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{{Oscillator
{{Oscillator
|name         = Tumbler
|name             = Tumbler
|pname       = tumbler
|pname           = tumbler
|c           = 16
|c               = 16
|bx           = 9
|bx               = 9
|by           = 7
|by               = 7
|p           = 14
|fc              = 29.9
|m           = 7
|p               = 14
|h           = 10.3
|m               = 7
|v           = 1.00
|h               = 10.3
|discoverer   = George Collins
|v               = 1.00
|discoveryear = 1970
|sv              = 0.88
|rulemin     = B3/S23
|symmetry        = -c+c
|rulemax     = B378/S023678
|discoverer       = George Collins
|rulespecial  = [[Conway's Game of Life|Conway Life]]
|discoveryear     = 1970
|synthesis   = 8
|rulemin         = B3/S23
|synthesisRLE = true
|rulemax         = B378/S023678
|life105      = true
|isorulemin      = B3-cky/S23-ceky
|life106      = true
|isorulemax      = B2n34aektwz5-ijqr6-ik78/S0234-ajkr5-y678
|plaintext    = true
|synthesis       = 5
|rle          = true
|synthesisRLE     = true
|animated     = true
|plaintext        = true
|viewerconfig = #C [[ GPS 7 THUMBSIZE 2 HEIGHT 400 ]]
|rle              = true
|apgcode          = xp14_j9d0d9j
|pentadecathlonid = 16P14.1
|animated         = true
|viewerconfig     = #C [[ HEIGHT 500 WIDTH 600 THUMBSIZE 3 ZOOM 36 GPS 7 ]]
}}
}}
The '''tumbler''' is the smallest known and first discovered [[period]] [[:Category:Oscillators with period 14|14]] [[oscillator]] and was found by [[:Category:Patterns found by George Collins|George Collins]] in [[:Category:Patterns found in 1970|1970]].<ref>{{cite web|url=http://pentadecathlon.com/objects/class2/class2.php?part=1 |title=Class 2 Objects Catalog |accessdate=April 11, 2009}}</ref> It was the only known period 14 oscillator until the discovery of [[44P14]] on April 21, [[:Category:patterns found in 1997|1997]].
The '''tumbler''' is the smallest known and first discovered {{period|14}} [[oscillator]] and was found by [[George Collins]] in {{year|1970}}.<ref>{{CiteHickersonOscillators|accessdate=March 14, 2020}}</ref> It was the only known non-trivial period-14 oscillator until the discovery of [[44P14]] on April 21, {{year|1997}}.


==[[List of common oscillators|Commonness]]==
== Use as a sparker ==
Tumbler is about the twenty-eighth most [[common]] naturally-occurring oscillator in [[Achim Flammenkamp's census]], being less common than [[octagon 2]] and [[unix]] but more common than [[tub test tube baby]].<ref>{{citeAchim|accessdate=January 15, 2009}}</ref>


==Synthesis==
The tumbler has a few applications where it can act as a weak [[sparker]], although its high period makes it completely incompatible with most oscillators. In most cases, the tumbler is not the only thing that works, but it can be useful to reduce the population.
In November 2014, Aidan F. Pierce found a predecessor for this pattern based on a soup from [[Adam P. Goucher]]'s apgsearch script, which allowed for a 6-glider synthesis.<ref>{{cite web|url=http://www.conwaylife.com/forums/viewtopic.php?f=2&t=1452&start=50#p14104|title=Soup search results|date=|accessdate=November 9, 2014}}</ref>
{{gallery top}}
{{gallery item|{{EmbedViewer
|pname        = p28bheptominohassler
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 8 GPS 14 ]]
|position    = center
|caption      = Period-28 [[B-heptomino]] hassler;<ref name="post137087" /> a [[T-nosed p4]] can substitute for the tumbler spark but at the cost of increased population.
|style        = width:300px;
|apgcode      = xp28_yg69lqozyhk811zyegg8ozwgg0ggy634c63w61qk0kq16z685202586ws6jiczy7h1zy4ooh2zy415a96
}}}}
{{gallery item|{{EmbedViewer
|pname        = p70glidershuttle
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 8 GPS 35 ]]
|position    = center
|caption      = Period-70 glider [[relay]]<ref name="post133722" />
|style        = width:300px;
|apgcode      = xp70_y3c88blg8k46p3zy532gh2in5la96zj9d0d9jy011w18nge2zzy4g88gw247zy32jgf0c80ccy0j9d0d9jzy3342t57aic8imggzy564311w56w1
}}}}


