH THUMBSIZE 2 THEME 6 ZOOM 12 HEIGHT 600 WIDTH 600 ]]
|pname = prepulsarshuttle60
|caption = p60, left: (30,6), right: (30,6)
|position = center
}}
{{EmbedViewer
|viewerconfig = #C [[ AUTOSTART GPS 50 THUMBLAUNCH THUMBSIZE 2 THEME 6 ZOOM 10 HEIGHT 600 WIDTH 600 ]]
|pname = prepulsarshuttle64
|caption = p64, left: (29,5), right: (35,5)
|position = center
}}
{{EmbedViewer
|viewerconfig = #C [[ AUTOSTART GPS 50 THUMBLAUNCH THUMBSIZE 2 THEME 6 ZOOM 10 HEIGHT 600 WIDTH 600 ]]
|pname = prepulsarshuttle90
|caption = p90, left: (45,9), right: (45,9)
|position = center
}}

Bounding box

2018-01-02T17:43:41Z

BlinkerSpawn: /* Spaceships */

{{Glossary}}
The '''bounding box''' of a [[pattern]] is the smallest rectangular array of cells that contains the entire pattern.

==Moving objects==

The bounding box of a moving object is often considered in only one [[phase]], but may also refer to the bounding box that contains the object in all phases of its [[period]]. For [[puffer]]s and [[rake]]s this usually does not include their output.

===Leading edge===

The '''leading edge''' of a moving object is the edge of that object's bounding box that is farthest in the direction of travel, essentially, the "front" of the object. The leading edge of a diagonally moving object can be considered in two ways: it may incorporate both edges of the bounding box in its direction of travel, or, alternatively, it may be defined as the diagonal row of cells that is farthest in the direction of travel. Most known moving objects have a leading edge that only ever moves forward; in [[:Category:Patterns_found_in_1991|1991]], however, [[Dean Hickerson]] constructed the [[13-engine Cordership]], the first [[Types_of_spaceships#Non-monotonic_spaceship|non-monotonic]] [[spaceship]] -- a spaceship whose leading edge "falls back" in at least one generation.<ref>{{CiteLexicon|file=lex_n.htm#nonmonotonic|name=non-monotonic|accessdate=April 24, 2009}}</ref>. In [[:Category:Patterns_found_in_1992|1992]], [[Hartmut Holzwart]] found the [[Non-monotonic_spaceship_1|first orthogonal example]]. Since then many other spaceships have been found which exhibit this property, such as the [[weekender]].

===Trailing edge===

The '''trailing edge''' of a moving object may be considered the "back" of the object. It is the edge of the bounding box which is farthest opposite the direction of travel. For puffers and rakes this does not generally include their output. The trailing edge is described most commonly in reference to spaceships, as their shape often determines their reactions with [[tagalong]]s or other objects.

==Stationary objects==

The bounding box of a [[still life]] is the bounding box which contains the pattern in its only phase. The bounding box of an [[oscillator]] is sometimes considered in one phase, but is most often expanded so as to include the entire oscillator in all of its phases. A [[gun]]'s bounding box is similar to that of an oscillator but it does not include any outgoing streams of spaceships.

==Other life-like cellular automata==

The same definitions of bounding box also apply in other [[Cellular_automata#Life-like_cellular_automata |life-like cellular automata]], and the [[Rule#Rules|rules]] for these cellular automata determine bounding box properties. For example, it is quite simple to show that a rule with no births cannot contain any oscillators or moving patterns because patterns are unable to expand in any direction.

