LifeWiki - User contributions [en]

File:P49pihassler.png

2023-04-18T22:54:20Z

Book: {{PatternImage}}

== Summary ==
{{PatternImage}}

P17 R-pentomino hassler

2023-04-14T19:46:39Z

Book:

{{Oscillator
|name = p17 R-pentomino hassler
|pname = p17rhassler202304
|c = 92
|bx = 25
|by = 25
|p = 17
|m = 17
|h = 20.2
|v = 0.16
|sv = 0.65
|discoverer = Nico Brown
|discoveryear = 2023
|rulemin = B3/S23
|rulemax = B38/S2378
|rulespecial = [[Conway's Game of Life|Conway Life]]
|isorulemin = B3-c/S23
|isorulemax = B34e6c7c8/S234cet5cijy6ik78
|plaintext = true
|rle = true
|viewerconfig = #C [[ HEIGHT 500 THUMBSIZE 2 ZOOM 16 GPS 8 TRACKLOOP 17 0 0 ]]
|apgcode = xp17_wckggci9b88gzca268661x11zwckxea8y5c4oz311y4746xoo4kb853zy4gs246xpie0346
}}{{stub}}
A {{period|17}} [[R-pentomino]] [[hassle]]r was discovered by Nico Brown on April 13, {{year|2023}}.<ref name="post160434" />
The oscillator is infinitely [[extensible]]; there are at least two possible connections.<ref name="post160456" />

==References==
<references>
<ref name="post160434">{{LinkForumThread
|format = ref
|p = 160434
|title = Re: Oscillator Discussion Thread
|author = Nico Brown
|date = April 13, 2023
}}</ref>
<ref name="post160456">{{LinkForumThread
|format = ref
|p = 160456
|title = Re: Oscillator Discussion Thread
|author = May13
|date = April 14, 2023
}}</ref>
</references>

==External links==
* {{LinkCatagolue|xp17_wckggci9b88gzca268661x11zwckxea8y5c4oz311y4746xoo4kb853zy4gs246xpie0346|patternname=p17 R-pentomino hassler}}

[[Category:R-pentomino hasslers|017]]
{{DISPLAYTITLE:p17 R-pentomino hassler}}

File:P17rhassler202304.png

2023-04-14T19:45:52Z

Book: {{PatternImage}}

== Summary ==
{{PatternImage}}

File:P59dependentreflectorloop.png

2023-04-12T17:12:05Z

Book: {{PatternImage}}

== Summary ==
{{PatternImage}}

Period-61 glider gun (2023)

2023-04-08T23:50:43Z

Book: no ani image

{{Gun
|name = Period-61 glider gun
|pname = period61glidergun2023
|c = 210
|bx = 47
|by = 44
|p = 61
|b = 2
|discoverer = Mitchell Riley
|discoveryear = 2023
|rulemin = B3/S23
|rulemax = B38/S238
|rulespecial = [[Conway's Game of Life|Conway Life]], {{rl|EightLife}}, {{rl|Pedestrian Life}}, {{rl|HoneyLife}}
|isorulemin = B3/S23
|isorulemax = B34c8/S235e8
|rle = true
|viewerconfig = #C [[ HEIGHT 500 THUMBSIZE 2 ZOOM 10 GPS 15 LOOP 61 ]]
}}{{for|other period-61 guns|p61 gun (disambiguation)}}
The first [[engine]]-based period-61 glider gun was discovered by Mitchell Riley on April 5, {{year|2023}}. The active part of this gun consists of two symmetrically arranged honey farm sequences.<ref name="post160181" /><ref name="post160185" /><ref name="j4069285462" />
With bounding box {{times|47|44}}, it is the smallest known glider gun of this period,<ref name="guntrue_61_current" /> beating the previous signal-loop-based design with bounding box {{times|101|88}}.<ref name="guntrue_61_8888" />

==References==
<references>
<ref name="guntrue_61_8888">{{cite web
|url = https://web.archive.org/web/20230405174134/https://catagolue.hatsya.com/textsamples/guntrue_61/b3s23/synthesis
|title = guntrue_61 costs 8888 cells
|work = Catagolue
}}</ref>
<ref name="guntrue_61_current">{{LinkCatagolue|guntrue_61|style=nobullet}}</ref>
<ref name="j4069285462">{{CiteCatagolueJob|job=4069285462|date=April 5, 2023}}</ref>
<ref name="post160181">{{LinkForumThread
|format = ref
|p = 160181
|title = Re: Gun Discussion Thread
|author = Mitchell Riley
|date = April 7, 2023
}}</ref>
<ref name="post160185">{{LinkForumThread
|format = ref
|p = 160185
|title = Re: NewLifeCA discussion thread
|author = Matthias Merzenich
|date = April 7, 2023
}}</ref>
</references>

File:Period61glidergun2023.png

2023-04-08T23:50:19Z

Book: {{PatternImage}}

== Summary ==
{{PatternImage}}

File:P47lumpsofmuckhassler.png

2023-04-05T17:00:12Z

Book: {{PatternImage}}

== Summary ==
{{PatternImage}}

File:Honeycombinator.png

2023-04-05T16:57:32Z

Book: {{PatternImage}}

== Summary ==
{{PatternImage}}

File:72p119.png

2023-04-01T17:16:02Z

Book: {{PatternImage}}

== Summary ==
{{PatternImage}}

File:64p63.png

2023-04-01T17:14:14Z

Book: {{PatternImage}}

== Summary ==
{{PatternImage}}

File:51p384.png

2023-04-01T17:10:42Z

Book: {{PatternImage}}

== Summary ==
{{PatternImage}}

File:59p192.png

2023-04-01T17:09:06Z

Book: {{PatternImage}}

== Summary ==
{{PatternImage}}

File:62p128.png

2023-04-01T17:07:26Z

Book: {{PatternImage}}

== Summary ==
{{PatternImage}}

Talk:Snake

2023-03-22T17:49:53Z

Book:

I think that the proper symmetry is S2. --[[User:Scotgot|Scot Ellison]] 15:55, 15 July 2011 (CDT)

== Long^7 snake image orientation ==

I'm not sure how these images are generated, but the long^7 one should be flipped to match the others. --[[User:Galoomba|Galoomba]] ([[User talk:Galoomba|talk]]) 03:16, 17 March 2023 (UTC)

* I just checked orientations of snakes in the Mark Niemiec's glider synthesis database. At least up to 15 bits, they all seem to be oriented the same way: {{LV:Viewer|x = 66, y = 98, rule = B3/S23
56b2o$56bobo$59bo$29b2o29bo$29bobo29bo$32bo29bo$2b2obo27bobo27bobo$2bo
b2o28b2o28b2o22$55b2o$55bobo$58bo$28b2o29bo$28bobo29bo$31bo29bo$b2o29b
o29bo$bobobo27bobo27bobo$4b2o28b2o28b2o21$54b2o$54bobo$57bo$27b2o29bo$
27bobo29bo$30bo29bo$2o29bo29bo$obo29bo29bo$3bobo27bobo27bobo$4b2o28b2o
28b2o20$53b2o$53bobo$56bo$57bo$58bo$59bo$60bo$61bo$62bo$63bobo$64b2o!
#C [[ THUMBNAIL THUMBLAUNCH THUMBSIZE 4 ZOOM 4 ]]
}} Probably this orientation could be consistently preserved for all RLEs/images whenever possible -- I'm trying to keep the orientation when formatting syntheses for the wiki, anyway. [[User:Confocal|Confocal]] ([[User talk:Confocal|talk]]) 02:09, 22 March 2023 (UTC)
* Update: I changed RLEs of snakes to match the synthesis orientation. Now it remains to reupload images [[:File:snake.png]], [[:File:longsnake.png]], [[:File:verylongsnake.png]], [[:File:long3snake.png]], [[:File:long4snake.png]], [[:File:long5snake.png]], [[:File:long6snake.png]] to match the same orientation. [[User:Confocal|Confocal]] ([[User talk:Confocal|talk]]) 16:15, 22 March 2023 (UTC)
** images reuploaded [[User:Book|Book]] ([[User talk:Book|talk]]) 17:49, 22 March 2023 (UTC)

File:Long6snake.png

2023-03-22T17:48:14Z

Book: Book uploaded a new version of File:Long6snake.png

{{Strict still life image
|pattern=Long^6 snake
|population=12
|createdwith=Microsoft Paint
|specifications=Dead: #ffffff Alive: #000000 Grid: #bfbfbf Grid thickness: 2 pixels Cell size (ignoring grid): 14 pixels by 14 pixels
|license=Simple geometry
}}

File:Long5snake.png

2023-03-22T17:47:01Z

Book: Book uploaded a new version of File:Long5snake.png

{{Strict still life image
|pattern=Long^5 snake
|population=11
|createdwith=Microsoft Paint
|specifications=Dead: #ffffff Alive: #000000 Grid: #bfbfbf Grid thickness: 2 pixels Cell size (ignoring grid): 14 pixels by 14 pixels
|license=Simple geometry
}}

File:Long4snake.png

2023-03-22T17:45:16Z

Book: Book uploaded a new version of File:Long4snake.png

{{Strict still life image
|pattern=Long^4 snake
|population=10
|createdwith=Microsoft Paint; compressed with FileOptimizer
|specifications=Dead: #ffffff Alive: #000000 Grid: #bfbfbf Grid thickness: 2 pixels Cell size (ignoring grid): 14 pixels by 14 pixels
|license=Simple geometry
}}

File:Long3snake.png

2023-03-22T17:43:46Z

Book: Book uploaded a new version of File:Long3snake.png

{{Strict still life image
|pattern=Long^3 snake
|population=9
|createdwith=Microsoft Paint; compressed with FileOptimizer
|specifications=Dead: #ffffff Alive: #000000 Grid: #bfbfbf Grid thickness: 2 pixels Cell size (ignoring grid): 14 pixels by 14 pixels
|license=Simple geometry
}}

File:Verylongsnake.png

2023-03-22T17:41:56Z

Book: Book uploaded a new version of File:Verylongsnake.png

{{Strict still life image
|pattern=Very long snake
|population=8
|createdwith=Microsoft Paint; compressed with FileOptimizer
|specifications=Dead: #ffffff Alive: #000000 Grid: #bfbfbf Grid thickness: 2 pixels Cell size (ignoring grid): 14 pixels by 14 pixels
|license=Simple geometry
}}

File:Longsnake.png

2023-03-22T17:40:07Z

Book: Book uploaded a new version of File:Longsnake.png

{{Strict still life image
|pattern=Long snake
|population=7
|createdwith=Microsoft Paint; compressed with FileOptimizer
|specifications=Dead: #ffffff Alive: #000000 Grid: #bfbfbf Grid thickness: 2 pixels Cell size (ignoring grid): 14 pixels by 14 pixels
|license=Simple geometry
}}

File:Snake.png

2023-03-22T17:37:02Z

Book: Book uploaded a new version of File:Snake.png

{{Strict still life image
|pattern=Snake
|population=6
|createdwith=Microsoft Paint; compressed with FileOptimizer
|specifications=Dead: #ffffff Alive: #000000 Grid: #bfbfbf Grid thickness: 2 pixels Cell size (ignoring grid): 14 pixels by 14 pixels
|license=Simple geometry
}}

Claw with tub with tail

2023-03-18T23:05:05Z

Book: moving this note from List of still lifes with 11 cells, it seems to make more sense here

{{Stilllife
|name = Claw with tub with tail
|pname = clawwithtubwithtail
|c = 11
|bx = 6
|by = 7
|fc = 28.6
|rulemin = B/S23
|rulemax = B35678/S012345678
|rulespecial = [[Conway's Game of Life|Conway Life]], [[HighLife]]
|isorulemin = B/S2-in3cr
|isorulemax = B2cin34-aejkn5678/S012345678
|synthesis = 5
|plaintext = true
|rle = true
|apgcode = xs11_25iczx113
|niemiecid = 11.27
|pentadecathlonid = 11.44
}}
'''Claw with tub with tail'''<ref name="catagolue_object" /><ref name="niemiec" /><ref name="clawwrong" group="notes">name is inconsistent with [[Long tub-claw with tail]]; opinions are needed on the canonical naming for patterns like these</ref> is a small [[still life]] consisting of a [[claw]] with a [[tub]] and a [[tail]].

== Construction==

{|style="margin:auto;width:300px;"
|{{EmbedViewer
|rle = x = 38, y = 22, rule = B3/S23
obo$b2o$bo9bo$9bobo$10b2o6$31b2o$32bo$32bob2o$26b2o5bo2bo$25b2o8bobo$
27bo8bo2$8b2o$7bobo$9bo19b2o$29bobo$29bo!
|viewerconfig = #C [[ THEME Book ZOOM 10 X 0 Y 0 AUTOSTART GPS 12 T 0 PAUSE 1 T 20 PAUSE 3 T 56 PAUSE 2 LOOP 57 ]]
|position = center
|caption = A 5G synthesis<ref name="j2370176486" />
}}
|-
|{{EmbedViewer
|rle = x = 39, y = 67, rule = B3/S23
17bo$16bo$16b3o10$8bo$9bo$7b3o2$32b2o$33bo$33bob2o$34bo2bo$36bobo$37bo
$b2o$2b2o$bo$21b2o$21bobo$3o18bo$2bo$bo6bo$8b2o7bo$7bobo6bo$16b3o5$23b
o$23bobo$23b2o3$25bo$24bo$24b3o2$32b2o$10bo22bo$11bo21bob2o$9b3o22bo2b
o$36bobo$37bo$b2o$2b2o$bo10$21bo$20b2o$20bobo!
|viewerconfig = #C [[ HEIGHT 750 THEME Book ZOOM 10 X 0 Y 0 AUTOSTART GPS 12 T 0 PAUSE 1 T 20 PAUSE 5 T 39 PAUSE 1 T 46 PAUSE 3 LOOP 47 ]]
|position = center
|caption = Two 6G syntheses<ref name="niemiec" />
}}
|}

This still life is known to be [[Glider synthesis|constructible]] with 5 gliders.<ref name="catagolue_object" /> Some known syntheses can be found in [[Mark Niemiec's database]].<ref name="niemiec" /> A {{gliders|5}} synthesis was found and submitted to [[Catagolue]] by [[Carson Cheng]]<ref name="message997664404323709048" /> in April {{year|2022}}.<ref name="j2370176486" />

== Occurrence ==

It is the eighth [[List of common still lifes|rarest]] 11-cell still life out of 46.

Claw with tub with tail does not occur in final patterns of collisions in [[Octohash database|octohash]], octo3obj or octo3g databases.

