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__NOTOC__{{Oscillator|p=5|name=Fumarole|pname=fumarole|bx=8|by=7|animated=true|c=18|h=12.8|discoverer=Dean Hickerson|discoveryear=1989|life105=true|life106=true|plaintext=true|rle=true|synthesis=7|synthesisRLE=true}}
{{Oscillator
'''Fumarole''' is a [[period]] [[:Category:Oscillators with period 5|5]] [[oscillator]] that was found by [[:Category:Patterns found by Dean Hickerson|Dean Hickerson]] in September [[:Category:Patterns found in 1989|1989]]. In terms of its 7&times;8 [[bounding box]], it is the smallest known period 5 oscillator. On September 1, [[:Category:Patterns found in 1995|1995]], [[:Category:Patterns found by Noam Elkies|Noam Elkies]] found a way to non-trivially combine two fumaroles and a [[blinker]] into a period [[:Category:Oscillators with period 10|10]] oscillator, shown below.<ref>x-oscs-new-p001-019.lif pattern collection</ref> In February [[:Category:patterns found in 2000|2000]] [[Stephen Silver]] found a [[:Category:patterns that can be constructed with 7 gliders|7]]-[[glider]] [[glider synthesis|synthesis]] of this oscillator.<ref>{{CiteSummersPattern|name=jslife}}</ref>
|name             = Fumarole
|pname           = fumarole
|c                = 18
|bx               = 8
|by               = 7
|fc              = 35.8
|p                = 5
|m                = 5
|h               = 12.8
|v                = 0.72
|symmetry        = -e
|discoverer       = Dean Hickerson
|discoveryear     = 1989
|rulemin          = B3/S23
|rulemax          = B3678/S02378
|rulespecial      = [[Conway's Game of Life|Conway Life]], {{rl|HighLife}}
|isorulemin      = B3aijq/S2-cn3jnqr
|isorulemax      = B2n34-aknry5-jnq678/S0234-aqr5-ainq6-a78
|synthesis        = 6
|synthesisRLE    = true
|plaintext       = true
|rle             = true
|apgcode          = xp5_3pmwmp3zx11
|pentadecathlonid = 18P5.1
|animated        = true
|viewerconfig    = #C [[ HEIGHT 500 THUMBSIZE 3 ZOOM 33 GPS 2 ]]
}}
'''Fumarole''' is a {{period|5}} [[oscillator]] that was found by [[Dean Hickerson]] on September 3, {{year|1989}}.<ref>{{CiteHickersonOscillators|accessdate=March 14, 2020}}</ref> In terms of its {{cells|18}} [[cell]]s it is the fourth smallest period 5 oscillator, after [[pseudo-barberpole]], [[octagon 2]], and [[Silver's p5]]; however, its {{times|7|8}} [[bounding box]] is the smallest of any known period 5 oscillator.


==Image gallery==
The [[domino]] [[spark]] that it provides makes it useful in the construction of higher period oscillators such as the [[p35 beehive hassler]], [[p40 B-heptomino shuttle]], and [[98P25]]. On September 1, {{year|1995}}, [[Noam Elkies]] found a way to non-trivially combine two fumaroles and a [[blinker]] into a {{period|10}} oscillator, shown below;<ref>{{filename|x-oscs-new-p001-019.lif}} pattern collection</ref> 4 can be combined in a similar fashion.
{|
 
|-
{{EmbedViewer
|[[Image:Two_fumaroles.png|framed|left|Noam Elkies' period 10 oscillator involving two fumaroles and a blinker<br />{{JavaRLE|2fumaroles|brief}}]]
|pname        = 2fumaroles
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 16 GPS 3 AUTOSTART ]]
|position    = center
|caption      = 2 fumaroles and a blinker
|style        = width:300px;
|apgcode      = xp10_3542usz6512310gh11zy0ojdwdjo
}}
 
There is an unusual fumarole [[Periodic catalyst|catalysis]] used in 45P25 shown below. The {{LinkCatagolue|code=gun_70|patternname=smallest p70 gun|style=raw}} and {{LinkCatagolue|code=xp70_y432acy3g0s4zy915dx11zy57ros4yfc4owo4cz0o0440oy1136yf708807zc96w69cycgoc4408gzyj3ffwoi053zye8e13y3ckggzys1|patternname=a certain p70 dependent reflector|style=raw}} use the same catalysis.
 