===Spaceships===

The nonexistence of spaceships in life-like cellular automata can often be determined by simple patterns in the rulestrings, which affect the changes in a patterns bounding box. For an object to be considered a spaceship it must return to its initial phase (but in a different location), thus ensuring that the bounding box returns to a fixed size. For cellular automata with rules that include a birth with only one live neighbour, the bounding box of all patterns (excluding the pattern with no on cells) expands at the speed of light in every direction. Spaceships also cannot exist in rules with survival at zero, one, two, three, and four cells, as the trailing edge of a moving pattern could never completely die. For rules that do not have births at one, two, or three cells, the pattern can never expand beyond its initial bounding box, preventing any spaceships from existing. Such a rule can have oscillators however (provided it has births), but these oscillators will never leave their initial bounding box, and so their bounding boxes can be treated in the same way as those of still lifes.

==Notes==
<references />

==External links==
{{LinkLexicon|lex_b.htm#boundingbox}}

Tutorials/Rules

2017-07-13T02:34:07Z

BlinkerSpawn:

OK, so you want to understand rules, or even make your own cellular automata? Here's the place to learn how!

==Preliminaries==
Some care needs to be taken to distinguish between ''rules'', which are part of the specification of a cellular automaton (CA), the rules according to which patterns in that CA evolve; and ''rulestrings'', which are string representations of rules in the previous sense.

There are several ways of specifying rules beyond rulestrings, such as [[rule integer]]s or rule tables, and different rulestrings may yet represent the same rule. Nonetheless, in common parlance the term "rule" is often used where "rulestring" would be more appropriate.

==Outer-totalistic rules==
'''[[Life-like cellular automata|Outer-totalistic]] rules''' are defined in terms of [[birth]] and [[survival]] conditions: the circumstances under which dead cells get born, and live cells survive.

There's different ways of specifying these; two common ways to write rulestrings are called "B/S notation" and "S/B" notation respectively. [[Conway's Game of Life|Life]] itself is specified by "B3/S23" or "23/3", but since S/B notation has fallen out of style, we'll only be focussing on B/S notation for the rest of this tutorial.

So, let's look at Life's B3/S23. In Life:

* A ''dead'' cell gets ''born'' if and only if it has three live neighbors; this is expressed by "B3".
* A ''live'' cell ''survives'' if and only if it has two ''or'' three live neighbors; this is expressed by "S23".

{| style="margin-left: auto; margin-right: auto;"
| colspan="2" align="center" | [[File:Neighborhood 3i dead.png]]
|-
| align="center" colspan="2" style="max-width: 25em;" | Cell birth in Life: if the cells in green are live, the center cell will be born in the next generation.
|-
| align="right" | [[File:Neighborhood 2a.png]]
| align="left" | [[File:Neighborhood 3i.png]]
|-
| align="center" colspan="2" style="max-width: 25em;" | Cell survival in Life: if the cells in green are live, the center cell will survive in the next generation.
|}

As you can see, birth and survival conditions are each encoded as a string of numbers following the respective letter ("B" for birth, "S" for survival). Since there are eight cells directly neighboring a given cell, all numbers from 0 to 8 can be specified, and each combination yields a different outer-totalistic rule.

Let's look at two more examples. [[Day & Night]] has the rulestring B3678/S34678, so in this rule, dead cells get born if they have 3, 6, 7 or 8 live neighbors, and live cells survive if they have 3, 4, 6, 7 or 8 live neighbors. [[Live Free or Die]] has the rulestring B2/S0, so in this rule, dead cells are born if they have precisely two live neighbors, and live cells only survive if they have no live neighbors at all — if they are surrounded entirely by dead cells. (Knowing this, you can probably tell how the rule got its name.)

Why are these CAs called "outer-totalistic"? The reason is simply that a cell's fate depends on (in addition to the state of the cell itself) on the ''total'' number of live ''outer'' cells. Outer-totalistic CAs are also called semi-totalistic, in the sense that they are "sort of (but not quite)" totalistic in the sense of the next section.