== See also ==
* [[Claw with tail]]

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

== References ==
<references>
<ref name="message997664404323709048">{{CiteDiscord
|author = Carson Cheng
|date = July 15, 2022
|channel = cgol
|id = 997664404323709048
}}</ref>
<ref name="j2370176486">{{CiteCatagolueJob|job=2370176486|date=April 24, 2022|accessdate=May 13, 2022}}</ref>
<ref name="catagolue_object">{{LinkCatagolue|xs11_25iczx113|style=nobullet}}</ref>
<ref name="niemiec">{{LinkNiemiec|p1.htm#p1-11|The 46 eleven-bit still-lifes|rle=11/11-27.rle|nobullet=nobullet}}</ref>
</references>

== External links ==
* {{LinkCatagolue|xs11_25iczx113}}
* {{LinkNiemiec|p1.htm#p1-11|The 46 eleven-bit still-lifes|rle=11/11-27.rle}}
* {{LinkPentadecathlonObject|id=11.44|archivedate=20221101180852}}

__NOTOC__

List of still lifes with 11 cells

2023-03-18T23:04:51Z

Book: move note to Claw with tub with tail page

The following page '''lists still lifes with a population of 11'''.

Other still life populations can be found at the following pages: [[List of still lifes with 4-10 cells|4 to 10 cells]], [[List of still lifes with 12 cells|12 cells]], [[List of still lifes with 13 cells|13 cells]], [[List of still lifes with 14 cells|14 cells]], [[List of still lifes with 15 cells|15 cells]], [[List of still lifes with 16 cells|16 cells]], [[List of still lifes with 17 cells|17 cells]], [[List of still lifes with 18 cells|18 cells]], [[Large natural still lifes|19+ cells]]

== List ==
There are 46 still lifes with 11 cells.
<div class="mw-collapsible-content">
{| class="wikitable" style="margin-left:auto; margin-right:auto; clear:both; text-align:center"
!
! colspan="2" | Still life
! [[apgcode]]
! [[Frequency class]]
! [[Glider synthesis|Cost in gliders]]
|-
! 1
! [[File:Boattieship.png|64px]]
! [[Boat tie ship]]
| {{LinkCatagolue|xs11_g8o652z11|style=raw}}
| 15.2
| 4
|-
! 2
! [[File:Elevener.png|64px]]
! [[Elevener]]
| {{LinkCatagolue|xs11_g0s453z11|style=raw}}
| 19.1
| 4
|-
! 3
! [[File:Transloafwithtail.png|64px]]
! [[Trans-loaf with tail]]
| {{LinkCatagolue|xs11_ggm952z1|style=raw}}
| 19.3
| 4
|-
! 4
! [[File:Loafsiameseloaf.png|64px]]
! [[Loaf siamese loaf]]
| {{LinkCatagolue|xs11_69lic|style=raw}}
| 20.5
| 4
|-
! 5
! [[File:Elevenloop.png|64px]]
! [[Eleven loop]]
| {{LinkCatagolue|xs11_178jd|style=raw}}
| 20.8
| 4
|-
! 6
! [[File:Cisloafwithtail.png|64px]]
! [[Cis-loaf with tail]]
| {{LinkCatagolue|xs11_178kic|style=raw}}
| 20.9
| 4
|-
! 7
! [[File:Cisboatontable.png|64px]]
! [[Cis-boat on table]]
| {{LinkCatagolue|xs11_2530f9|style=raw}}
| 21.7
| 4
|-
! 8
! [[File:Transboatwithnine.png|64px]]
! [[Trans-boat with nine]]
| {{LinkCatagolue|xs11_g0s253z11|style=raw}}
| 21.7
| 4
|-
! 9
! [[File:Translongboatwithtail.png|64px]]
! [[Trans-long boat with tail]]
| {{LinkCatagolue|xs11_ggka53z1|style=raw}}
| 22.0
| 4
|-
! 10
! [[File:Hungryhat.png|64px]]
! [[Hungry hat]]
| {{LinkCatagolue|xs11_2ege13|style=raw}}
| 22.2
| 4
|-
! 11
! [[File:Transboatontable.png|64px]]
! [[Trans-boat on table]]
| {{LinkCatagolue|xs11_2560ui|style=raw}}
| 22.2
| 4
|-
! 12
! [[File:Cisboatwithnine.png|64px]]
! [[Cis-boat with nine]]
| {{LinkCatagolue|xs11_g0s256z11|style=raw}}
| 22.2
| 5
|-
! 13
! [[File:Boatwithhookedtail.png|64px]]
! [[Boat with hooked tail]]
| {{LinkCatagolue|xs11_3586246|style=raw}}
| 23.0
| 4
|-
! 14
! [[File:Snakewithfeather.png|64px]]
! [[Snake with feather]]
| {{LinkCatagolue|xs11_3586246|style=raw}}
| 23.1
| 4
|-
! 15
! [[File:Carrierwithfeather.png|64px]]
! [[Carrier with feather]]
| {{LinkCatagolue|xs11_31461ac|style=raw}}
| 23.1
| 4
|-
! 16
! [[File:Long3boat.png|64px]]
! [[Long^3 boat|Long3 boat]]
| {{LinkCatagolue|xs11_g8ka52z11|style=raw}}
| 23.2
| 4
|-
! 17
! [[File:Eaterwithcape.png|64px]]
! [[Eater with cape]]
| {{LinkCatagolue|xs11_31e853|style=raw}}
| 24.0
| 5
|-
! 18
! [[File:Carriersiameseeaterhead.png|64px]]
! [[Carrier siamese eater head]]
| {{LinkCatagolue|xs11_178c4go|style=raw}}
| 24.1
| 5
|-
! 19
! [[File:Eatertailsiamesesnake.png|64px]]
! [[Eater tail siamese snake]]
| {{LinkCatagolue|xs11_32132ac|style=raw}}
| 24.2
| 4
|-
! 20
! [[File:Long3shillelagh.png|64px]]
! [[Long^3 shillelagh|Long3 shillelagh]]
| {{LinkCatagolue|xs11_69jzx56|style=raw}}
| 24.4
| 5
|-
! 21
! [[File:Carriersiameseeatertail.png|64px]]
! [[Carrier siamese eater tail]]
| {{LinkCatagolue|xs11_354c826|style=raw}}
| 24.5
| 5
|-
! 22
! [[File:Transtubwithlong3tail.png|64px]]
! [[Trans-tub with long^3 tail|Trans-tub with long3 tail]]
| {{LinkCatagolue|xs11_25icz65|style=raw}}
| 24.8
| 6
|-
! 23
! [[File:Boattiesnake.png|64px]]
! [[Boat tie snake]]
| {{LinkCatagolue|xs11_256o8go|style=raw}}
| 25.0
| 4
|-
! 24
! [[File:Carriertieboat.png|64px]]
! [[Carrier tie boat]]
| {{LinkCatagolue|xs11_08o652z32|style=raw}}
| 25.0
| 4
|-
! 25
! [[File:Verylongintegral.png|64px]]
! [[Very long integral]]
| {{LinkCatagolue|xs11_3542156|style=raw}}
| 25.3
| 5
|-
! 26
! [[File:Longprodigal.png|64px]]
! [[Long prodigal]]
| {{LinkCatagolue|xs11_25a84ko|style=raw}}
| 25.3
| 5
|-
! 27
! [[File:Cislongboatwithtail.png|64px]]
! [[Cis-long boat with tail]]
| {{LinkCatagolue|xs11_178ka6|style=raw}}
| 25.6
| 5
|-
! 28
! [[File:Longcisshillelagh.png|64px]]
! [[Long cis-shillelagh]]
| {{LinkCatagolue|xs11_69jzx123|style=raw}}
| 26.0
| 5
|-
! 29
! [[File:Cistubwithlong3tail.png|64px]]
! [[Cis-tub with long^3 tail|Cis-tub with long3 tail]]
| {{LinkCatagolue|xs11_358gka4|style=raw}}
| 26.5
| 4
|-
! 30
! [[File:Eaterheadsiamesesnake.png|64px]]
! [[Eater head siamese snake]]
| {{LinkCatagolue|xs11_178c48c|style=raw}}
| 26.5
| 5
|-
! 31
! [[File:Carriersiameselongsnake.png|64px]]
! [[Carrier siamese long snake]]
| {{LinkCatagolue|xs11_0cp3z65|style=raw}}
| 26.5
| 5
|-
! 32
! [[File:Bargewithlongtail.png|64px]]
! [[Barge with long tail]]
| {{LinkCatagolue|xs11_25akg8o|style=raw}}
| 26.5
| 5
|-
! 33
! [[File:Cislong3hookwithtail.png|64px]]
! [[Cis-long^3 hook with tail|Cis-long3 hook with tail]]
| {{LinkCatagolue|xs11_4ai3zx123|style=raw}}
| 26.6
| 5
|-
! 34
! [[File:Longhookwithnine.png|64px]]
! [[Long hook with nine]]
| {{LinkCatagolue|xs11_31eg84c|style=raw}}
| 26.7
| 4
|-
! 35
! [[File:Boatwithverylongtail.png|64px]]
! [[Boat with very long tail]]
| {{LinkCatagolue|xs11_35a8426|style=raw}}
| 27.1
| 5
|-
! 36
! [[File:Longclawwithtail.png|64px]]
! [[Long claw with tail]]
| {{LinkCatagolue|xs11_17842ac|style=raw}}
| 27.2
| 4
|-
! 37
! [[File:Snakesiameselongsnake.png|64px]]
! [[Snake siamese long snake]]
| {{LinkCatagolue|xs11_0drz65|style=raw}}
| 28.3
| 5
|-
! 38
! [[File:Tubtranslinetub.png|64px]]
! [[Tub trans-line tub]]
| {{LinkCatagolue|xs11_0g0s252z121|style=raw}}
| 28.3
| 6
|-
! 39
! [[File:Clawwithtubwithtail.png|64px]]
! [[Claw with tub with tail]]
| {{LinkCatagolue|xs11_wg84213z65|style=raw}}
| 28.6
| 5
|-
! 40
! [[File:Long3canoe.png|64px]]
! [[Long^3 canoe|Long3 canoe]]
| {{LinkCatagolue|xs11_25iczx113|style=raw}}
| 28.9
| 5
|-
! 41
! [[File:Fusewithtailandlongtail.png|64px]]
! [[Fuse with tail and long tail]]
| {{LinkCatagolue|xs11_wg84213z65|style=raw}}
| 29.7
| 5
|-
! 42
! [[File:Hooklinetub.png|64px]]
! [[Hook line tub]]
| {{LinkCatagolue|xs11_g88a52z23|style=raw}}
| 29.8
| 6
|-
! 43
! [[File:Longfusewithtwotails.png|64px]]
! [[Long fuse with two tails]]
| {{LinkCatagolue|xs11_17842sg|style=raw}}
| 31.9
| 6
|-
! 44
! [[File:Translong3hookwithtail.png|64px]]
! [[Trans-long^3 hook with tail|Trans-long3 hook with tail]]
| {{LinkCatagolue|xs11_03ia4z65|style=raw}}
| 32.0
| 6
|-
! 45
! [[File:Amphisbaena.png|64px]]
! [[Amphisbaena]]
| {{LinkCatagolue|xs11_321eg8o|style=raw}}
| 33.3
| 6
|-
! 46
! [[File:Long5snake.png|64px]]
! [[Long^5 snake|Long5 snake]]
| {{LinkCatagolue|xs11_xg853zca1|style=raw}}
| 33.8
| 6
|}

== See also ==
* [[List of common still lifes]]

== External links ==
* {{LinkNiemiec|bits-11.htm#p1-11|title=The 46 eleven-bit still-lifes}}
* {{CiteCatagolue|page=census/b3s23/C1/xs11|title=b3s23/C1/xs11}}
* {{CiteCatagolue|page=census/b3s23/synthesis-costs/xs11|title=b3s23/synthesis-costs/xs11}}

[[Category:Lists of patterns]]
[[Category:Strict still lifes with 11 cells| ]]

__NOTOC__

Talk:List of oscillators with 3 to 16 cells

2023-03-18T19:03:32Z

Book: /* What are the numbers in the left-most column? */

what is significance of yellow background for some cost in gliders cells? [[User:Book|Book]] ([[User talk:Book|talk]]) 20:57, 20 February 2022 (UTC)
: The cost in gliders is greater than the number of cells. [[User:HotdogPi|HotdogPi]] ([[User talk:HotdogPi|talk]]) 21:03, 20 February 2022 (UTC)

== What are the numbers in the left-most column? ==

Seems like it's ordering by frequency but those with "unknown" frequency class still have entries --[[User:Galoomba|Galoomba]] ([[User talk:Galoomba|talk]]) 18:36, 18 March 2023 (UTC)

* Given that some entries are numbered with specified frequency class, other entries are numbered with "unknown", other entries are "N/A" with "unknown" (e.g. "Boat tie pentapole" which is "N/A" between #91 and #92), and other entries are "N/A" with "[No natural occurrences]", I think it might be better to remove the leftmost column as redundant. [[User:Confocal|Confocal]] ([[User talk:Confocal|talk]]) 19:00, 18 March 2023 (UTC)
** Agree, and for the same reasons [[User:Book|Book]] ([[User talk:Book|talk]]) 19:03, 18 March 2023 (UTC)

Inflate

2023-03-17T23:43:23Z

Book: Redirected page to Inflation

#REDIRECT[[Inflation]]

116P101

2023-03-17T18:22:35Z

Book: linkify

{{Oscillator
|name = 116P101
|pname = 116p101
|c = 116
|bx = 46
|by = 39
|p = 101
|m = 101
|h = 53.6
|v = 0.90
|sv = 0.90
|discoverer = iNoMed
|discoverer2 = Mitchell Riley
|discoveryear = 2023
|rulemin = B3/S23
|rulemax = B3/S23
|rulespecial = [[Conway's Game of Life|Conway Life]]
|isorulemin = B3/S23
|isorulemax = B3/S234c6i
|synthesis2 = 44
|plaintext = true
|rle = true
|apgcode = xp101_y0ggy58oy23lk2mkk8zy1346y4123y11101zy6ggygoozy46761ygcecy3c871z8e13y33njygome6zy811zycggo0ooy1c4oy462sgzyb122642acy211
|viewerconfig = #C [[ GPS 8 THUMBSIZE 3 ZOOM 15 WIDTH 800 HEIGHT 700 ]]
}}{{stub}}
'''116P101''' is a {{period|101}} [[oscillator]] completed on March 17, {{year|2023}} by iNoMed based on a partial by Mitchell Riley.<ref name="post159153" /> It is the first known period-101 oscillator that is not based on adjustable signal loops.
With minimum population {{cells|116|text=116 cells}}, it is smaller than the previously smallest known oscillator of this period, which has 160 cells and uses a [[NW-2T16]]-based 180-degree reflector.<ref name="post152506" />

The active reaction consists in some phases of two copies of an [[evolution]]ary sequence #242 (zero-indexed) in [[census.rle]], which consists of a block plus a [[bullet heptomino]]. Another phase is a [[procrastinator]] plus a transparent [[loaf]] in another area.