{{EmbedViewer
|pname        = 45p25
|position    = center
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 16 GPS 6 AUTOSTART ]]
|caption      = 45P25, showing the unusual fumarole catalysis on the right.
|apgcode      = xp25_35426oz65123y0eey3o62453zy7111y132156
}}
 
== Construction ==
In February {{year|2000}}, [[Stephen Silver]] found a {{gliders|7}} [[Glider synthesis|synthesis]] of this oscillator.<ref>{{CiteSummersPattern|name=jslife}}</ref> There are known alternate syntheses.<ref name="niemiec" /><ref name="post159582" /> In {{year|2024}}, [[Carson Cheng]] found a {{gliders|6}} synthesis.<ref name="post179445"/>
 
== Occurrence ==
{{related|List of common oscillators}}
On [[Catagolue]], it is the second most common period 5 oscillator, being less common than [[octagon II]] but more common than [[Elkies' p5]].<ref>{{citeCatagolueStats|October 27, 2018}}</ref>
 
{|style="margin-left:auto;margin-right:auto;width:300px;"
|{{EmbedViewer
|pname        = fumarolepredecessor
|viewerconfig = #C [[ THUMBNAIL THUMBSIZE 2 ZOOM 16 ]]
|position    = center
|caption      = A  very common predecessor of fumarole involves two [[block]]s and a region resembling two [[xWSS]] heads [[weld]]ed together.<ref name="post17876" />
|style        = width:300px;
}}
|{{EmbedViewer
|rle          = x = 18, y = 7, rule = B3/S23
8b2o$7bo2bo$7bo2bo$3o5b2o5b3o$o2bo10bo2bo$o2bo10bo2bo$b3o10b3o!
|viewerconfig = #C [[ THUMBNAIL THUMBSIZE 2 ZOOM 16 ]]
|position    = center
|caption      = A stator variant of fumarole can form from a [[pond]] and two [[fleet]] predecessors.<ref>https://catagolue.hatsya.com/hashsoup/C1/c_YqtsFrdbvyAm218509887/b3s23</ref>
|style        = width:300px;
}}
|}
|}


==See also==
== See also ==
*[[Fumarole on Achim's p11]]
* [[66P62]]
*[[Hebdarole]]
* [[Fumarole on Achim's p11]]
*[[Mold on fumarole]]
* [[Hebdarole]]
* [[Mold on fumarole]]
* [[Smallest period 5 oscillators]]
 
== References ==
<references>
<ref name="niemiec">{{LinkNiemiec|p5.htm#p5-18|The 4 eighteen-bit period 5 oscillators|rle=18/18fm.rle|nobullet=nobullet}}</ref>
<ref name="post17876">{{LinkForumThread
|format = ref
|p      = 17876
|title  = Re: Soup search results
|author = Dave Greene
|date  = March 12, 2015
}}</ref>
<ref name="post159582">{{LinkForumThread
|format = ref
|p      = 159582
|title  = Re: Synthesising Oscillators
|author = Carson Cheng
|date  = March 25, 2023
}}</ref>
<ref name="post179445">{{LinkForumThread
|format = ref
|p      = 179445
|title  = Re: Synthesising Oscillators
|author = Carson Cheng
|date  = March 1, 2024
}}</ref>
</references>


==References==
== External links ==
<references />
* {{LinkLexicon|filename=lex_f.htm#fumarole}}
* {{LinkCatagolue|xp5_3pmwmp3zx11}}
* {{LinkPentadecathlonObject|18P5.1}}
* {{LinkWikipedia|Fumarole}} (origin of name)


==External links==
{{Sparker|p=5|type=domino|strength=moderate}}
{{LinkWeisstein|filename=Fumarole.html}}
__NOTOC__
{{LinkLexicon|filename=lex_f.htm#fumarole}}

Latest revision as of 06:50, 8 February 2025

Fumarole
x = 8, y = 7, rule = B3/S23 2o4b2o$obo2bobo$2bo2bo$bo4bo$bo4bo$bo4bo$3b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ AUTOSTART ]] #C [[ HEIGHT 500 THUMBSIZE 3 ZOOM 33 GPS 2 ]]
View animated image
View static image
Pattern type Oscillator
Number of cells 18
Bounding box 8 × 7
Frequency class 35.8
Period 5 (mod: 5)
Heat 12.8
Volatility 0.72 | 0.72
Kinetic symmetry -e
Discovered by Dean Hickerson
Year of discovery 1989

Fumarole is a period-5 oscillator that was found by Dean Hickerson on September 3, 1989.[1] In terms of its 18 cells it is the fourth smallest period 5 oscillator, after pseudo-barberpole, octagon 2, and Silver's p5; however, its 7 × 8 bounding box is the smallest of any known period 5 oscillator.