There are many ways to generalize such CAs. For instance, one could:

* Take into account the (relative or absolute) alignment of live neighbors, in addition to their total count; this leads to [[Non-totalistic Life-like cellular automaton|non-totalistic rules]].
* Change the definition of what constitutes a "[[neighbourhood|neighbor]]", e.g. using the [[von Neumann neighbourhood]] rather than the [[Moore neighbourhood]], or increasing the distance at which cells are considered ([[Larger than Life]] rules).
* Increase the number of states a cell can be in, up from 2 ("dead" and "live").
* Change the [[topology]] of the [[universe]]: operate on e.g. a [[cylinder]], [[torus]] or [[Klein bottle]], rather than an infinite plane.
* Increase the dimension of the universe, considering [[1-dimensional cellular automata]] (e.g. Wolfram's [[rule 30]]), 3-dimensional cellular automata, etc.
* Change the tiling of the universe: instead of square cells, use [[hexagonal]] cells, or even exotic tilings such as [[hyperbolic]] or [[Penrose]] tilings.
* ...and much more.

==Totalistic rules==
'''[[Totalistic Life-like cellular automaton|Totalistic rules]]''' are a sub-class of outer-totalistic rules in which the center cell is not afforded special treatment anymore when determining its fate. With outer-totalistic rules, the center cell and the total number of live neighbors are considered separately; in totalistic rules, the center cell is counted like any other cell, and only the total number of live cells in the neighborhood, ''including'' the center cell, is used to determine evolution.

Totalistic rules can be described using B/S notation, of course; alternatively, they can be expressed by a string of digits listing the live-cells-in-the-neighborhood counts which lead to the center cell being alive in the next generation.

Let's look at an example. B3/S2 is an outer-totalistic rule (more precisely, a rulestring encoding a rule) in which dead cells get born if they have precisely three live neighbors, and live cells survive if they have precisely two live neighbors. But if a live cell has two live neighbors, that means the total number of live cells in the neighborhood is three as well — so this rule is actually not just outer-totalistic but also totalistic, and its totalistic rulestring would simply be 3.

{| style="margin-left: auto; margin-right: auto;"
| align="center" | [[File:Neighborhood 3i dead.png]]
|-
| align="center" style="max-width: 25em;" | Cell birth in B3/S2: if the cells in green are live, the center cell will be born in the next generation.
|-
| align="center" | [[File:Neighborhood 2a.png]]
|-
| align="center" style="max-width: 25em;" | Cell survival in B3/S2: if the cells in green are live, the center cell will survive in the next generation.
|}

[[Replicator 2|Fredkin]], also known as Replicator 2, is another example. Its rulestring is B1357/S02468; look closely, and you will see that this means that a cell will be alive in the next generation if and only if the number of live cells in its neighborhood is odd (1, 3, 5, 7 or 9). Its totalistic rulestring, therefore, is 13579.

==Non-totalistic rules==
'''[[Non-totalistic Life-like cellular automaton|Non-totalistic rules]]''' differ from outer-totalistic rules in that not only the number of live neighbors of a cell is considered when deciding whether the cell should be born (or survive, if it is already live) — birth and survival also depend on the relative alignment of the cell's live neighbors.

Rulestrings for non-totalistic rules are typically given in [[Hensel notation]]. As an example, let's look at a hypothetical rule, B2ek/S12. We understand "S12" well enough – a live cell survives if it has one or two live neighbors –, but what does "B2ek" mean?

Imagine, if you will, a cell with two live neighbors. How can these two live neighbors be aligned, relative to each other? All the following configurations are possible:

{| style="margin-left: auto; margin-right: auto;"
| [[File:Neighborhood 2c.png]]
| [[File:Neighborhood 2e.png]]
| [[File:Neighborhood 2k.png]]
| [[File:Neighborhood 2a.png]]
| [[File:Neighborhood 2i.png]]
| [[File:Neighborhood 2n.png]]
|-
| align="center" | c
| align="center" | e
| align="center" | k
| align="center" | a
| align="center" | i
| align="center" | n
|}

(Some of these configurations have mnemonic names; "c" stands for "corner", "e" for "edge", "k" for "knightwise", "a" for adjacent, and so on. Others are less obvious and simply have to be remembered, or looked up as necessary.)