A [[glider synthesis]] for a variant of the oscillator was found on the day of its discovery.{{cn}}<ref>{{CiteCatagolueJob|job=3954924662|date=March 17, 2023}}</ref>

The oscillator costs 44 gliders. The breakdown:

* [[Eater 2]] (using a regular eater 2 rather than the shorter variant): 6 [total: 6]
* [[Fishhook]] next to eater 2: 2 [total: 8]
* [[Block]] as part of the active region: 2 [total: 10]
* Block as catalyst: 2 [total: 12]
* Fishhook at corner: 4 [total: 16]
* Fishhook at central edge: 4 [total: 20]
* Bullet heptomino to activate the active region: 2 [total: 22]

All of these are done twice because of rotational symmetry, so the total is {{times|22|2}} = 44 gliders.

==References==
<references>
<ref name="post152506">{{LinkForumThread
|format = ref
|p = 152506
|title = Re: Oscillator Discussion Thread
|author = Entity Valkyrie 2
|date = October 22, 2022
}}</ref>
<ref name="post159153">{{LinkForumThread
|format = ref
|p = 159153
|title = Re: Oscillator Discussion Thread
|author = iNoMed
|date = March 17, 2023
}}</ref>
</references>

==External links==
* {{LinkCatagolue|xp101_y0ggy58oy23lk2mkk8zy1346y4123y11101zy6ggygoozy46761ygcecy3c871z8e13y33njygome6zy811zycggo0ooy1c4oy462sgzyb122642acy211}}

[[Category:Unnamed periodic objects]]

File:116p101.png

2023-03-17T16:33:36Z

Book: {{PatternImage}}

== Summary ==
{{PatternImage}}

Snake

2023-03-17T16:31:03Z

Book: /* Extensibility */

{{Stilllife
|name = Snake
|pname = snake
|c = 6
|bx = 4
|by = 2
|fc = 13.9
|discoverer = JHC group
|discoveryear = 1970
|rulemin = B/S23
|rulemax = B35678/S012345678
|rulespecial = [[Conway's Game of Life|Conway Life]], [[HighLife]]
|isorulemin = B/S2ae3n
|isorulemax = B2-ac34-r5678/S012345678
|synthesis = 4
|synthesisRLE = true
|plaintext = true
|rle = true
|apgcode = xs6_bd
|pentadecathlonid = 6.1
}}
'''Snake''' is a {{slcells|6|text=6-bit}} [[still life]]. It was discovered by the [[JHC group]] in {{year|1970}}.<ref>{{CiteHickersonOscillators|accessdate=June 18, 2009}}</ref>

== Use as a rock ==
The snake can act as a [[rock]]. An example is shown below in [[Conduit 1]].

{{EmbedViewer
|pname = conduit1
|viewerconfig = #C [[ GPS 20 THUMBSIZE 2 THEME Book AUTOSTART T 0 PAUSE 2 T 59 PAUSE 1 LOOP 60 ]]
|position = center
|caption = Conduit 1, showing the snake as a rock catalyst
|style = width:360px;
}}

== Use as an induction coil ==
A snake is the cheapest way in both population and bounding box to stabilize a line of three cells, such as in [[cauldron]], and the cheapest in bounding box but not population for a line of five, such as in the [[rectifier]]. Snakes are also the most efficient way to stabilize certain non-flat regions such as those in [[55P10]] and [[28P7.2]], although [[aircraft carrier]]s also work for this purpose.

== Commonness ==
{{main|List of common still lifes}}
Snake is the twenty-first most common [[still life]] in [[Achim Flammenkamp's census]], being less common than [[boat-tie]] but slightly more common than [[big S]].<ref>{{citeAchim|accessdate=January 15, 2009}}</ref> It is also the twenty-eighth most common object on [[Adam P. Goucher]]'s [[Catagolue]]. It is the rarest of the five 6-bit still lifes.<ref>{{citeCatagolueStats|June 24, 2016}}</ref>

The snake is about twice as common in C2_4 (the symmetry it has) compared to asymmetric soups.

== Construction ==
There are known ways to [[Glider synthesis|construct]] a snake with {{gliders|4|text=four gliders}}. A number of different syntheses for the snake can be found in [[Mark Niemiec's database|Mark Niemiec's glider synthesis database]].<ref>{{LinkNiemiec|p1.htm#p1-6|patternname=The 5 six-bit still-lifes|nobullet=nobullet}}</ref>

On February 20, {{year|2022}}, a method was found to construct [[pseudo still life]]s consisting of an arbitrarily large stack of snakes.<ref name="post141897" /> These objects were previously notoriously difficult to synthesize – a stack of three snakes<ref>A stack of three snakes on Catagolue: {{LinkCatagolue|xs18_bd0db0bd|style=raw}}</ref> formerly cost 67 gliders to construct, making it by far the most expensive pseudo still life with 18 cells.<ref>{{CiteCatagolue|page=census/b3s23/synthesis-costs-2022-02-15/xs18?offset=19000|title=Census|accessdate=February 15, 2022}}</ref>

{|style="margin:auto;width:360px;"
|-
|{{EmbedViewer
|rle = x = 98, y = 50, rule = B3/S23
bo$2bo$3o13$95bo$95bobo$95b2o27$63bo$64b2o$63b2o$68bo$67b2o$67bobo!
|viewerconfig = #C [[ HEIGHT 420 ZOOM 10 X 6 Y 27 THEME Book GPS 32 AUTOSTART T 0 PAUSE 2 T 164 PAUSE 1 T 208 PAUSE 1 LOOP 209 ]]
|position = center
|caption = A two-stage four-glider synthesis for the snake<ref name="post141932" />
}}
|{{EmbedViewer
|rle = x = 34, y = 37, rule = B3/S23
15bo$16bo$14b3o18$32b2o$32bo$25b2o3bobo$24bo2bo2b2o$25bobo$26bo$8b2o$
7bobo$7b2o3$2o$b2o$o$8bo$7bobo$7b2o!
|viewerconfig = #C [[ HEIGHT 420 ZOOM 8 THEME Book GPS 32 AUTOSTART T 0 PAUSE 2 T 108 PAUSE 1 LOOP 109 ]]
|position = center
|caption = Two [[one-glider seed]] constellations for the snake from the [[octohash database]]
}}
|}

== Extensibility==
Snake can be infinitely extended, as illustrated below:

<gallery widths="96px" style="text-align:center;">
File:longsnake.png|[[Long snake]]
File:verylongsnake.png|[[Very long snake]]
File:long3snake.png|[[Long^3 snake]]
File:long4snake.png|[[Long^4 snake]]
File:long5snake.png|[[Long^5 snake]]
File:long6snake.png|[[Long^6 snake]]
File:long7snake.png|[[Long^7 snake]]
File:long9snake.png|[[Long^9 snake]]
</gallery>

== See also ==
* [[Aircraft carrier]]
* [[Snake siamese snake]]
* [[Snake bridge snake]]
* [[Silver's p5]], period 5 oscillator
* [[Rattlesnake]], period 11 oscillator

== References ==
<references>
<ref name="post141897">{{LinkForumThread
|format = ref
|title = Re: Still Life Synthesis Thread
|p = 141897
|author = iNoMed
|date = February 20, 2022
}}</ref>
<ref name="post141932">{{LinkForumThread
|format = ref
|title = Re: Thread for basic questions
|p = 141932
|author = GUYTU6J
|date = February 21, 2022
}}</ref>
</references>

== External links ==
* {{LinkLexicon|filename=lex_s.htm#snake}}
* {{LinkCatagolue|xs6_bd}}
* {{LinkNiemiec|p1.htm#p1-6|The 5 six-bit still-lifes|rle=0/6sn.rle}}
* {{LinkPentadecathlonObject|id=6.1|patternname=Snake}}

{{Symmetry|180degree}}

[[Category:Catalysts]]
[[Category:Diagonal line stabilisations]]

File:Long9snake.png

2023-03-17T16:29:54Z

Book: {{PatternImage}}

== Summary ==
{{PatternImage}}

Snake

2023-03-17T00:26:53Z

Book: /* Extensibility */

{{Stilllife
|name = Snake
|pname = snake
|c = 6
|bx = 4
|by = 2
|fc = 13.9
|discoverer = JHC group
|discoveryear = 1970
|rulemin = B/S23
|rulemax = B35678/S012345678
|rulespecial = [[Conway's Game of Life|Conway Life]], [[HighLife]]
|isorulemin = B/S2ae3n
|isorulemax = B2-ac34-r5678/S012345678
|synthesis = 4
|synthesisRLE = true
|plaintext = true
|rle = true
|apgcode = xs6_bd
|pentadecathlonid = 6.1
}}
'''Snake''' is a {{slcells|6|text=6-bit}} [[still life]]. It was discovered by the [[JHC group]] in {{year|1970}}.<ref>{{CiteHickersonOscillators|accessdate=June 18, 2009}}</ref>

== Use as a rock ==
The snake can act as a [[rock]]. An example is shown below in [[Conduit 1]].

{{EmbedViewer
|pname = conduit1
|viewerconfig = #C [[ GPS 20 THUMBSIZE 2 THEME Book AUTOSTART T 0 PAUSE 2 T 59 PAUSE 1 LOOP 60 ]]
|position = center
|caption = Conduit 1, showing the snake as a rock catalyst
|style = width:360px;
}}

== Use as an induction coil ==
A snake is the cheapest way in both population and bounding box to stabilize a line of three cells, such as in [[cauldron]], and the cheapest in bounding box but not population for a line of five, such as in the [[rectifier]]. Snakes are also the most efficient way to stabilize certain non-flat regions such as those in [[55P10]] and [[28P7.2]], although [[aircraft carrier]]s also work for this purpose.

== Commonness ==
{{main|List of common still lifes}}
Snake is the twenty-first most common [[still life]] in [[Achim Flammenkamp's census]], being less common than [[boat-tie]] but slightly more common than [[big S]].<ref>{{citeAchim|accessdate=January 15, 2009}}</ref> It is also the twenty-eighth most common object on [[Adam P. Goucher]]'s [[Catagolue]]. It is the rarest of the five 6-bit still lifes.<ref>{{citeCatagolueStats|June 24, 2016}}</ref>

The snake is about twice as common in C2_4 (the symmetry it has) compared to asymmetric soups.

== Construction ==
There are known ways to [[Glider synthesis|construct]] a snake with {{gliders|4|text=four gliders}}. A number of different syntheses for the snake can be found in [[Mark Niemiec's database|Mark Niemiec's glider synthesis database]].<ref>{{LinkNiemiec|p1.htm#p1-6|patternname=The 5 six-bit still-lifes|nobullet=nobullet}}</ref>

On February 20, {{year|2022}}, a method was found to construct [[pseudo still life]]s consisting of an arbitrarily large stack of snakes.<ref name="post141897" /> These objects were previously notoriously difficult to synthesize – a stack of three snakes<ref>A stack of three snakes on Catagolue: {{LinkCatagolue|xs18_bd0db0bd|style=raw}}</ref> formerly cost 67 gliders to construct, making it by far the most expensive pseudo still life with 18 cells.<ref>{{CiteCatagolue|page=census/b3s23/synthesis-costs-2022-02-15/xs18?offset=19000|title=Census|accessdate=February 15, 2022}}</ref>

{|style="margin:auto;width:360px;"
|-
|{{EmbedViewer
|rle = x = 98, y = 50, rule = B3/S23
bo$2bo$3o13$95bo$95bobo$95b2o27$63bo$64b2o$63b2o$68bo$67b2o$67bobo!
|viewerconfig = #C [[ HEIGHT 420 ZOOM 10 X 6 Y 27 THEME Book GPS 32 AUTOSTART T 0 PAUSE 2 T 164 PAUSE 1 T 208 PAUSE 1 LOOP 209 ]]
|position = center
|caption = A two-stage four-glider synthesis for the snake<ref name="post141932" />
}}
|{{EmbedViewer
|rle = x = 34, y = 37, rule = B3/S23
15bo$16bo$14b3o18$32b2o$32bo$25b2o3bobo$24bo2bo2b2o$25bobo$26bo$8b2o$
7bobo$7b2o3$2o$b2o$o$8bo$7bobo$7b2o!
|viewerconfig = #C [[ HEIGHT 420 ZOOM 8 THEME Book GPS 32 AUTOSTART T 0 PAUSE 2 T 108 PAUSE 1 LOOP 109 ]]
|position = center
|caption = Two [[one-glider seed]] constellations for the snake from the [[octohash database]]
}}
|}

== Extensibility==
Snake can be infinitely extended, as illustrated below:

<gallery widths="180px" style="text-align:center;">
File:longsnake.png|[[Long snake]]
File:verylongsnake.png|[[Very long snake]]
File:long3snake.png|[[Long^3 snake]]
File:long4snake.png|[[Long^4 snake]]
File:long5snake.png|[[Long^5 snake]]
File:long6snake.png|[[Long^6 snake]]
File:long7snake.png|[[Long^7 snake]]
</gallery>

== See also ==
* [[Aircraft carrier]]
* [[Snake siamese snake]]
* [[Snake bridge snake]]
* [[Silver's p5]], period 5 oscillator
* [[Rattlesnake]], period 11 oscillator

== References ==
<references>
<ref name="post141897">{{LinkForumThread
|format = ref
|title = Re: Still Life Synthesis Thread
|p = 141897
|author = iNoMed
|date = February 20, 2022
}}</ref>
<ref name="post141932">{{LinkForumThread
|format = ref
|title = Re: Thread for basic questions
|p = 141932
|author = GUYTU6J
|date = February 21, 2022
}}</ref>
</references>

== External links ==
* {{LinkLexicon|filename=lex_s.htm#snake}}
* {{LinkCatagolue|xs6_bd}}
* {{LinkNiemiec|p1.htm#p1-6|The 5 six-bit still-lifes|rle=0/6sn.rle}}
* {{LinkPentadecathlonObject|id=6.1|patternname=Snake}}

{{Symmetry|180degree}}

[[Category:Catalysts]]
[[Category:Diagonal line stabilisations]]

File:Long7snake.png

2023-03-17T00:25:24Z

Book: {{PatternImage}}

== Summary ==
{{PatternImage}}

File:P112puffer20220212.png

2023-03-15T14:55:47Z

Book: {{PatternImage}}

== Summary ==
{{PatternImage}}

File:Zerodegreereflector202303.png

2023-03-13T17:04:20Z

Book: {{StaticImage}}

== Summary ==
{{StaticImage}}

Natural oscillators above period 3

2023-03-12T18:33:39Z

Book: catagolue link

This page documents all oscillators with period 4 or greater that [[Natural#Catagolue|have occurred in the C1 and/or G1 censuses]] on the [[Catagolue]], excluding stator variants. Ordered by frequency.