==See also==
== Occurrence ==
{{related|List of common oscillators}}
Tumbler is about the twenty-eighth most [[common]] naturally-occurring oscillator in [[Achim Flammenkamp's census]], being less common than [[octagon 2]] and [[unix]] but more common than [[tub test tube baby]].<ref>{{citeAchim|accessdate=January 15, 2009}}</ref> On [[Catagolue]], it is the thirty-first most common oscillator and the only known period 14 oscillator to have occurred naturally.<ref>{{citeCatagolueStats|October 27, 2018}}</ref>
 
== Glider synthesis ==
 
Before 2014, at least 8 gliders were needed to synthesize the tumbler.<ref name="post4762" /> In August {{year|2014}}, [[Bob Shemyakin]] found a 4-glider [[component]] that converts a [[bi-block]] to a tumbler, resulting in a {{gliders|6}} synthesis.<ref name="post12917" /> Another one-step 6-glider [[recipe]] based on a random [[soup]] was found by [[Tanner Jacobi]] in November that year, which involves a [[honey farm]] [[predecessor]] being hit on three sides.<ref name="post14107" /> Later in January {{year|2020}}, Tanner Jacobi also found a similar clean reaction arising from a [[Catagolue]]-based randomized {{gliders|5}} search.<ref name="post87363" />
 
== LCM oscillators ==
The [[LCM oscillator]]s below are listed due to being the smallest known ones by population while satisfying the condition that at least one cell oscillates at the full period.
{{gallery top}}
{{gallery item|{{EmbedViewer
|pname        = tumbleronrichsp16
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 12 GPS 56 THEME Book STARTFROM 112 ]]
|position    = center
|caption      = Tumbler on [[Rich's p16]],<ref name="post80153" /> the smallest known p112 oscillator by population
|style        = width:300px;
|apgcode      = xp112_om999e0e999mozx8kc0ck8zzw8if505fi8
}}}}
{{gallery item|{{EmbedViewer
|pname        = tumbleron70p26
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 12 GPS 60 THEME Book STARTFROM 182 ]]
|position    = center
|caption      = Tumbler on [[70P26]], the smallest known p182 oscillator by population<ref name="message1298162206055206967"/>
|style        = width:300px;
|apgcode      = xp182_ycj9d0d9jzy1o8gyjg8ozgs26w11o4cx4rry1rr4xc4o11w62sgzy16511y377x77y31156
}}}}
{{gallery bottom}}
 
== See also ==
* [[Rich's p16]]
* [[Rich's p16]]
* [[34P14 shuttle]]


==References==
== References ==
<references />
<references>
<ref name="post4762">{{LinkForumThread
|format = ref
|p      = 4762
|title  = Re: Thread For Your Accidental Discoveries
|author = Heinrich Koenig
|date  = June 19, 2011
}}</ref>
<ref name="post12917">{{LinkForumThread
|format = ref
|p      = 12917
|title  = Re: Synthesising Oscillators
|author = Bob Shemyakin
|date  = August 16, 2014
}}</ref>
<ref name="post14107">{{LinkForumThread
|format = ref
|p      = 14107
|title  = Re: Soup search results
|author = Tanner Jacobi
|date  = November 3, 2014
}}</ref>
<ref name="post80153">{{LinkForumThread
|format = ref
|p      = 80153
|title  = Re: Thread for your unsure discoveries
|author = GUYTU6J
|date  = July 27, 2019
}}</ref>
<ref name="post87363">{{LinkForumThread
|format = ref
|p      = 87363
|title  = Re: Randomly enumerating glider syntheses
|author = Hdjensofjfnen
|date  = January 12, 2020
}}</ref>
<ref name="post133722">{{LinkForumThread
|format = ref
|p      = 133722
|title  = Re: Oscillator Discussion Thread
|author = Matthias Merzenich
|date  = July 18, 2021
}}</ref>
<ref name="post137087">{{LinkForumThread
|format = ref
|p      = 137087
|title  = Re: Oscillator Discussion Thread
|author = David Raucci
|date  = October 28, 2021
}}</ref>
<ref name="message1298162206055206967">{{CiteDiscord
|author  = Entity Valkyrie
|date    = October 22, 2024
|channel = cgol
|id      = 1298162206055206967
}}</ref>
</references>