For an outer-totalistic rule, say B2/S12, any of these configurations would cause the center cell to be born. By contrast, in non-totalistic rules, each configuration is considered separately: in B2ek/S12 a dead cell gets born if and only if it has two live neighbors ''which are in "e" or "k" alignment'' (as shown above).

For some neighbor counts, particularly 4, there is a fairly large number of possible alignments, so it is sometimes convenient to negate rather than specify, essentially saying "...in ''all but'' these alignments". As an example, consider the first non-totalistic rule ever explored, [[Just Friends]], which is described by the rulestring B2-a/S12. In this rule, a dead cell will get born if it has two live neighbors... unless those two live neighbors are in "a" alignment! Cells in this rule don't like getting cozy; they're "just friends".

==Non-isotropic rules==
The above non-totalistic rules are sometimes called ''isotropic'': although birth or survival of a cell may depend on the relative alignment of its live neighbors, no attempt is made to distinguish between the absolute alignment. Put another way, two live neighbors north and northwest of a cell will satisfy the "B2a" or "S2a" conditions, but so will two live neighbors south and southeast of the same cell.

'''[[Non-isotropic Life-like cellular automaton|Non-isotropic rules]]''' further distinguish such cases. This part of the tutorial isn't written yet; for now you may want to look at the [[rule integer]] article, which briefly talks about <tt>MAP</tt> strings, a different way of encoding rules as 512-bit strings unrelated to B/S notation that naturally lends itself to describing non-isotropic rules.

==Rules with larger neighbourhoods==
This part of the tutorial isn't written yet, either; for now you may want to look at the [[Larger than Life]] article, which talks about such rules.

==Creating custom rules==
[[Golly]] has powerful facilities to run a very large class of different rules. You want to create your own custom rules? Then look no further than the ''[[Tutorials/Creating custom rules|Creating custom rules]]'' tutorial. If you're not familiar with Golly yet, you may also want to take a look at the [[Tutorials/Golly|Golly tutorial]] first.

[[Category:Tutorials|Rules]]
__NOTOC__

Coolout Conjecture

2017-07-03T02:51:12Z

BlinkerSpawn:

{{Pattern
|name = Coolout Conjecture
|pname = cooloutconjecture
|c = 8
|bx = 6
|by = 2
|discoverer = Richard Schroeppel
|discoveryear = 2001
|rle = true
}}
The '''Coolout Conjecture''' is a conjecture proposed by [[Richard Schroeppel]] before 1992, and disproven by counterexample in 2001. The conjecture has been stated as:

:''Given a partial Life pattern that's internally consistent with being part of a still life (stable pattern), is there always a way to add a stabilizing boundary?

or alternatively,

:''If a configuration <tt>C</tt> is locally stable over a rectangle <tt>R</tt>, does there exist a configuration <tt>C*</tt> such that:''
:# ''<tt>C*</tt> is locally equal to <tt>C</tt> over <tt>R</tt>; and''
:# ''<tt>C*</tt> is globally stable?''

In August 2001, Schroeppel published the following 6x2 pattern as a counterexample to the conjecture:

<center>{{LV:Viewer|x = 6, y = 2, rule = B3/S23:P6,2
2o2b2o$ob2obo!
[[ THEME 6 GRID GRIDMAJOR 0 VIEWONLY THUMBNAIL ]]}}</center>

The row above the top edge must have six consecutive OFF cells; if it does not, the ON cells in the second and/or fifth columns will turn OFF. However, six consecutive OFF cells prevent the OFF cells in the third and fourth columns from being stabilized: without an ON neighbor above the top row, they will turn ON.