The following are excluded:
* Trivial p6 oscillators consisting of p2 and p3 components.
* Pentadecathlon pairs other than bi-pentadecathlon 1 and skewed bi-pentadecathlon 1.
* Pentadecathlon eating something with an [[eater 1]] edge, even though the rotor is technically different from a pentadecathlon alone.
* Queen bee shuttle and twin bees shuttle variants.

{|class="wikitable sortable" style="margin-left:auto; margin-right:auto; clear:both; text-align:center"
! Rank !! Name !! Image !! Period !! Minimum glider cost
|-
|1||[[Pentadecathlon]]||[[File:pentadecathlon.png|96px]]||15||3
|-
|2||[[Figure eight]]||[[File:figureeight.png|96px]]||8||4
|-
|3||[[Mold]]||[[File:mold.png|96px]]||4||5
|-
|4||[[Mazing]]||[[File:mazing.png|96px]]||4||5
|-
|5||[[Blocker]]||[[File:blocker.png|96px]]||8||5
|-
|6||[[Queen bee shuttle]]{{br}}(trans- and cis-)||[[File:transqueenbeeshuttle.png|96px]]{{br}}[[File:cisqueenbeeshuttle.png|96px]]||30||5
|-
|7||[[Achim's p4]]||[[File:achimsp4.png|96px]]||4||5
|-
|8||[[Octagon 2]]||[[File:octagon2.png|96px]]||5||5
|-
|9||[[Unix]]||[[File:unix.png|96px]]||6||5 
|-
|10||[[Tumbler]]||[[File:tumbler.png|96px]]||14||5
|-
|11||[[Coe's p8]]||[[File:coesp8.png|96px]]||8||5
|-
|12||[[Fumarole]]||[[File:fumarole.png|96px]]||5||7
|-
|13||[[Bi-pentadecathlon 1]]||[[File:bipentadecathlon1.png|96px]]||15||6
|-
|14||[[Twin bees shuttle]] (all types)||[[File:transtwinbeesshuttle.png|96px]]||46||7
|-
|15||{{LinkCatagolue|code=xp15_g0444g0g4440gy14r4z30kkk303kkk03y14r4z70ggg707ggg07|style=raw|patternname=Pulsar-on-pentadecathlon II}}||[[File:pulsaronpentadecathlonii.png|96px]]||15||6
|-
|16||[[Monogram]]||[[File:monogram.png|96px]]||4||7
|-
|17||[[Pentadecathlon#Occurrence|Pulsar-on-pentadecathlon I]]||[[File:pulsaronpentadecathloni.png|96px]]||15||6
|-
|18||[[Smiley]]||[[File:smiley.png|96px]]||8||8
|-
|19||[[Boring p24]]||[[File:boringp24.png|96px]]||24||7
|-
|20||[[Uninteresting p24]]||[[File:uninterestingp24.png|96px]]||24||7
|-
|21||[[Achim's p8]]||[[File:achimsp8.png|96px]]||8||8
|-
|22||[[Elkies' p5]]||[[File:elkiesp5.png|96px]]||5||8
|-
|23||[[Silver's p5]]||[[File:silversp5onaircraftcarrier.png|96px]]||5||8
|-
|24||[[Heart]] stator variant||[[File:heart.png|96px]]||5||8
|-
|25||{{LinkCatagolue|code=xp4_g88rb88c0cicz11x3dd11|style=raw}}||[[File:xp4_g88rb88c0cicz11x3dd11.png|96px]]||4||13
|-
|26||[[Polypentadecathlon#Pentadecathlon_pairs|Skewed bi-pentadecathlon 1]]||[[File:Pentadecathlonpair2.png|96px]]||15||8
|-
|27||[[Gray counter]] stator variant||[[File:xp4_02596zmlhhhlmz1226221.png|96px]]||4||11
|-
|28||[[1-2-3-4]] stator variant||[[File:xp4_69abaab96z69bo5ob96.png|96px]]||4||24
|-
|29||[[Confused eaters]]||[[File:confusedeaters.png|96px]]||4||9
|-
|30||[[Rob's p16]]||[[File:robsp16.png|96px]]||16||9
|-
|31||[[Tempest]]||[[File:tempest.png|96px]]||4||8
|-
|32||[[20P4]]||[[File:20p4.png|96px]]||4||8
|-
|33||[[Hooks]] stator variant||[[File:hooks.png|96px]]||5||12
|-
|34||Cis-[[figure eight on pentadecathlon]]||[[File:xp120_4r4y13bg2kgz4r4y511.png|96px]]||120||7
|-
|35||{{LinkCatagolue|code=xp4_g88g04a96z122dh953156|style=raw}}||[[File:xp4_g88g04a96z122dh953156.png|96px]]||4||null
|-
|36||[[Burloaferimeter]] stator variant||[[File:burloaferimeter.png|96px]]||7||9
|-
|37||{{LinkCatagolue|code=xp4_39egu1t6zcicw4b871|style=raw}}||[[File:xp4_39egu1t6zcicw4b871.png|96px]]||4||null
|-
|38||{{LinkCatagolue|code=xp4_w2llmzogjkj0v4zw6221|style=raw}}||[[File:xp4_w2llmzogjkj0v4zw6221.png|96px]]||4||null
|-
|39||Trans-[[figure eight on pentadecathlon]]||[[File:xp120_vtvz757y1ssszy7777.png|96px]]||120||7
|}

== See also ==
* [[List of common oscillators]]

[[Category:Lists of patterns]]

File:Pulsaronpentadecathlonii.png

2023-03-12T18:29:24Z

Book: {{StaticImage}}

== Summary ==
{{StaticImage}}

File:Pulsaronpentadecathloni.png

2023-03-12T18:16:51Z

Book: {{StaticImage}}

== Summary ==
{{StaticImage}}

Natural oscillators above period 3

2023-03-12T18:15:13Z

Book: linkify

This page documents all oscillators with period 4 or greater that [[Natural#Catagolue|have occurred in the C1 and/or G1 censuses]] on the [[Catagolue]], excluding stator variants. Ordered by frequency.

The following are excluded:
* Trivial p6 oscillators consisting of p2 and p3 components.
* Pentadecathlon pairs other than bi-pentadecathlon 1 and skewed bi-pentadecathlon 1.
* Pentadecathlon eating something with an [[eater 1]] edge, even though the rotor is technically different from a pentadecathlon alone.
* Queen bee shuttle and twin bees shuttle variants.

{|class="wikitable sortable" style="margin-left:auto; margin-right:auto; clear:both; text-align:center"
! Rank !! Name !! Image !! Period !! Minimum glider cost
|-
|1||[[Pentadecathlon]]||[[File:pentadecathlon.png|96px]]||15||3
|-
|2||[[Figure eight]]||[[File:figureeight.png|96px]]||8||4
|-
|3||[[Mold]]||[[File:mold.png|96px]]||4||5
|-
|4||[[Mazing]]||[[File:mazing.png|96px]]||4||5
|-
|5||[[Blocker]]||[[File:blocker.png|96px]]||8||5
|-
|6||[[Queen bee shuttle]]{{br}}(trans- and cis-)||[[File:transqueenbeeshuttle.png|96px]]{{br}}[[File:cisqueenbeeshuttle.png|96px]]||30||5
|-
|7||[[Achim's p4]]||[[File:achimsp4.png|96px]]||4||5
|-
|8||[[Octagon 2]]||[[File:octagon2.png|96px]]||5||5
|-
|9||[[Unix]]||[[File:unix.png|96px]]||6||5 
|-
|10||[[Tumbler]]||[[File:tumbler.png|96px]]||14||5
|-
|11||[[Coe's p8]]||[[File:coesp8.png|96px]]||8||5
|-
|12||[[Fumarole]]||[[File:fumarole.png|96px]]||5||7
|-
|13||[[Bi-pentadecathlon 1]]||[[File:bipentadecathlon1.png|96px]]||15||6
|-
|14||[[Twin bees shuttle]] (all types)||[[File:transtwinbeesshuttle.png|96px]]||46||7
|-
|15||Pulsar-on-pentadecathlon II||[[File:pulsaronpentadecathlonii.png|96px]]||15||6
|-
|16||[[Monogram]]||[[File:monogram.png|96px]]||4||7
|-
|17||[[Pentadecathlon#Occurrence|Pulsar-on-pentadecathlon I]]||[[File:pulsaronpentadecathloni.png|96px]]||15||6
|-
|18||[[Smiley]]||[[File:smiley.png|96px]]||8||8
|-
|19||[[Boring p24]]||[[File:boringp24.png|96px]]||24||7
|-
|20||[[Uninteresting p24]]||[[File:uninterestingp24.png|96px]]||24||7
|-
|21||[[Achim's p8]]||[[File:achimsp8.png|96px]]||8||8
|-
|22||[[Elkies' p5]]||[[File:elkiesp5.png|96px]]||5||8
|-
|23||[[Silver's p5]]||[[File:silversp5onaircraftcarrier.png|96px]]||5||8
|-
|24||[[Heart]] stator variant||[[File:heart.png|96px]]||5||8
|-
|25||{{LinkCatagolue|code=xp4_g88rb88c0cicz11x3dd11|style=raw}}||[[File:xp4_g88rb88c0cicz11x3dd11.png|96px]]||4||13
|-
|26||[[Polypentadecathlon#Pentadecathlon_pairs|Skewed bi-pentadecathlon 1]]||[[File:Pentadecathlonpair2.png|96px]]||15||8
|-
|27||[[Gray counter]] stator variant||[[File:xp4_02596zmlhhhlmz1226221.png|96px]]||4||11
|-
|28||[[1-2-3-4]] stator variant||[[File:xp4_69abaab96z69bo5ob96.png|96px]]||4||24
|-
|29||[[Confused eaters]]||[[File:confusedeaters.png|96px]]||4||9
|-
|30||[[Rob's p16]]||[[File:robsp16.png|96px]]||16||9
|-
|31||[[Tempest]]||[[File:tempest.png|96px]]||4||8
|-
|32||[[20P4]]||[[File:20p4.png|96px]]||4||8
|-
|33||[[Hooks]] stator variant||[[File:hooks.png|96px]]||5||12
|-
|34||Cis-[[figure eight on pentadecathlon]]||[[File:xp120_4r4y13bg2kgz4r4y511.png|96px]]||120||7
|-
|35||{{LinkCatagolue|code=xp4_g88g04a96z122dh953156|style=raw}}||[[File:xp4_g88g04a96z122dh953156.png|96px]]||4||null
|-
|36||[[Burloaferimeter]] stator variant||[[File:burloaferimeter.png|96px]]||7||9
|-
|37||{{LinkCatagolue|code=xp4_39egu1t6zcicw4b871|style=raw}}||[[File:xp4_39egu1t6zcicw4b871.png|96px]]||4||null
|-
|38||{{LinkCatagolue|code=xp4_w2llmzogjkj0v4zw6221|style=raw}}||[[File:xp4_w2llmzogjkj0v4zw6221.png|96px]]||4||null
|-
|39||Trans-[[figure eight on pentadecathlon]]||[[File:xp120_vtvz757y1ssszy7777.png|96px]]||120||7
|}

== See also ==
* [[List of common oscillators]]

[[Category:Lists of patterns]]

Pentadecathlon

2023-03-12T18:11:45Z

Book: /* Occurrence */ add apgcode

{{Oscillator
|name = Pentadecathlon
|pname = pentadecathlon
|c = 12
|bx = 16
|by = 9
|fc = 18.6
|p = 15
|m = 15
|h = 22.4
|v = 1.00
|sv = 1.00
|discoverer = John Conway
|discoveryear = 1970
|rulemin = B3/S23
|rulemax = B3/S023
|rulespecial = [[Conway's Game of Life|Conway Life]]
|isorulemin = B3-ckny/S23aeiy
|isorulemax = B2n34-aeiw5-e6-ik7c/S0234cjkqyz5-aiqy6-c
|synthesis = 3
|synthesisRLE = true
|plaintext = true
|rle = true
|apgcode = xp15_4r4z4r4
|pentadecathlonid = 12P15.1
|animated = yes
|viewerconfig = #C [[ THUMBSIZE 3 GPS 5 ZOOM 24 HEIGHT 300 WIDTH 600 ]]
}}
{{for|the website named "Pentadecathlon"|Game of Life News}}
'''Pentadecathlon''' (or '''PD'''; plural '''pentadecathlons'''{{refn|group=note|The correct Ancient Greek dual and plural forms, ''pentadecathlo'' and ''pentadecathla'',<ref name="wiktionary" /> are not in common use.}}) is a {{period|15}} [[oscillator]] that was found in {{year|1970}} by [[John Conway]]<ref>{{CiteHickersonOscillators|accessdate=March 14, 2020}}</ref> while tracking the history of short rows of cells (see [[one-cell-thick pattern]]); indeed, an orthogonal row of 10 cells evolves into this object. It is the only known oscillator that is a [[polyomino]] in more than one [[phase]] (besides the [[blinker]]), and is the smallest oscillator with a period greater than its minimum population.

== Uses of the pentadecathlon ==
The pentadecathlon is so called because it has a period of 15 generations. This, being a factor of 30, means that it can be elegantly used in combination with period 30 devices (based on the [[queen bee shuttle]]). Firstly, it can reflect a glider 180° as in [[p60 glider shuttle]], and a [[PD-pair reflector|pair of perpendicular pentadecathlons]] can rotate a glider 90° or 180° as in [[6 bits]] and [[106P135]].

A pentadecathlon can interact with another pentadecathlon to form a larger non-trivial oscillator, with [[bi-pentadecathlon 1]] being a notable such example.

=== Hassling capabilities ===
The pentadecathlon is classified as a '''pulsating''' oscillator, since it undulates throughout its cycle. During this process, the pentadecathlon throws off multiple accessible [[sparks]]. More specifically, the oscillator produces horizontal [[T-nose]] sparks and horizontal [[V spark]]s in the form of [[phi spark]]s, as well as vertical [[domino spark]]s. Two copies of these domino sparks can be used to [[hassle]] [[toad]]s in two distinct ways. The V sparks elegantly convert blocks into gliders, which forms the basis of the p30 [[xWSS]]-to-glider [[converter]] and aforementioned glider reflectors. This property is also exploited in numerous oscillators.