The domino spark that it provides makes it useful in the construction of higher period oscillators such as the p35 beehive hassler, p40 B-heptomino shuttle, and 98P25. On September 1, 1995, Noam Elkies found a way to non-trivially combine two fumaroles and a blinker into a period-10 oscillator, shown below;[2] 4 can be combined in a similar fashion.

x = 15, y = 12, rule = b3/s23 2o13b$o2b2o4bo5b$b2ob2o3bo5b$4b2o3bo5b$4b2o9b$b2ob2o4b2o3b$o2b2o3bo4bo b$2o6bo4bob$8bo4bob$9bo2bo2b$7bobo2bobo$7b2o4b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ZOOM 16 GPS 3 AUTOSTART ]]
2 fumaroles and a blinker
(click above to open LifeViewer)
RLE: here Plaintext: here
Catagolue: here

There is an unusual fumarole catalysis used in 45P25 shown below. The smallest p70 gun and a certain p70 dependent reflector use the same catalysis.

x = 24, y = 13, rule = B3/S23 22b2o$19b2o2bo$19bob2o$18bo$18bo$2o17bob2o$o2b2o8b2o4b2o2bo$b2obo8b2o 7b2o$5bo7b2o$5bo$b2obo5b3o$o2b2o$2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ZOOM 16 GPS 6 AUTOSTART ]]
45P25, showing the unusual fumarole catalysis on the right.
(click above to open LifeViewer)
RLE: here Plaintext: here
Catagolue: here

Construction

In February 2000, Stephen Silver found a 7-glider synthesis of this oscillator.[3] There are known alternate syntheses.[4][5] In 2024, Carson Cheng found a 6-glider synthesis.[6]

Occurrence

See also: List of common oscillators

On Catagolue, it is the second most common period 5 oscillator, being less common than octagon II but more common than Elkies' p5.[7]

x = 9, y = 11, rule = B3/S23 o5bo$o2b2o$2bo2bo$3bobo$4bo5$b2o4b2o$b2o4b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBNAIL THUMBSIZE 2 ZOOM 16 ]]
A very common predecessor of fumarole involves two blocks and a region resembling two xWSS heads welded together.[8]
(click above to open LifeViewer)
RLE: here Plaintext: here
x = 18, y = 7, rule = B3/S23 8b2o$7bo2bo$7bo2bo$3o5b2o5b3o$o2bo10bo2bo$o2bo10bo2bo$b3o10b3o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBNAIL THUMBSIZE 2 ZOOM 16 ]]
A stator variant of fumarole can form from a pond and two fleet predecessors.[9]
(click above to open LifeViewer)

See also

References

  1. ↑ Dean Hickerson's oscillator stamp collection. Retrieved on March 14, 2020.
  2. ↑ x-oscs-new-p001-019.lif pattern collection
  3. ↑ Jason Summers' jslife pattern collection.
  4. ↑ The 4 eighteen-bit period 5 oscillators at Mark D. Niemiec's Life Page (download pattern file: 18/18fm.rle)
  5. ↑ Carson Cheng (March 25, 2023). Re: Synthesising Oscillators (discussion thread) at the ConwayLife.com forums
  6. ↑ Carson Cheng (March 1, 2024). Re: Synthesising Oscillators (discussion thread) at the ConwayLife.com forums
  7. ↑ Adam P. Goucher. "Statistics". Catagolue. Retrieved on October 27, 2018.
  8. ↑ Dave Greene (March 12, 2015). Re: Soup search results (discussion thread) at the ConwayLife.com forums
  9. ↑ https://catagolue.hatsya.com/hashsoup/C1/c_YqtsFrdbvyAm218509887/b3s23


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