Difference between revisions of "Twin hat"

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|rulemax          = B378/S012345678
|rulemax          = B378/S012345678
|rulespecial      = [[Conway's Game of Life|Conway Life]]
|rulespecial      = [[Conway's Game of Life|Conway Life]]
|synthesis        = 5
|isorulemin      = B/S2-n3r
|isorulemax      = B2ikn34-ai5-y6-i78/S012345678
|synthesis        = 4
|synthesisRLE    = true
|synthesisRLE    = true
|life105          = true
|life106          = true
|plaintext        = true
|plaintext        = true
|rle              = true
|rle              = true
Line 18: Line 18:
|niemiecid        = 17.242
|niemiecid        = 17.242
|pentadecathlonid = 17.7483
|pentadecathlonid = 17.7483
|viewerconfig    = #C [[ ZOOM 48 ]]
}}
}}
'''Twin hat''' (or '''twin peaks''', or '''bi-hat''') is a [[:Category:strict still lifes with 17 cells|17]]-[[cell]] [[still life]] that roughly consists of two [[hat]]s.
'''Twin hat''' (or '''twin peaks''', or '''bi-hat''') is a {{slcells|17|text=17-cell}} [[still life]] that roughly consists of a [[weld]] of two [[hat]]s.


==[[List of common still lifes|Commonness]]==
== Occurrence ==
Twin hat is the thirty-sixth most common still life in [[Achim Flammenkamp's census]], being less common than [[block and dock]] but more common than [[beehive and dock]]; <ref>{{citeAchim|accessdate=January 15, 2009}}</ref> it is the most common object in this census for which no four-glider [[Glider synthesis|synthesis]] is known. The twin hat is also the fourty-eighth most common object on [[Adam P. Goucher]]'s [[Catagolue]].<ref>{{citeCatagolueStats|June 24, 2016}}</ref>
{{related|List of common still lifes}}
Twin hat is the thirty-sixth most common still life in [[Achim Flammenkamp's census]], being less common than [[block on dock]] but more common than [[beehive on dock]].<ref>{{citeAchim|accessdate=January 15, 2009}}</ref>


==See also==
It is the 41st most common still life on [[Adam P. Goucher]]'s [[Catagolue]], being less common than [[beehive with tail]] but more common than [[loop]].<ref name="stats">{{citeCatagolueStats|May 5, 2023}}</ref>
*[[Sesquihat]]


==References==
It is the most common 17-bit still life, being about 25 times more common than the [[paperclip with tail]].<ref name="stats" /> The main reason that the twin hat is so common is because it results from a [[pi heptomino]] hitting two blinkers arranged like they are on opposite sides of a traffic light, as shown below:
 
{{EmbedViewer
|pname        = twinhatgenerators1
|viewerconfig = #C [[ THUMBSIZE 2 WIDTH 800 GPS 2 AUTOSTART T 0 PAUSE 3 LOOP 15 ]]
|position    = center
|caption      = A pi hitting two blinkers
|style        = width:300px;
}}
 
This setup can occur if a traffic light has one blinker destroyed, then the blinker on the opposite side is hit by a variety of objects:
 
{{EmbedViewer
|pname        = twinhatgenerators2
|viewerconfig = #C [[ THUMBSIZE 2 WIDTH 800 GPS 4 AUTOSTART T 0 PAUSE 3 LOOP 30 ]]
|position    = center
|caption      = The blinker hit by a variety of objects
|style        = width:300px;
}}
 
== Glider synthesis ==
{{Small constructible periodic object}}
 
== See also ==
* [[Sesquihat]]
 
== References ==
<references />
<references />


==External links==
== External links ==
{{LinkWeisstein|TwinHat.html}}
* {{LinkLexicon|lex_t.htm#twinhat}}
{{LinkLexicon|lex_t.htm#twinhat}}
* {{LinkCatagolue|xs17_2ege1ege2}}
{{LinkCatagolue|xs17_2ege1ege2}}
* {{LinkNiemiec|p1-17.htm|The 7773 seventeen-bit still-lifes|rle=17/17-242.rle}}
{{LinkNiemiec|p1-17.htm|patternname=The 7773 seventeen-bit still-lifes}}


{{Symmetry|orthogonal2}}
{{Symmetry|orthogonal2}}
__NOTOC__
__NOTOC__

Latest revision as of 14:09, 9 August 2023

Twin hat
x = 9, y = 5, rule = B3/S23 2bo3bo$bobobobo$bobobobo$2obobob2o$4bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 3 ZOOM 21 HEIGHT 400 SUPPRESS ]] #C [[ ZOOM 48 ]]
Pattern type Strict still life
Number of cells 17
Bounding box 9 × 5
Frequency class 18.2
Discovered by Unknown
Year of discovery Unknown

Twin hat (or twin peaks, or bi-hat) is a 17-cell still life that roughly consists of a weld of two hats.

Occurrence

See also: List of common still lifes

Twin hat is the thirty-sixth most common still life in Achim Flammenkamp's census, being less common than block on dock but more common than beehive on dock.[1]

It is the 41st most common still life on Adam P. Goucher's Catagolue, being less common than beehive with tail but more common than loop.[2]

It is the most common 17-bit still life, being about 25 times more common than the paperclip with tail.[2] The main reason that the twin hat is so common is because it results from a pi heptomino hitting two blinkers arranged like they are on opposite sides of a traffic light, as shown below:

x = 26, y = 7, rule = B3/S23 19bo5bo$3o3b3o10bo5bo$19bo5bo$22bo$3b3o15b3o$2bo2bo$22bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 WIDTH 800 GPS 2 AUTOSTART T 0 PAUSE 3 LOOP 15 ]]
A pi hitting two blinkers
(click above to open LifeViewer)
RLE: here Plaintext: here

This setup can occur if a traffic light has one blinker destroyed, then the blinker on the opposite side is hit by a variety of objects:

x = 54, y = 13, rule = B3/S23 46bo$45bobo$bo5bo38b2o$bo5bo12bo26bo$bo5bo11bob2o$20b2o8b3o16b3o$3b3o$ 28bo18bo5bo$28bo18bo5bo$bo26bo18bo5bo$3o$30b3o$bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 WIDTH 800 GPS 4 AUTOSTART T 0 PAUSE 3 LOOP 30 ]]
The blinker hit by a variety of objects
(click above to open LifeViewer)
RLE: here Plaintext: here

Glider synthesis

All strict still lifes with a population of 21 or fewer cells, all oscillators with 16 or fewer cells, and all spaceships with 31 or fewer cells are known to be glider-constructible. A glider synthesis of this object can be found in the infobox to the right.

See also

References

  1. Achim Flammenkamp (September 7, 2004). "Most seen natural occurring ash objects in Game of Life". Retrieved on January 15, 2009.
  2. 2.0 2.1 Adam P. Goucher. "Statistics". Catagolue. Retrieved on May 5, 2023.

External links