{|style="margin:auto;width:300px;"
|-
| {{EmbedViewer
|pname = pentadecathlonhasslingalongbarge
|viewerconfig = #C [[ GPS 15 LOOP 15 ZOOM 8 ]]
|position = center
|caption = Hassling a [[long barge]]; p15
|apgcode = xp15_vtvy0g8gz757y11252zy3skssssks
}}
| {{EmbedViewer
|pname = pentadecathlonhasslingbutterflysequenceobject
|viewerconfig = #C [[ GPS 15 LOOP 15 ZOOM 8 ]]
|position = center
|caption = Hassling an object in the [[butterfly]] sequence; p15 buddleia
|apgcode = xp15_0gg06iiy175777757z03w3zskszvnv
}}
|-
| {{EmbedViewer
|pname = toadflipper
|viewerconfig = #C [[ GPS 15 LOOP 60 ZOOM 8 ]]
|position = center
|caption = Hassling a [[toad]]; p60 toadflipper
|apgcode = xp60_vtvy1esy1vtvz757y8757
}}
| {{EmbedViewer
|pname = toadsucker
|viewerconfig = #C [[ GPS 15 LOOP 60 ZOOM 8 ]]
|position = center
|caption = Hassling a [[toad]]; p60 toadsucker
|apgcode = xp60_uquy1sey1vtvzfbfy8757
}}
|}

=== Phase changing ===
The pentadecathlon can undergo phase-changing reactions. The first two in the gallery below are in the form {{nowrap|14 + 15N}}, while the last two are in the form {{nowrap|6 + 15N}}.

{|style="margin:auto;width:300px;"
|-
| {{EmbedViewer
|pname = tetradecathlon
|viewerconfig = #C [[ GPS 15 ZOOM 8 ]]
|position = center
|caption = Period 14 (see [[tetradecathlon]])
|apgcode = xp14_64wo0k297x66zo8w60ag4oxoozy411zy4uquzy4fbfzy4ggz32wc0a143x33zc4w3058isxcc
}}
| {{EmbedViewer
|pname = p29pentadecathlonhassler
|viewerconfig = #C [[ GPS 15 ZOOM 8 ]]
|position = center
|caption = Period 29 (see [[p29 pentadecathlon hassler]])
|apgcode = xp29_y5252y1252ye252y1252zxo8y14c4x4c4x4ewe0aa0ewe4x4c4x4c4y18oz354r2asyac4oy6o4cyasa2r453zy01169bhe88cw33y111y411y133wc88ehb9611zy5123yu321
}}
|-
| {{EmbedViewer
|pname = p21pentadecathlonhassler
|viewerconfig = #C [[ GPS 15 ZOOM 8 ]]
|position = center
|caption = Period 21 (monoicosathlon)<ref name="post139656" /><ref name="post139659" /> (using [[p7 pipsquirter]]s)
|apgcode = xp21_03iab2qjk46ys64kjq2bai3z0iv0jqaq6he8yq8eh6qaqj0vizc4gf8383sj2w62cyic26w2js3838fg4czxd55d2oa7wo0gey2eaeeeeaey2eg0ow7ao2d55dzy2321yw123
}}
| {{EmbedViewer
|pname = p36pentadecathlonhassler
|viewerconfig = #C [[ GPS 15 ZOOM 6 ]]
|position = center
|caption = Period 36<ref name="message927211272360067092" /> (see [[traffic jam]]; sparker found by [[James Pascua]]<ref name="post131750" /><ref name="post131820" />)
|apgcode = xp36_wmq4o0354m92rkkozw1p0o85cc51giq2qkzw11xemj62amge21z0cscy011zzceczz9f9zbrbz232zoooz01z0osozy3om6g08k4ozw2e0c8hprh155c1dmzwmegc02ggma0dlldzw11x3201213
}}
|}
[[Category:Pages using extended apgcodes]]

A related pattern, the [[snacker]], involves a pentadecathlon being forced to oscillate at period 9.

== Occurrence ==
{{related|List of common oscillators}}
Pentadecathlon is the most common natural [[oscillator]] of [[period]] greater than {{period|3|text=three}} (and indeed, the second most common natural oscillator of period greater than 2) in [[Achim Flammenkamp's census]]. In fact, it is the fifth or sixth most common oscillator overall in this census, being about as frequent as the [[clock]], but much less frequent than the [[blinker]], [[toad]], [[beacon]] or [[pulsar]].<ref name="achim" /> It is also the most common oscillator with a [[volatility]] of 1. The pentadecathlon is also the fifty-second most common object on [[Adam P. Goucher]]'s [[Catagolue]] and by far the most common period 15 oscillator, with all other natural oscillators of that period featuring it combined with some other object.<ref name="statistics">{{citeCatagolueStats|September 22, 2020}}</ref>

The frequency of the pentadecathlon significantly depends on soup parameters; they are more common in smaller soups and lower densities, while they are less common on a torus.<ref group="note">12 times as common {{cata|census/b3s23/8x8/xp15|in an {{times|8|8}} soup}}, 5.5 times as common {{cata|census/b3s23/10x10/xp15|in a {{times|10|10}} soup}}, 1.8 times as common {{cata|census/b3s23/25pct/xp15|in a {{times|16|16}} soup at 25% density}}, and 0.75 times as common [https://conwaylife.com/forums/viewtopic.php?f=2&t=4995&p=119237&hilit=torus#p119237 on a torus].</ref>

The [[pulsar]]-on-pentadecathlon I is the largest object to have occurred in the B3/S23/C1 census as of February 2023, with 100 cells in its maximum phase, and with first known natural occurrence on Catagolue in in April {{year|2015}}.<ref name="post18884" /><ref name="statistics" />

{{EmbedViewer
|pname = pulsaronpentadecathloni
|apgcode = xp15_co9nas0san9oczgoldlo0oldlogxuquz1047210127401xfbf
|position = center
|viewerconfig = #C [[ THUMBSIZE 2 ]]
|caption = pulsar-on-pentadecathlon I
|style = width:300px;
}}

There are 35 results in the [[octohash database]] with the final pattern containing a pentadecathlon.<ref group=note name="note_octohash" /> There are also 173 results in the octo3obj database and 6 results in the octo3g database<ref group=note name="note_octo3g" /> with a pentadecathlon in the ash.

== Construction ==
A 5-glider [[Glider synthesis|synthesis]] was reported by [[Douglas G. Petrie]] in June 1973.<ref name="lifeline_v10_p6" /> Soon [[Peter Raynham]] found a 4-glider recipe.<ref name="lifeline_v11_p19" />

On April 11, {{year|1997}}, Heinrich Koenig found a [[three-glider collision]] that produced a clean pentadecathlon. This was a surprising result at the time. Four-glider pentadecathlon [[recipe]]s had been known and used for many years, so this was an unlooked-for improvement, very similar to Luka Okanishi's discovery of a three-glider synthesis of a [[switch engine]] almost twenty years later. This also makes the pentadecathlon the rarest object in [[Catagolue]] for which a 3-glider synthesis is known.

{|style="margin:auto;width:300px;"
|{{EmbedViewer
|rle = x = 14, y = 15, rule = B3/S23
5bo$4bo$4b3o$11bobo$11b2o$12bo7$2o$b2o$o!
|viewerconfig = #C [[ THEME Book ZOOM 12 AUTOSTART GPS 12 T 0 PAUSE 3 LOOP 80 ]]
|position = center
|caption = A 3G synthesis for the pentadecathlon
}}
|{{EmbedViewer
|rle = x = 17, y = 10, rule = B3/S23
9b2o$9b2o3$3o6b2o$2bo5bo2bo$bo7b2o4bo$14bobo$13bo2bo$14b2o!
|viewerconfig = #C [[ THEME Book ZOOM 12 AUTOSTART GPS 12 T 0 PAUSE 3 LOOP 100 ]]
|position = center
|caption = A three-object [[1G seed]]<ref name="niemiec" />
}}
|-
|{{EmbedViewer
|rle = x = 16, y = 11, rule = B3/S23
obo10bobo$b2o10b2o$bo12bo6$2b2o8b2o$3b2o6b2o$2bo10bo!
|viewerconfig = #C [[ THEME Book ZOOM 12 AUTOSTART GPS 12 T 0 PAUSE 3 LOOP 80 ]]
|position = center
|caption = A 4G synthesis<ref name="lifeline_v11_p19" />
}}
|{{EmbedViewer
|rle = x = 19, y = 10, rule = B3/S23
7b2o$2b2o3bobo$2bo5bo$obo$2o3$16b3o$16bo$17bo!
|viewerconfig = #C [[ THEME Book ZOOM 12 AUTOSTART GPS 12 T 0 PAUSE 3 LOOP 80 ]]
|position = center
|caption = A two-object 1G seed from the [[octohash database]]
}}
|-
|{{EmbedViewer
|rle = x = 22, y = 14, rule = B3/S23
19bobo$14bo4b2o$12bobo5bo$13b2o5$8b2o3b2o$7b2o4bobo$9bo3bo$3o$2bo$bo!
|viewerconfig = #C [[ THEME Book ZOOM 12 AUTOSTART GPS 12 T 0 PAUSE 3 LOOP 80 ]]
|position = center
|caption = A 5G synthesis<ref name="lifeline_v10_p6" />
}}
|{{EmbedViewer
|rle = x = 11, y = 14, rule = B3/S23
5b2o$4bo2bo$5b2o2$bo6b3o$obo$obo$bo4$8b2o$7b2o$9bo!
|viewerconfig = #C [[ THEME Book ZOOM 12 AUTOSTART GPS 12 T 0 PAUSE 3 LOOP 80 ]]
|position = center
|caption = An 1G seed from the [[octo3obj database]]
}}
|}

== In other rules ==
* In [[EightLife]], it still functions as a period 15 oscillator, but it generates extra internal [[spark]]s.

== See also ==
* [[Pentadecathlons jostling two blocks]]
* [[Karel's p15]]
* [[Loaflipflop]]
* [[Mold on pentadecathlon]]
* [[Pentadecathlon on 37P7.1]]
* [[Pentadecathlon on thumb 1]]

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

<ref name="note_octo3g">One 3G collision is the clean synthesis (headerless RLE: {{headerlessRLE|3bo$4bo$2b3o3$5b2o$5bobo$o4bo$b2o$2o!}}). Two other collisions ({{headerlessRLE|9bo$8bo$8b3o$o$b2o$2o2$5bo$3b2o$4b2o!}} and {{headerlessRLE|bo$2bo$3o$18bo$19bo$17b3o3$17b2o$18b2o$17bo!}}) converge to [[Lifeline Volume 4#Page 5|a pi+block collision]]. Three more collisions evolve to a B+glider collision ({{headerlessRLE|bo$2bo$3o25$21b3o$21bo2bo$21bob2o!}}) via 2G syntheses of the B-heptomino sequence.</ref>

<ref name="note_octohash">There is one clean 1G seed (headerless RLE: {{headerlessRLE|7b2o$2b2o3bobo$2bo5bo2b3o$obo8bo$2o10bo!}}). There are two other "exceptional" results: {{headerlessRLE|b2o$o2bo$o2bo$b2o2$5b2o$5bo$3bobo$3b2o2$2bo$b2o$bobo!}} creates 7 escaping gliders and has final population 271 ''excluding the pentadecathlon''; {{headerlessRLE|8b2o$8bobo$9bobo$10bo5$b2o$o2bo$obo2b2o$bo3bobo$5bo!}} creates 30 escaping gliders and has final population 1593 ''excluding the pentadecathlon''. Eight other results converge to a sequence ({{headerlessRLE|bo$2o$2bo2$bo2bo$2o2b2o$o4bo4$3b2o$3b2o!}}) which evolves to an escaping glider and [[Lifeline Volume 4#Page 5|a pi+block collision]]. All other results converge to the pi+block sequence.</ref>

</references>

== References ==
<references>
<ref name="wiktionary">{{cite web
|url = https://en.wiktionary.org/wiki/%E1%BC%86%CE%B8%CE%BB%CE%BF%CE%BD
|title = ἆθλον
|work = English Wiktionary
|accessdate = 2016-06-16
}}</ref>
<ref name="achim">{{citeAchim
|accessdate = January 15, 2009
}}</ref>
<ref name="niemiec">{{LinkNiemiec|p15.htm|Life Period-15 Oscillators|rle=12/12pc.rle|nobullet=nobullet}}</ref>
<ref name="lifeline_v10_p6">{{CiteLifeline|vol=10|pages=page 6}}</ref>
<ref name="lifeline_v11_p19">{{CiteLifeline|vol=11|pages=pages 18, 19}}</ref>
<ref name="post139656">{{LinkForumThread
|format = ref
|title = Re: Symbiosis
|p = 139656
|author = hotcrystal0
|date = January 2, 2022
}}</ref>
<ref name="post139659">{{LinkForumThread
|format = ref
|title = Re: Oscillator Discussion Thread
|p = 139659
|author = iNoMed
|date = January 2, 2022
}}</ref>
<ref name="message927211272360067092">{{CiteDiscord
|author = David Raucci
|date = January 2, 2022
|channel = cgol
|id = 927211272360067092
}}</ref>
<ref name="post131750">{{LinkForumThread
|format = ref
|title = Re: JP21's Lonely Freedomical Room
|p = 131750
|author = James Pascua
|date = June 10, 2021
}}</ref>
<ref name="post131820">{{LinkForumThread
|format = ref
|title = Re: Oscillator Discussion Thread
|p = 131820
|author = James Pascua
|date = June 11, 2021
}}</ref>
<ref name="post18884">{{LinkForumThread
|format = ref
|title = Re: Soup search results
|p = 18884
|author = gameoflifeboy
|date = April 20, 2015
}}</ref>
</references>

== External links ==
* {{LinkLexicon|lex_p.htm#pentadecathlon}}
* {{LinkCatagolue|xp15_4r4z4r4}}
* {{LinkPentadecathlonObject|12P15.1|patternname=Pentadecathlon|archivedate=20221102180907}}
* {{LinkNiemiec|p15.htm|Life Period-15 Oscillators|rle=12/12pc.rle}}
* {{LinkGoLNews|2009/01/pentadecathalon_crane.html|title=Pentadecathlon Crane|date=January 11, 2009|author=Heinrich Koenig}}

{{Symmetry|orthogonal4}}
{{Sparker|p=15|type=domino|type2=V|strength=strong|strength2=weak|strength3=moderate}}

[[Category:Polyominoes]]

Pentadecathlon

2023-03-12T01:53:41Z

Book: /* Occurrence */ show pulsar-on-pentadecathlon I

{{Oscillator
|name = Pentadecathlon
|pname = pentadecathlon
|c = 12
|bx = 16
|by = 9
|fc = 18.6
|p = 15
|m = 15
|h = 22.4
|v = 1.00
|sv = 1.00
|discoverer = John Conway
|discoveryear = 1970
|rulemin = B3/S23
|rulemax = B3/S023
|rulespecial = [[Conway's Game of Life|Conway Life]]
|isorulemin = B3-ckny/S23aeiy
|isorulemax = B2n34-aeiw5-e6-ik7c/S0234cjkqyz5-aiqy6-c
|synthesis = 3
|synthesisRLE = true
|plaintext = true
|rle = true
|apgcode = xp15_4r4z4r4
|pentadecathlonid = 12P15.1
|animated = yes
|viewerconfig = #C [[ THUMBSIZE 3 GPS 5 ZOOM 24 HEIGHT 300 WIDTH 600 ]]
}}
{{for|the website named "Pentadecathlon"|Game of Life News}}
'''Pentadecathlon''' (or '''PD'''; plural '''pentadecathlons'''{{refn|group=note|The correct Ancient Greek dual and plural forms, ''pentadecathlo'' and ''pentadecathla'',<ref name="wiktionary" /> are not in common use.}}) is a {{period|15}} [[oscillator]] that was found in {{year|1970}} by [[John Conway]]<ref>{{CiteHickersonOscillators|accessdate=March 14, 2020}}</ref> while tracking the history of short rows of cells (see [[one-cell-thick pattern]]); indeed, an orthogonal row of 10 cells evolves into this object. It is the only known oscillator that is a [[polyomino]] in more than one [[phase]] (besides the [[blinker]]), and is the smallest oscillator with a period greater than its minimum population.