==External links==
== External links ==
{{LinkWeisstein|Tumbler.html}}
* {{LinkLexicon|lex_t.htm#tumbler}}
{{LinkLexicon|lex_t.htm#tumbler}}
* {{LinkCatagolue|xp14_j9d0d9j}}
{{LinkCatagolue|xp14_j9d0d9j}}
* {{LinkNiemiec|osc.htm#osc-16|The 108 sixteen-bit oscillators|rle=16/16tu.rle}}
* {{LinkPentadecathlonObject|id=16P14.1|archivedate=20210716161231}}


{{Symmetry|orthogonal2|osc=flip}}
__NOTOC__
__NOTOC__

Latest revision as of 12:52, 20 January 2026

Tumbler
bo5bob$obo3bobo$o2bobo2bo$2bo3bo2b$2b2ob2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ AUTOSTART ]] #C [[ HEIGHT 500 WIDTH 600 THUMBSIZE 3 ZOOM 36 GPS 7 ]]
View animated image
View static image
Pattern type Oscillator
Number of cells 16
Bounding box 9 × 7
Frequency class 29.9
Period 14 (mod: 7)
Heat 10.3
Volatility 1.00 | 0.88
Kinetic symmetry -c+c
Discovered by George Collins
Year of discovery 1970

The tumbler is the smallest known and first discovered period-14 oscillator and was found by George Collins in 1970.[1] It was the only known non-trivial period-14 oscillator until the discovery of 44P14 on April 21, 1997.

Use as a sparker

The tumbler has a few applications where it can act as a weak sparker, although its high period makes it completely incompatible with most oscillators. In most cases, the tumbler is not the only thing that works, but it can be useful to reduce the population.

x = 39, y = 31, rule = B3/S23 16b3o$16bo3b2o$17b5o2$17b5o$16bo3b2o$4bo11b3o$2b2obo$bo$obo2bo$o2bo4b 2o4b2o$b2o4b2obo3bobo$16bo$14b3o4$22b3o$22bo$22bobo3bob2o4b2o$23b2o4b 2o4bo2bo$33bo2bobo$37bo$33bob2o$20b3o11bo$17b2o3bo$17b5o2$17b5o$17b2o 3bo$20b3o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ZOOM 8 GPS 14 ]]
Period-28 B-heptomino hassler;[2] a T-nosed p4 can substitute for the tumbler spark but at the cost of increased population.
(click above to open LifeViewer)
RLE: here Plaintext: here
Catagolue: here
x = 38, y = 28, rule = B3/S23 26b3o$23b2o3bo$23b5o2$23b5o$23b2o3bo$26b3o$6b2o3bo22b2o$5bo2bo2b3o20bo $2o4bobo5bo16b2obo$o2b3obob4obo16bo2bob2o$b2o2bobo4b2o13b2o4bobobo$2bo 4bo2b2o14bo2bo2b2o$2bob2obo3bo14bo7bo$3bo7bo14bo3bob2obo$4b2o2bo2bo3bo 10b2o2bo4bo$obobo4b2o4bobo6b2o4bobo2b2o$2obo2bo8b2o6bob4obob3o2bo$3bob 2o16bo5bobo4b2o$3bo20b3o2bo2bo$2b2o22bo3b2o$11b3o$8b2o3bo$8b5o2$8b5o$ 8b2o3bo$11b3o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ZOOM 8 GPS 35 ]]
Period-70 glider relay[3]
(click above to open LifeViewer)
RLE: here Plaintext: here
Catagolue: here