By similar logic, this pattern can be shown to be a counterexample to the conjecture:<ref>{{cite web|url=http://conwaylife.com/forums/viewtopic.php?f=12&t=2703&hilit=coolout&start=75#p44437|title=Re: Random posts|author=BlinkerSpawn|date=June 16, 2017|accessdate=July 2, 2017|work=ConwayLife.com forums}}</ref>

<center>{{LV:Viewer|x = 5, y = 2, rule = B3/S23:P5,2
2ob2o$obobo!
[[ THEME 6 GRID GRIDMAJOR 0 VIEWONLY THUMBNAIL ]]}}</center>

Similarly to the original counterexample, the cells in the top row allow the center OFF cell to turn on if they are OFF and turn OFF the flanking ON cells if they are ON.
Some other counterexamples have also been found<ref>{{cite web|url=http://conwaylife.com/forums/viewtopic.php?f=7&t=2919&start=0|title=Coolout Conjecture Counterexamples|author=wwei23|date=June 24, 2017|accessdate=July 2, 2017|work=ConwayLife.com forums}}</ref>, including this one:

<center>{{LV:Viewer|x = 6, y = 2, rule = B3/S23:P6,2
2ob3o$2o2bo!
[[ THEME 6 GRID GRIDMAJOR 0 VIEWONLY THUMBNAIL ]]}}</center>

It has been shown via a small brute-force search that a 2-by-5 rectangle is the smallest bounding box that allows a counterexample to exist.

== References ==
<references />

Coolout Conjecture

2017-07-03T02:20:16Z

BlinkerSpawn:

{{Pattern
|name = Coolout Conjecture
|pname = cooloutconjecture
|c = 8
|bx = 6
|by = 2
|discoverer = Richard Schroeppel
|discoveryear = 2001
|rle = true
}}
The '''Coolout Conjecture''' is a conjecture proposed by [[Richard Schroeppel]] before 1992, and disproven by counterexample in 2001. The conjecture has been stated as:

:''Given a partial Life pattern that's internally consistent with being part of a still life (stable pattern), is there always a way to add a stabilizing boundary?

or alternatively,

:''If a configuration <tt>C</tt> is locally stable over a rectangle <tt>R</tt>, does there exist a configuration <tt>C*</tt> such that:''
:# ''<tt>C*</tt> is locally equal to <tt>C</tt> over <tt>R</tt>; and''
:# ''<tt>C*</tt> is globally stable?''

In August 2001, Schroeppel published the following 6x2 pattern as a counterexample to the conjecture:

<center>{{LV:Viewer|x = 6, y = 2, rule = B3/S23:P6,2
2o2b2o$ob2obo!
[[ THEME 6 GRID GRIDMAJOR 0 VIEWONLY THUMBNAIL ]]}}</center>

The row above the top edge must have six consecutive OFF cells; if it does not, the ON cells in the second and/or fifth columns will turn OFF. However, six consecutive OFF cells prevent the OFF cells in the third and fourth columns from being stabilized: without an ON neighbor above the top row, they will turn ON.

By similar logic, it can be shown that this pattern is also a counterexample to the conjecture:

<center>{{LV:Viewer|x = 5, y = 2, rule = B3/S23:P5,2
2ob2o$obobo!
[[ THEME 6 GRID GRIDMAJOR 0 VIEWONLY THUMBNAIL ]]}}</center>

Similarly to the original counterexample, the cells in the top row allow the center OFF cell to turn on if they are OFF and turn OFF the flanking ON cells if they are ON.
Some other counterexamples to the Coolout Conjecture have been found, including these three small patterns:

<center>{{LV:Viewer|x = 27, y = 3, rule = B3/S23:P27,3
A3.A$.A.A6.3A.2A5.2A.3A$A.A.A5.A4.A5.2A2.A!
[[ THEME 6 GRID GRIDMAJOR 0 VIEWONLY THUMBNAIL ]]}}</center>

It has been proven via a small brute-force search that a 2-by-5 rectangle is the smallest bounding box that allows a counterexample to exist.
It has been conjectured that no nontrivial counterexample exists with fewer than seven ON cells but this has yet to be proven.