== Uses of the pentadecathlon ==
The pentadecathlon is so called because it has a period of 15 generations. This, being a factor of 30, means that it can be elegantly used in combination with period 30 devices (based on the [[queen bee shuttle]]). Firstly, it can reflect a glider 180° as in [[p60 glider shuttle]], and a [[PD-pair reflector|pair of perpendicular pentadecathlons]] can rotate a glider 90° or 180° as in [[6 bits]] and [[106P135]].

A pentadecathlon can interact with another pentadecathlon to form a larger non-trivial oscillator, with [[bi-pentadecathlon 1]] being a notable such example.

=== Hassling capabilities ===
The pentadecathlon is classified as a '''pulsating''' oscillator, since it undulates throughout its cycle. During this process, the pentadecathlon throws off multiple accessible [[sparks]]. More specifically, the oscillator produces horizontal [[T-nose]] sparks and horizontal [[V spark]]s in the form of [[phi spark]]s, as well as vertical [[domino spark]]s. Two copies of these domino sparks can be used to [[hassle]] [[toad]]s in two distinct ways. The V sparks elegantly convert blocks into gliders, which forms the basis of the p30 [[xWSS]]-to-glider [[converter]] and aforementioned glider reflectors. This property is also exploited in numerous oscillators.

{|style="margin:auto;width:300px;"
|-
| {{EmbedViewer
|pname = pentadecathlonhasslingalongbarge
|viewerconfig = #C [[ GPS 15 LOOP 15 ZOOM 8 ]]
|position = center
|caption = Hassling a [[long barge]]; p15
|apgcode = xp15_vtvy0g8gz757y11252zy3skssssks
}}
| {{EmbedViewer
|pname = pentadecathlonhasslingbutterflysequenceobject
|viewerconfig = #C [[ GPS 15 LOOP 15 ZOOM 8 ]]
|position = center
|caption = Hassling an object in the [[butterfly]] sequence; p15 buddleia
|apgcode = xp15_0gg06iiy175777757z03w3zskszvnv
}}
|-
| {{EmbedViewer
|pname = toadflipper
|viewerconfig = #C [[ GPS 15 LOOP 60 ZOOM 8 ]]
|position = center
|caption = Hassling a [[toad]]; p60 toadflipper
|apgcode = xp60_vtvy1esy1vtvz757y8757
}}
| {{EmbedViewer
|pname = toadsucker
|viewerconfig = #C [[ GPS 15 LOOP 60 ZOOM 8 ]]
|position = center
|caption = Hassling a [[toad]]; p60 toadsucker
|apgcode = xp60_uquy1sey1vtvzfbfy8757
}}
|}

=== Phase changing ===
The pentadecathlon can undergo phase-changing reactions. The first two in the gallery below are in the form {{nowrap|14 + 15N}}, while the last two are in the form {{nowrap|6 + 15N}}.

{|style="margin:auto;width:300px;"
|-
| {{EmbedViewer
|pname = tetradecathlon
|viewerconfig = #C [[ GPS 15 ZOOM 8 ]]
|position = center
|caption = Period 14 (see [[tetradecathlon]])
|apgcode = xp14_64wo0k297x66zo8w60ag4oxoozy411zy4uquzy4fbfzy4ggz32wc0a143x33zc4w3058isxcc
}}
| {{EmbedViewer
|pname = p29pentadecathlonhassler
|viewerconfig = #C [[ GPS 15 ZOOM 8 ]]
|position = center
|caption = Period 29 (see [[p29 pentadecathlon hassler]])
|apgcode = xp29_y5252y1252ye252y1252zxo8y14c4x4c4x4ewe0aa0ewe4x4c4x4c4y18oz354r2asyac4oy6o4cyasa2r453zy01169bhe88cw33y111y411y133wc88ehb9611zy5123yu321
}}
|-
| {{EmbedViewer
|pname = p21pentadecathlonhassler
|viewerconfig = #C [[ GPS 15 ZOOM 8 ]]
|position = center
|caption = Period 21 (monoicosathlon)<ref name="post139656" /><ref name="post139659" /> (using [[p7 pipsquirter]]s)
|apgcode = xp21_03iab2qjk46ys64kjq2bai3z0iv0jqaq6he8yq8eh6qaqj0vizc4gf8383sj2w62cyic26w2js3838fg4czxd55d2oa7wo0gey2eaeeeeaey2eg0ow7ao2d55dzy2321yw123
}}
| {{EmbedViewer
|pname = p36pentadecathlonhassler
|viewerconfig = #C [[ GPS 15 ZOOM 6 ]]
|position = center
|caption = Period 36<ref name="message927211272360067092" /> (see [[traffic jam]]; sparker found by [[James Pascua]]<ref name="post131750" /><ref name="post131820" />)
|apgcode = xp36_wmq4o0354m92rkkozw1p0o85cc51giq2qkzw11xemj62amge21z0cscy011zzceczz9f9zbrbz232zoooz01z0osozy3om6g08k4ozw2e0c8hprh155c1dmzwmegc02ggma0dlldzw11x3201213
}}
|}
[[Category:Pages using extended apgcodes]]

A related pattern, the [[snacker]], involves a pentadecathlon being forced to oscillate at period 9.

== Occurrence ==
{{related|List of common oscillators}}
Pentadecathlon is the most common natural [[oscillator]] of [[period]] greater than {{period|3|text=three}} (and indeed, the second most common natural oscillator of period greater than 2) in [[Achim Flammenkamp's census]]. In fact, it is the fifth or sixth most common oscillator overall in this census, being about as frequent as the [[clock]], but much less frequent than the [[blinker]], [[toad]], [[beacon]] or [[pulsar]].<ref name="achim" /> It is also the most common oscillator with a [[volatility]] of 1. The pentadecathlon is also the fifty-second most common object on [[Adam P. Goucher]]'s [[Catagolue]] and by far the most common period 15 oscillator, with all other natural oscillators of that period featuring it combined with some other object.<ref name="statistics">{{citeCatagolueStats|September 22, 2020}}</ref>

The frequency of the pentadecathlon significantly depends on soup parameters; they are more common in smaller soups and lower densities, while they are less common on a torus.<ref group="note">12 times as common {{cata|census/b3s23/8x8/xp15|in an {{times|8|8}} soup}}, 5.5 times as common {{cata|census/b3s23/10x10/xp15|in a {{times|10|10}} soup}}, 1.8 times as common {{cata|census/b3s23/25pct/xp15|in a {{times|16|16}} soup at 25% density}}, and 0.75 times as common [https://conwaylife.com/forums/viewtopic.php?f=2&t=4995&p=119237&hilit=torus#p119237 on a torus].</ref>

The [[pulsar]]-on-pentadecathlon I is the largest object to have occurred in the B3/S23/C1 census as of February 2023, with 100 cells in its maximum phase, and with first known natural occurrence on Catagolue in in April {{year|2015}}.<ref name="post18884" /><ref name="statistics" />

{{EmbedViewer
|pname = pulsaronpentadecathloni
|position = center
|viewerconfig = #C [[ THUMBSIZE 2 ]]
|caption = pulsar-on-pentadecathlon I
|style = width:300px;
}}

There are 35 results in the [[octohash database]] with the final pattern containing a pentadecathlon.<ref group=note name="note_octohash" /> There are also 173 results in the octo3obj database and 6 results in the octo3g database<ref group=note name="note_octo3g" /> with a pentadecathlon in the ash.

== Construction ==
A 5-glider [[Glider synthesis|synthesis]] was reported by [[Douglas G. Petrie]] in June 1973.<ref name="lifeline_v10_p6" /> Soon [[Peter Raynham]] found a 4-glider recipe.<ref name="lifeline_v11_p19" />

On April 11, {{year|1997}}, Heinrich Koenig found a [[three-glider collision]] that produced a clean pentadecathlon. This was a surprising result at the time. Four-glider pentadecathlon [[recipe]]s had been known and used for many years, so this was an unlooked-for improvement, very similar to Luka Okanishi's discovery of a three-glider synthesis of a [[switch engine]] almost twenty years later. This also makes the pentadecathlon the rarest object in [[Catagolue]] for which a 3-glider synthesis is known.

{|style="margin:auto;width:300px;"
|{{EmbedViewer
|rle = x = 14, y = 15, rule = B3/S23
5bo$4bo$4b3o$11bobo$11b2o$12bo7$2o$b2o$o!
|viewerconfig = #C [[ THEME Book ZOOM 12 AUTOSTART GPS 12 T 0 PAUSE 3 LOOP 80 ]]
|position = center
|caption = A 3G synthesis for the pentadecathlon
}}
|{{EmbedViewer
|rle = x = 17, y = 10, rule = B3/S23
9b2o$9b2o3$3o6b2o$2bo5bo2bo$bo7b2o4bo$14bobo$13bo2bo$14b2o!
|viewerconfig = #C [[ THEME Book ZOOM 12 AUTOSTART GPS 12 T 0 PAUSE 3 LOOP 100 ]]
|position = center
|caption = A three-object [[1G seed]]<ref name="niemiec" />
}}
|-
|{{EmbedViewer
|rle = x = 16, y = 11, rule = B3/S23
obo10bobo$b2o10b2o$bo12bo6$2b2o8b2o$3b2o6b2o$2bo10bo!
|viewerconfig = #C [[ THEME Book ZOOM 12 AUTOSTART GPS 12 T 0 PAUSE 3 LOOP 80 ]]
|position = center
|caption = A 4G synthesis<ref name="lifeline_v11_p19" />
}}
|{{EmbedViewer
|rle = x = 19, y = 10, rule = B3/S23
7b2o$2b2o3bobo$2bo5bo$obo$2o3$16b3o$16bo$17bo!
|viewerconfig = #C [[ THEME Book ZOOM 12 AUTOSTART GPS 12 T 0 PAUSE 3 LOOP 80 ]]
|position = center
|caption = A two-object 1G seed from the [[octohash database]]
}}
|-
|{{EmbedViewer
|rle = x = 22, y = 14, rule = B3/S23
19bobo$14bo4b2o$12bobo5bo$13b2o5$8b2o3b2o$7b2o4bobo$9bo3bo$3o$2bo$bo!
|viewerconfig = #C [[ THEME Book ZOOM 12 AUTOSTART GPS 12 T 0 PAUSE 3 LOOP 80 ]]
|position = center
|caption = A 5G synthesis<ref name="lifeline_v10_p6" />
}}
|{{EmbedViewer
|rle = x = 11, y = 14, rule = B3/S23
5b2o$4bo2bo$5b2o2$bo6b3o$obo$obo$bo4$8b2o$7b2o$9bo!
|viewerconfig = #C [[ THEME Book ZOOM 12 AUTOSTART GPS 12 T 0 PAUSE 3 LOOP 80 ]]
|position = center
|caption = An 1G seed from the [[octo3obj database]]
}}
|}

== In other rules ==
* In [[EightLife]], it still functions as a period 15 oscillator, but it generates extra internal [[spark]]s.

== See also ==
* [[Pentadecathlons jostling two blocks]]
* [[Karel's p15]]
* [[Loaflipflop]]
* [[Mold on pentadecathlon]]
* [[Pentadecathlon on 37P7.1]]
* [[Pentadecathlon on thumb 1]]

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

<ref name="note_octo3g">One 3G collision is the clean synthesis (headerless RLE: {{headerlessRLE|3bo$4bo$2b3o3$5b2o$5bobo$o4bo$b2o$2o!}}). Two other collisions ({{headerlessRLE|9bo$8bo$8b3o$o$b2o$2o2$5bo$3b2o$4b2o!}} and {{headerlessRLE|bo$2bo$3o$18bo$19bo$17b3o3$17b2o$18b2o$17bo!}}) converge to [[Lifeline Volume 4#Page 5|a pi+block collision]]. Three more collisions evolve to a B+glider collision ({{headerlessRLE|bo$2bo$3o25$21b3o$21bo2bo$21bob2o!}}) via 2G syntheses of the B-heptomino sequence.</ref>

<ref name="note_octohash">There is one clean 1G seed (headerless RLE: {{headerlessRLE|7b2o$2b2o3bobo$2bo5bo2b3o$obo8bo$2o10bo!}}). There are two other "exceptional" results: {{headerlessRLE|b2o$o2bo$o2bo$b2o2$5b2o$5bo$3bobo$3b2o2$2bo$b2o$bobo!}} creates 7 escaping gliders and has final population 271 ''excluding the pentadecathlon''; {{headerlessRLE|8b2o$8bobo$9bobo$10bo5$b2o$o2bo$obo2b2o$bo3bobo$5bo!}} creates 30 escaping gliders and has final population 1593 ''excluding the pentadecathlon''. Eight other results converge to a sequence ({{headerlessRLE|bo$2o$2bo2$bo2bo$2o2b2o$o4bo4$3b2o$3b2o!}}) which evolves to an escaping glider and [[Lifeline Volume 4#Page 5|a pi+block collision]]. All other results converge to the pi+block sequence.</ref>