Occurrence

See also: List of common oscillators

Tumbler is about the twenty-eighth most common naturally-occurring oscillator in Achim Flammenkamp's census, being less common than octagon 2 and unix but more common than tub test tube baby.[4] On Catagolue, it is the thirty-first most common oscillator and the only known period 14 oscillator to have occurred naturally.[5]

Glider synthesis

Before 2014, at least 8 gliders were needed to synthesize the tumbler.[6] In August 2014, Bob Shemyakin found a 4-glider component that converts a bi-block to a tumbler, resulting in a 6-glider synthesis.[7] Another one-step 6-glider recipe based on a random soup was found by Tanner Jacobi in November that year, which involves a honey farm predecessor being hit on three sides.[8] Later in January 2020, Tanner Jacobi also found a similar clean reaction arising from a Catagolue-based randomized 5-glider search.[9]

LCM oscillators

The LCM oscillators below are listed due to being the smallest known ones by population while satisfying the condition that at least one cell oscillates at the full period.

x = 18, y = 13, rule = B3/S23 5b2o$4bo2bo$5bo2bo5b2o$bo6bo4bo$obo3bo2bo4bob2o$b2o3b3o6bobo2$b2o3b3o 6bobo$obo3bo2bo4bob2o$bo6bo4bo$5bo2bo5b2o$4bo2bo$5b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ZOOM 12 GPS 56 THEME Book STARTFROM 112 ]]
Tumbler on Rich's p16,[10] the smallest known p112 oscillator by population
(click above to open LifeViewer)
RLE: here Plaintext: here
Catagolue: here
x = 39, y = 19, rule = B3/S23 16b2o3b2o$16bobobobo$16bobobobo$18bobo$17b2ob2o$17b2ob2o4$5b2o25b2o$5b obo23bobo$6b2o7b2o5b2o7b2o$2b2o10bobo5bobo10b2o$bobo5b2o2b2o9b2o2b2o5b obo$bo6bobo4bo7bo4bobo6bo$2o6bo21bo6b2o$6b3o21b3o$5bo10b2o3b2o10bo$5b 2o9b2o3b2o9b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ZOOM 12 GPS 60 THEME Book STARTFROM 182 ]]
Tumbler on 70P26, the smallest known p182 oscillator by population[11]
(click above to open LifeViewer)
RLE: here Plaintext: here
Catagolue: here


See also

References

  1. ↑ Dean Hickerson's oscillator stamp collection. Retrieved on March 14, 2020.
  2. ↑ David Raucci (October 28, 2021). Re: Oscillator Discussion Thread (discussion thread) at the ConwayLife.com forums
  3. ↑ Matthias Merzenich (July 18, 2021). Re: Oscillator Discussion Thread (discussion thread) at the ConwayLife.com forums
  4. ↑ Achim Flammenkamp (September 7, 2004). "Most seen natural occurring ash objects in Game of Life". Retrieved on January 15, 2009.
  5. ↑ Adam P. Goucher. "Statistics". Catagolue. Retrieved on October 27, 2018.
  6. ↑ Heinrich Koenig (June 19, 2011). Re: Thread For Your Accidental Discoveries (discussion thread) at the ConwayLife.com forums
  7. ↑ Bob Shemyakin (August 16, 2014). Re: Synthesising Oscillators (discussion thread) at the ConwayLife.com forums
  8. ↑ Tanner Jacobi (November 3, 2014). Re: Soup search results (discussion thread) at the ConwayLife.com forums
  9. ↑ Hdjensofjfnen (January 12, 2020). Re: Randomly enumerating glider syntheses (discussion thread) at the ConwayLife.com forums
  10. ↑ GUYTU6J (July 27, 2019). Re: Thread for your unsure discoveries (discussion thread) at the ConwayLife.com forums
  11. ↑ Entity Valkyrie (October 22, 2024). Message in #cgol on the Conwaylife Lounge Discord server


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