</references>

== References ==
<references>
<ref name="wiktionary">{{cite web
|url = https://en.wiktionary.org/wiki/%E1%BC%86%CE%B8%CE%BB%CE%BF%CE%BD
|title = ἆθλον
|work = English Wiktionary
|accessdate = 2016-06-16
}}</ref>
<ref name="achim">{{citeAchim
|accessdate = January 15, 2009
}}</ref>
<ref name="niemiec">{{LinkNiemiec|p15.htm|Life Period-15 Oscillators|rle=12/12pc.rle|nobullet=nobullet}}</ref>
<ref name="lifeline_v10_p6">{{CiteLifeline|vol=10|pages=page 6}}</ref>
<ref name="lifeline_v11_p19">{{CiteLifeline|vol=11|pages=pages 18, 19}}</ref>
<ref name="post139656">{{LinkForumThread
|format = ref
|title = Re: Symbiosis
|p = 139656
|author = hotcrystal0
|date = January 2, 2022
}}</ref>
<ref name="post139659">{{LinkForumThread
|format = ref
|title = Re: Oscillator Discussion Thread
|p = 139659
|author = iNoMed
|date = January 2, 2022
}}</ref>
<ref name="message927211272360067092">{{CiteDiscord
|author = David Raucci
|date = January 2, 2022
|channel = cgol
|id = 927211272360067092
}}</ref>
<ref name="post131750">{{LinkForumThread
|format = ref
|title = Re: JP21's Lonely Freedomical Room
|p = 131750
|author = James Pascua
|date = June 10, 2021
}}</ref>
<ref name="post131820">{{LinkForumThread
|format = ref
|title = Re: Oscillator Discussion Thread
|p = 131820
|author = James Pascua
|date = June 11, 2021
}}</ref>
<ref name="post18884">{{LinkForumThread
|format = ref
|title = Re: Soup search results
|p = 18884
|author = gameoflifeboy
|date = April 20, 2015
}}</ref>
</references>

== External links ==
* {{LinkLexicon|lex_p.htm#pentadecathlon}}
* {{LinkCatagolue|xp15_4r4z4r4}}
* {{LinkPentadecathlonObject|12P15.1|patternname=Pentadecathlon|archivedate=20221102180907}}
* {{LinkNiemiec|p15.htm|Life Period-15 Oscillators|rle=12/12pc.rle}}
* {{LinkGoLNews|2009/01/pentadecathalon_crane.html|title=Pentadecathlon Crane|date=January 11, 2009|author=Heinrich Koenig}}

{{Symmetry|orthogonal4}}
{{Sparker|p=15|type=domino|type2=V|strength=strong|strength2=weak|strength3=moderate}}

[[Category:Polyominoes]]

RLE:Pulsaronpentadecathloni

2023-03-12T01:51:39Z

Book: Created page with "x = 26, y = 22, rule = B3/S23 3$12b3o3b3o2$10bo4bobo4bo$10bo4bobo4bo$10bo4bobo4bo$3bo8b3o3b3o$3bo$2b obo7b3o3b3o$3bo6bo4bobo4bo$3bo6bo4bobo4bo$3bo6bo4bobo4bo$3bo$2bobo7b3o 3b3o$3bo$3bo!"

x = 26, y = 22, rule = B3/S23
3$12b3o3b3o2$10bo4bobo4bo$10bo4bobo4bo$10bo4bobo4bo$3bo8b3o3b3o$3bo$2b
obo7b3o3b3o$3bo6bo4bobo4bo$3bo6bo4bobo4bo$3bo6bo4bobo4bo$3bo$2bobo7b3o
3b3o$3bo$3bo!

Natural oscillators above period 3

2023-03-12T01:41:17Z

Book: name and show both qbs types

This page documents all oscillators with period 4 or greater that [[Natural#Catagolue|have occurred in the C1 and/or G1 censuses]] on the [[Catagolue]], excluding stator variants. Ordered by frequency.

The following are excluded:
* Trivial p6 oscillators consisting of p2 and p3 components.
* Pentadecathlon pairs other than bi-pentadecathlon 1 and skewed bi-pentadecathlon 1.
* Pentadecathlon eating something with an [[eater 1]] edge, even though the rotor is technically different from a pentadecathlon alone.
* Queen bee shuttle and twin bees shuttle variants.

{|class="wikitable sortable" style="margin-left:auto; margin-right:auto; clear:both; text-align:center"
! Rank !! Name !! Image !! Period !! Minimum glider cost
|-
|1||[[Pentadecathlon]]||[[File:pentadecathlon.png|96px]]||15||3
|-
|2||[[Figure eight]]||[[File:figureeight.png|96px]]||8||4
|-
|3||[[Mold]]||[[File:mold.png|96px]]||4||5
|-
|4||[[Mazing]]||[[File:mazing.png|96px]]||4||5
|-
|5||[[Blocker]]||[[File:blocker.png|96px]]||8||5
|-
|6||[[Queen bee shuttle]]{{br}}(trans- and cis-)||[[File:transqueenbeeshuttle.png|96px]]{{br}}[[File:cisqueenbeeshuttle.png|96px]]||30||5
|-
|7||[[Achim's p4]]||[[File:achimsp4.png|96px]]||4||5
|-
|8||[[Octagon 2]]||[[File:octagon2.png|96px]]||5||5
|-
|9||[[Unix]]||[[File:unix.png|96px]]||6||5 
|-
|10||[[Tumbler]]||[[File:tumbler.png|96px]]||14||5
|-
|11||[[Coe's p8]]||[[File:coesp8.png|96px]]||8||5
|-
|12||[[Fumarole]]||[[File:fumarole.png|96px]]||5||7
|-
|13||[[Bi-pentadecathlon 1]]||[[File:bipentadecathlon1.png|96px]]||15||6
|-
|14||[[Twin bees shuttle]] (all types)||[[File:transtwinbeesshuttle.png|96px]]||46||7
|-
|15||Pulsar-on-pentadecathlon II||[[File:pulsaronpentadecathlonii.png|96px]]||15||6
|-
|16||[[Monogram]]||[[File:monogram.png|96px]]||4||7
|-
|17||Pulsar-on-pentadecathlon I||[[File:pulsaronpentadecathloni.png|96px]]||15||6
|-
|18||[[Smiley]]||[[File:smiley.png|96px]]||8||8
|-
|19||[[Boring p24]]||[[File:boringp24.png|96px]]||24||7
|-
|20||[[Uninteresting p24]]||[[File:uninterestingp24.png|96px]]||24||7
|-
|21||[[Achim's p8]]||[[File:achimsp8.png|96px]]||8||8
|-
|22||[[Elkies' p5]]||[[File:elkiesp5.png|96px]]||5||8
|-
|23||[[Silver's p5]]||[[File:silversp5onaircraftcarrier.png|96px]]||5||8
|-
|24||[[Heart]] stator variant||[[File:heart.png|96px]]||5||8
|-
|25||{{LinkCatagolue|code=xp4_g88rb88c0cicz11x3dd11|style=raw}}||[[File:xp4_g88rb88c0cicz11x3dd11.png|96px]]||4||23
|-
|26||[[Polypentadecathlon#Pentadecathlon_pairs|Skewed bi-pentadecathlon 1]]||[[File:Pentadecathlonpair2.png|96px]]||15||8
|-
|27||[[Gray counter]] stator variant||[[File:xp4_02596zmlhhhlmz1226221.png|96px]]||4||11
|-
|28||[[1-2-3-4]] stator variant||[[File:xp4_69abaab96z69bo5ob96.png|96px]]||4||24
|-
|29||[[Confused eaters]]||[[File:confusedeaters.png|96px]]||4||9
|-
|30||[[Rob's p16]]||[[File:robsp16.png|96px]]||16||9
|-
|31||[[Tempest]]||[[File:tempest.png|96px]]||4||8
|-
|32||[[20P4]]||[[File:20p4.png|96px]]||4||8
|-
|33||[[Hooks]] stator variant||[[File:hooks.png|96px]]||5||12
|-
|34||Cis-[[figure eight on pentadecathlon]]||[[File:xp120_4r4y13bg2kgz4r4y511.png|96px]]||120||7
|-
|35||{{LinkCatagolue|code=xp4_g88g04a96z122dh953156|style=raw}}||[[File:xp4_g88g04a96z122dh953156.png|96px]]||4||null
|-
|36||[[Burloaferimeter]] stator variant||[[File:burloaferimeter.png|96px]]||7||9
|-
|37||{{LinkCatagolue|code=xp4_39egu1t6zcicw4b871|style=raw}}||[[File:xp4_39egu1t6zcicw4b871.png|96px]]||4||null
|-
|38||{{LinkCatagolue|code=xp4_w2llmzogjkj0v4zw6221|style=raw}}||[[File:xp4_w2llmzogjkj0v4zw6221.png|96px]]||4||null
|-
|39||Trans-[[figure eight on pentadecathlon]]||[[File:xp120_vtvz757y1ssszy7777.png|96px]]||120||7
|}

== See also ==
* [[List of common oscillators]]

[[Category:Lists of patterns]]

Natural oscillators above period 3

2023-03-11T18:52:25Z

Book: wiki link and image with alt name

This page documents all oscillators with period 4 or greater that [[Natural#Catagolue|have occurred in the C1 and/or G1 censuses]], excluding stator variants. Ordered by frequency.

The following are excluded:
* Trivial p6 oscillators consisting of p2 and p3 components.
* Pentadecathlon pairs other than bi-pentadecathlon 1 and skewed bi-pentadecathlon 1.
* Pentadecathlon eating something with an [[eater 1]] edge, even though the rotor is technically different from a pentadecathlon alone.
* Queen bee shuttle and twin bees shuttle variants.

{|class="wikitable sortable" style="margin-left:auto; margin-right:auto; clear:both; text-align:center"
! Rank !! Name !! Image !! Period
|-
|1||[[Pentadecathlon]]||[[File:pentadecathlon.png|96px]]||15
|-
|2||[[Figure eight]]||[[File:figureeight.png|96px]]||8
|-
|3||[[Mold]]||[[File:mold.png|96px]]||4
|-
|4||[[Mazing]]||[[File:mazing.png|96px]]||4
|-
|5||[[Blocker]]||[[File:blocker.png|96px]]||8
|-
|6||[[Queen bee shuttle]] (both types)||[[File:transqueenbeeshuttle.png|96px]]||30
|-
|7||[[Achim's p4]]||[[File:achimsp4.png|96px]]||4
|-
|8||[[Octagon 2]]||[[File:octagon2.png|96px]]||5
|-
|9||[[Unix]]||[[File:unix.png|96px]]||6 
|-
|10||[[Tumbler]]||[[File:tumbler.png|96px]]||14
|-
|11||[[Coe's p8]]||[[File:figureeight.png|96px]]||8
|-
|12||[[Fumarole]]||[[File:fumarole.png|96px]]||5
|-
|13||[[Bi-pentadecathlon 1]]||[[File:bipentadecathlon1.png|96px]]||15
|-
|14||[[Twin bees shuttle]] (all types)||[[File:transtwinbeesshuttle.png|96px]]||46
|-
|15||Pulsar-on-pentadecathlon II||[[File:pulsaronpentadecathlonii.png|96px]]||15
|-
|16||[[Monogram]]||[[File:monogram.png|96px]]||4
|-
|17||Pulsar-on-pentadecathlon I||[[File:pulsaronpentadecathloni.png|96px]]||15
|-
|18||[[Smiley]]||[[File:smiley.png|96px]]||8
|-
|19||[[Boring p24]]||[[File:boringp24.png|96px]]||24
|-
|20||[[Uninteresting p24]]||[[File:uninterestingp24.png|96px]]||24
|-
|21||[[Achim's p8]]||[[File:achimsp8.png|96px]]||8
|-
|22||[[Elkies' p5]]||[[File:elkiesp5.png|96px]]||5
|-
|23||[[Silver's p5]]||[[File:silversp5onaircraftcarrier.png|96px]]||5
|-
|24||[[Heart]] stator variant||[[File:heart.png|96px]]||5
|-
|25||{{LinkCatagolue|code=xp4_g88rb88c0cicz11x3dd11|style=raw}}||[[File:xp4_g88rb88c0cicz11x3dd11.png|96px]]||4
|-
|26||[[Polypentadecathlon#Pentadecathlon_pairs|Skewed bi-pentadecathlon 1]]||[[File:Pentadecathlonpair2.png|96px]]||15
|-
|27||[[Gray counter]] stator variant||[[File:xp4_02596zmlhhhlmz1226221.png|96px]]||4
|-
|28||[[1-2-3-4]] stator variant||[[File:xp4_69abaab96z69bo5ob96.png|96px]]||4
|-
|29||[[Confused eaters]]||[[File:confusedeaters.png|96px]]||4
|-
|30||[[Rob's p16]]||[[File:robsp16.png|96px]]||16
|-
|31||[[Tempest]]||[[File:tempest.png|96px]]||4
|-
|32||[[20P4]]||[[File:20p4.png|96px]]||4
|-
|33||[[Hooks]] stator variant||[[File:hooks.png|96px]]||5
|-
|34||Cis-[[figure eight on pentadecathlon]]||[[File:xp120_4r4y13bg2kgz4r4y511.png|96px]]||120
|-
|35||{{LinkCatagolue|code=xp4_g88g04a96z122dh953156|style=raw}}||[[File:xp4_g88g04a96z122dh953156.png|96px]]||4
|-
|36||[[Burloaferimeter]] stator variant||[[File:burloaferimeter.png|96px]]||7
|-
|37||{{LinkCatagolue|code=xp4_39egu1t6zcicw4b871|style=raw}}||[[File:xp4_39egu1t6zcicw4b871.png|96px]]||4
|-
|38||{{LinkCatagolue|code=xp4_w2llmzogjkj0v4zw6221|style=raw}}||[[File:xp4_w2llmzogjkj0v4zw6221.png|96px]]||4
|-
|39||Trans-[[figure eight on pentadecathlon]]||[[File:xp120_vtvz757y1ssszy7777.png|96px]]||120
|}

== See also ==
* [[List of common oscillators]]

[[Category:Lists of patterns]]

Natural oscillators above period 3

2023-03-11T18:46:51Z

Book:

This page documents all oscillators with period 4 or greater that have occurred in the C1 and/or G1 censuses, excluding stator variants. Ordered by frequency.

The following are excluded:
* Trivial p6 oscillators consisting of p2 and p3 components.
* Pentadecathlon pairs other than bi-pentadecathlon 1 and skewed bi-pentadecathlon 1.
* Pentadecathlon eating something with an [[eater 1]] edge, even though the rotor is technically different from a pentadecathlon alone.
* Queen bee shuttle and twin bees shuttle variants.

{|class="wikitable sortable" style="margin-left:auto; margin-right:auto; clear:both; text-align:center"
! Rank !! Name !! Image !! Period
|-
|1||[[Pentadecathlon]]||[[File:pentadecathlon.png|96px]]||15
|-
|2||[[Figure eight]]||[[File:figureeight.png|96px]]||8
|-
|3||[[Mold]]||[[File:mold.png|96px]]||4
|-
|4||[[Mazing]]||[[File:mazing.png|96px]]||4
|-
|5||[[Blocker]]||[[File:blocker.png|96px]]||8
|-
|6||[[Queen bee shuttle]] (both types)||[[File:transqueenbeeshuttle.png|96px]]||30
|-
|7||[[Achim's p4]]||[[File:achimsp4.png|96px]]||4
|-
|8||[[Octagon 2]]||[[File:octagon2.png|96px]]||5
|-
|9||[[Unix]]||[[File:unix.png|96px]]||6 
|-
|10||[[Tumbler]]||[[File:tumbler.png|96px]]||14
|-
|11||[[Coe's p8]]||[[File:figureeight.png|96px]]||8
|-
|12||[[Fumarole]]||[[File:fumarole.png|96px]]||5
|-
|13||[[Bi-pentadecathlon 1]]||[[File:bipentadecathlon1.png|96px]]||15
|-
|14||[[Twin bees shuttle]] (all types)||[[File:transtwinbeesshuttle.png|96px]]||46
|-
|15||Pulsar-on-pentadecathlon II||[[File:pulsaronpentadecathlonii.png|96px]]||15
|-
|16||[[Monogram]]||[[File:monogram.png|96px]]||4
|-
|17||Pulsar-on-pentadecathlon I||[[File:pulsaronpentadecathloni.png|96px]]||15
|-
|18||[[Smiley]]||[[File:smiley.png|96px]]||8
|-
|19||[[Boring p24]]||[[File:boringp24.png|96px]]||24
|-
|20||[[Uninteresting p24]]||[[File:uninterestingp24.png|96px]]||24
|-
|21||[[Achim's p8]]||[[File:achimsp8.png|96px]]||8
|-
|22||[[Elkies' p5]]||[[File:elkiesp5.png|96px]]||5
|-
|23||[[Silver's p5]]||[[File:silversp5onaircraftcarrier.png|96px]]||5
|-
|24||[[Heart]] stator variant||[[File:heart.png|96px]]||5
|-
|25||{{LinkCatagolue|code=xp4_g88rb88c0cicz11x3dd11|style=raw}}||[[File:xp4_g88rb88c0cicz11x3dd11.png|96px]]||4
|-
|26||Skewed bi-pentadecathlon 1||[[File:xp15_sksy1vtvzvnvy1757.png|96px]]||15
|-
|27||[[Gray counter]] stator variant||[[File:xp4_02596zmlhhhlmz1226221.png|96px]]||4
|-
|28||[[1-2-3-4]] stator variant||[[File:xp4_69abaab96z69bo5ob96.png|96px]]||4
|-
|29||[[Confused eaters]]||[[File:confusedeaters.png|96px]]||4
|-
|30||[[Rob's p16]]||[[File:robsp16.png|96px]]||16
|-
|31||[[Tempest]]||[[File:tempest.png|96px]]||4
|-
|32||[[20P4]]||[[File:20p4.png|96px]]||4
|-
|33||[[Hooks]] stator variant||[[File:hooks.png|96px]]||5
|-
|34||Cis-[[figure eight on pentadecathlon]]||[[File:xp120_4r4y13bg2kgz4r4y511.png|96px]]||120
|-
|35||{{LinkCatagolue|code=xp4_g88g04a96z122dh953156|style=raw}}||[[File:xp4_g88g04a96z122dh953156.png|96px]]||4
|-
|36||[[Burloaferimeter]] stator variant||[[File:burloaferimeter.png|96px]]||7
|-
|37||{{LinkCatagolue|code=xp4_39egu1t6zcicw4b871|style=raw}}||[[File:xp4_39egu1t6zcicw4b871.png|96px]]||4
|-
|38||{{LinkCatagolue|code=xp4_w2llmzogjkj0v4zw6221|style=raw}}||[[File:xp4_w2llmzogjkj0v4zw6221.png|96px]]||4
|-
|39||Trans-[[figure eight on pentadecathlon]]||[[File:xp120_vtvz757y1ssszy7777.png|96px]]||120
|}

== See also ==
* [[List of common oscillators]]

[[Category:Lists of patterns]]

Natural oscillators above period 3

2023-03-11T18:44:58Z

Book: use apgcode for image

This page documents all oscillators with period 4 or greater that have occurred in the C1 and/or G1 censuses, excluding stator variants. Ordered by frequency.

The following are excluded:
* Trivial p6 oscillators consisting of p2 and p3 components.
* Pentadecathlon pairs other than bi-pentadecathlon 1 and skewed bi-pentadecathlon 1.
* Pentadecathlon eating something with an [[eater 1]] edge, even though the rotor is technically different from a pentadecathlon alone.
* Queen bee shuttle and twin bees shuttle variants.

{|class="wikitable sortable" style="margin-left:auto; margin-right:auto; clear:both; text-align:center"
! Rank !! Name !! Image !! Period
|-
|1||[[Pentadecathlon]]||[[File:pentadecathlon.png|96px]]||15
|-
|2||[[Figure eight]]||[[File:figureeight.png|96px]]||8
|-
|3||[[Mold]]||[[File:mold.png|96px]]||4
|-
|4||[[Mazing]]||[[File:mazing.png|96px]]||4
|-
|5||[[Blocker]]||[[File:blocker.png|96px]]||8
|-
|6||[[Queen bee shuttle]] (both types)||[[File:transqueenbeeshuttle.png|96px]]||30
|-
|7||[[Achim's p4]]||[[File:achimsp4.png|96px]]||4
|-
|8||[[Octagon 2]]||[[File:octagon2.png|96px]]||5
|-
|9||[[Unix]]||[[File:unix.png|96px]]||6 
|-
|10||[[Tumbler]]||[[File:tumbler.png|96px]]||14
|-
|11||[[Coe's p8]]||[[File:figureeight.png|96px]]||8
|-
|12||[[Fumarole]]||[[File:fumarole.png|96px]]||5
|-
|13||[[Bi-pentadecathlon 1]]||[[File:bipentadecathlon1.png|96px]]||15
|-
|14||[[Twin bees shuttle]] (all types)||[[File:transtwinbeesshuttle.png|96px]]||46
|-
|15||Pulsar-on-pentadecathlon II||[[File:pulsaronpentadecathlonii.png|96px]]||15
|-
|16||[[Monogram]]||[[File:monogram.png|96px]]||4
|-
|17||Pulsar-on-pentadecathlon I||[[File:pulsaronpentadecathloni.png|96px]]||15
|-
|18||[[Smiley]]||[[File:smiley.png|96px]]||8
|-
|19||[[Boring p24]]||[[File:boringp24.png|96px]]||24
|-
|20||[[Uninteresting p24]]||[[File:uninterestingp24.png|96px]]||24
|-
|21||[[Achim's p8]]||[[File:achimsp8.png|96px]]||8
|-
|22||[[Elkies' p5]]||[[File:elkiesp5.png|96px]]||5
|-
|23||[[Silver's p5]]||[[File:silversp5onaircraftcarrier.png|96px]]||5
|-
|24||[[Heart]] stator variant||[[File:heart.png|96px]]||5
|-
|25||{{LinkCatagolue|code=xp4_g88rb88c0cicz11x3dd11|style=raw}}||[[File:xp4_g88rb88c0cicz11x3dd11.png|96px]]||4
|-
|26||Skewed bi-pentadecathlon 1||[[File:xp4_w2llmzogjkj0v4zw6221.png|96px]]||15
|-
|27||[[Gray counter]] stator variant||[[File:xp4_02596zmlhhhlmz1226221.png|96px]]||4
|-
|28||[[1-2-3-4]] stator variant||[[File:xp4_69abaab96z69bo5ob96.png|96px]]||4
|-
|29||[[Confused eaters]]||[[File:confusedeaters.png|96px]]||4
|-
|30||[[Rob's p16]]||[[File:robsp16.png|96px]]||16
|-
|31||[[Tempest]]||[[File:tempest.png|96px]]||4
|-
|32||[[20P4]]||[[File:20p4.png|96px]]||4
|-
|33||[[Hooks]] stator variant||[[File:hooks.png|96px]]||5
|-
|34||Cis-[[figure eight on pentadecathlon]]||[[File:xp120_4r4y13bg2kgz4r4y511.png|96px]]||120
|-
|35||{{LinkCatagolue|code=xp4_g88g04a96z122dh953156|style=raw}}||[[File:xp4_g88g04a96z122dh953156.png|96px]]||4
|-
|36||[[Burloaferimeter]] stator variant||[[File:burloaferimeter.png|96px]]||7
|-
|37||{{LinkCatagolue|code=xp4_39egu1t6zcicw4b871|style=raw}}||[[File:xp4_39egu1t6zcicw4b871.png|96px]]||4
|-
|38||{{LinkCatagolue|code=xp4_w2llmzogjkj0v4zw6221|style=raw}}||[[File:xp4_w2llmzogjkj0v4zw6221.png|96px]]||4
|-
|39||Trans-[[figure eight on pentadecathlon]]||[[File:xp120_vtvz757y1ssszy7777.png|96px]]||120
|}

== See also ==
* [[List of common oscillators]]

[[Category:Lists of patterns]]

Natural oscillators above period 3

2023-03-11T18:36:38Z

Book: link some

This page documents all oscillators with period 4 or greater that have occurred in the C1 and/or G1 censuses, excluding stator variants. Ordered by frequency.

The following are excluded:
* Trivial p6 oscillators consisting of p2 and p3 components.
* Pentadecathlon pairs other than bi-pentadecathlon 1 and skewed bi-pentadecathlon 1.
* Pentadecathlon eating something with an [[eater 1]] edge, even though the rotor is technically different from a pentadecathlon alone.
* Queen bee shuttle and twin bees shuttle variants.

{|class="wikitable sortable" style="margin-left:auto; margin-right:auto; clear:both; text-align:center"
! Rank !! Name !! Image !! Period
|-
|1||[[Pentadecathlon]]||[[File:pentadecathlon.png|96px]]||15
|-
|2||[[Figure eight]]||[[File:figureeight.png|96px]]||8
|-
|3||[[Mold]]||[[File:mold.png|96px]]||4
|-
|4||[[Mazing]]||[[File:mazing.png|96px]]||4
|-
|5||[[Blocker]]||[[File:blocker.png|96px]]||8
|-
|6||[[Queen bee shuttle]] (both types)||[[File:transqueenbeeshuttle.png|96px]]||30
|-
|7||[[Achim's p4]]||[[File:achimsp4.png|96px]]||4
|-
|8||[[Octagon 2]]||[[File:octagon2.png|96px]]||5
|-
|9||[[Unix]]||[[File:unix.png|96px]]||6 
|-
|10||[[Tumbler]]||[[File:tumbler.png|96px]]||14
|-
|11||[[Coe's p8]]||[[File:figureeight.png|96px]]||8
|-
|12||[[Fumarole]]||[[File:fumarole.png|96px]]||5
|-
|13||[[Bi-pentadecathlon 1]]||[[File:bipentadecathlon1.png|96px]]||15
|-
|14||[[Twin bees shuttle]] (all types)||[[File:transtwinbeesshuttle.png|96px]]||46
|-
|15||Pulsar-on-pentadecathlon II||[[File:pulsaronpentadecathlonii.png|96px]]||15
|-
|16||[[Monogram]]||[[File:monogram.png|96px]]||4
|-
|17||Pulsar-on-pentadecathlon I||[[File:pulsaronpentadecathloni.png|96px]]||15
|-
|18||[[Smiley]]||[[File:smiley.png|96px]]||8
|-
|19||[[Boring p24]]||[[File:boringp24.png|96px]]||24
|-
|20||[[Uninteresting p24]]||[[File:uninterestingp24.png|96px]]||24
|-
|21||[[Achim's p8]]||[[File:achimsp8.png|96px]]||8
|-
|22||[[Elkies' p5]]||[[File:elkiesp5.png|96px]]||5
|-
|23||[[Silver's p5]]||[[File:silversp5onaircraftcarrier.png|96px]]||5
|-
|24||[[Heart]] stator variant||[[File:heart.png|96px]]||5
|-
|25||{{LinkCatagolue|code=xp4_g88rb88c0cicz11x3dd11|style=raw}}||[[File:xp4_g88rb88c0cicz11x3dd11.png|96px]]||4
|-
|26||Skewed bi-pentadecathlon 1||[[File:skewedbipentadecathlon1.png|96px]]||15
|-
|27||[[Gray counter]] stator variant||[[File:xp4_02596zmlhhhlmz1226221.png|96px]]||4
|-
|28||[[1-2-3-4]] stator variant||[[File:xp4_69abaab96z69bo5ob96.png|96px]]||4
|-
|29||[[Confused eaters]]||[[File:confusedeaters.png|96px]]||4
|-
|30||[[Rob's p16]]||[[File:robsp16.png|96px]]||16
|-
|31||[[Tempest]]||[[File:tempest.png|96px]]||4
|-
|32||[[20P4]]||[[File:20p4.png|96px]]||4
|-
|33||[[Hooks]] stator variant||[[File:hooks.png|96px]]||5
|-
|34||Cis-[[figure eight on pentadecathlon]]||[[File:xp120_4r4y13bg2kgz4r4y511.png|96px]]||120
|-
|35||{{LinkCatagolue|code=xp4_g88g04a96z122dh953156|style=raw}}||[[File:xp4_g88g04a96z122dh953156.png|96px]]||4
|-
|36||[[Burloaferimeter]] stator variant||[[File:burloaferimeter.png|96px]]||7
|-
|37||{{LinkCatagolue|code=xp4_39egu1t6zcicw4b871|style=raw}}||[[File:xp4_39egu1t6zcicw4b871.png|96px]]||4
|-
|38||{{LinkCatagolue|code=xp4_w2llmzogjkj0v4zw6221|style=raw}}||[[File:xp4_w2llmzogjkj0v4zw6221.png|96px]]||4
|-
|39||Trans-[[figure eight on pentadecathlon]]||[[File:xp120_vtvz757y1ssszy7777.png|96px]]||120
|}

== See also ==
* [[List of common oscillators]]

[[Category:Lists of patterns]]

File:Xp4 g88rb88c0cicz11x3dd11.png

2023-03-11T17:59:38Z

Book: {{StaticImage}}

== Summary ==
{{StaticImage}}

File:Xp4 02596zmlhhhlmz1226221.png

2023-03-11T17:58:43Z

Book: {{StaticImage}}

== Summary ==
{{StaticImage}}

File:Xp4 69abaab96z69bo5ob96.png

2023-03-11T17:57:48Z

Book: {{StaticImage}}

== Summary ==
{{StaticImage}}

File:Xp2 039c8a6zc813.png

2023-03-11T17:56:36Z

Book: {{StaticImage}}

== Summary ==
{{StaticImage}}

File:Xp4 g88g04a96z122dh953156.png

2023-03-11T17:55:37Z

Book: {{StaticImage}}

== Summary ==
{{StaticImage}}