Block on cap: Difference between revisions

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{{Stilllife
{{Stilllife
|name            = Block on cap
|name            = Block on cap
|pname            = blockandcap
|pname            = blockoncap
|c                = 12
|c                = 12
|bx              = 4
|bx              = 6
|by              = 6
|by              = 4
|fc              = 19.3
|fc              = 19.3
|symmetry        = n
|discoverer      = Robert Wainwright
|discoverer2      = Everett Boyer
|discoveryear    = 1973
|rulemin          = B/S23
|rulemin          = B/S23
|rulemax          = B378/S012345678
|rulemax          = B378/S012345678
|rulespecial      = [[Conway's Game of Life|Conway Life]]
|rulespecial      = [[Conway's Game of Life|Conway Life]]
|isorulemin      = B/S2ek3anr
|isorulemax      = B1e2ikn34-in5-r6-k78/S012345678
|synthesis        = 4
|synthesis        = 4
|synthesisRLE    = true
|synthesisRLE    = true
|life105          = true
|life106          = true
|plaintext        = true
|plaintext        = true
|rle              = true
|rle              = true
Line 18: Line 22:
|niemiecid        = 12.27
|niemiecid        = 12.27
|pentadecathlonid = 12.2
|pentadecathlonid = 12.2
|viewerconfig    = [[ ZOOM 48 ]]
}}
}}
'''Block on cap''' is a 12-bit [[still life]]. It is composed of a [[cap]] being stabilized by a [[block]].
'''Block on cap''' is a {{slcells|12|text=12-cell}} [[still life]] composed of a [[cap]] being stabilized by a [[block]].


==[[List of common still lifes|Commonness]]==
== Construction ==
Block on cap is the forty-eighth most common [[still life]] in [[Achim Flammenkamp's census]], being less common than [[elevener]] but more common than [[trans-loaf with tail]].<ref>{{citeAchim|accessdate=January 15, 2009}}</ref> It is also the fifty-eighth most common object on [[Adam P. Goucher]]'s [[Catagolue]].<ref>{{citeCatagolueStats|June 24, 2016}}</ref>
{{EmbedViewer
|rle          = x = 81, y = 36, rule = B3/S23
8b2o$7bo2bo$7b4o2$7b2o$7b2o8$obo27bobo27bobo$b2o15bo12b2o15bo12b2o15bo
$bo16bobo10bo16bobo10bo16bobo$18b2o28b2o28b2o6$14bobo$14b2o$15bo5$31b
2o39b2o$32b2o37b2o$31bo7bo25bo7bo$38b2o25b2o$2o36bobo23bobo$b2o$o!
|viewerconfig = #C [[ THEME Book ZOOM 6 AUTOSTART GPS 12 T 0 PAUSE 3 T 32 PAUSE 2 LOOP 33 ]]
|position    = center
|caption      = 4G syntheses<ref name="drh_syntheses" /><ref name="niemiec" />
|style        = width:320px;
}}
 
The block on cap can be [[Glider synthesis|constructed]] with {{gliders|4|text=4 gliders}}. A number of known alternate syntheses can be found in [[Mark Niemiec's database]].<ref name="niemiec" />
 
== Commonness ==
{{main|List of common still lifes}}
Block on cap is the forty-eighth most common [[still life]] in [[Achim Flammenkamp's census]], being less common than [[elevener]] but more common than [[trans-loaf with tail]].<ref>{{citeAchim|accessdate=January 15, 2009}}</ref>
 
It is the 49th [[List of common still lifes|most common still life]] on [[Adam P. Goucher]]'s [[Catagolue]], being less common than [[mirrored dock]] but more common than [[trans-loaf with tail]]. It is the 3rd most common still life with 12 cells, being less common than [[mirrored table]] but more common than [[trans-block on long bookend]].<ref>{{citeCatagolueStats|May 5, 2023}}</ref>
 
There are 3 collisions in the [[octohash database]]{{refn|Two out of three collisions converge to the same sequence after 9 ticks; the headerless RLEs are {{headerlessRLE|b2o$obo$bo3$2b2o$bo2bo2b2o$2bobob2o$3bo4bo!}} and {{headerlessRLE|b2o$obo$bo3$3bo$2bobo2b2o$bo2bob2o$2b2o4bo!}} Third collision is {{headerlessRLE|8b2o$7bobo$7b2o6$b2o$o2bo$o2bo$b2o2b2o$5bobo$5bo!}}}} and 35 collisions in the [[octo3obj database]] where the final pattern contains a block on cap along with other junk.
 
== See also ==
* [[Mirrored cap]]
* [[Beehive on cap]]
 
== References ==
<references>
 
<ref name="drh_syntheses">[https://conwaylife.com/ref/DRH/syntheses.html 2, 3, and 4-glider syntheses] at [[Dean Hickerson]]'s Life page</ref>
<ref name="niemiec">{{LinkNiemiec|p1-12.htm|The 121 twelve-bit still-lifes|rle=12/12-27.rle|nobullet=nobullet}}</ref>


==See also==
</references>
*[[Bi-cap]]
*[[Beehive on cap]]


==References==
== External links ==
<references />
* {{LinkCatagolue|xs12_330f96}}
* {{LinkPentadecathlonObject|12.2}}


==External links==
{{LinkCatagolue|xs12_330f96}}
{{LinkNiemiec|p1-12.htm|patternname=The 121 twelve-bit still-lifes}}
__NOTOC__
__NOTOC__

Latest revision as of 04:53, 16 January 2025

Block on cap
x = 4, y = 6, rule = B3/S23 2o$2o2$4o$o2bo$b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 3 ZOOM 21 HEIGHT 400 SUPPRESS ]] [[ ZOOM 48 ]]
View static image
Pattern type Strict still life
Number of cells 12
Bounding box 6 × 4
Frequency class 19.3
Static symmetry n (C1)
Discovered by Robert Wainwright
Everett Boyer
Year of discovery 1973

Block on cap is a 12-cell still life composed of a cap being stabilized by a block.

Construction

x = 81, y = 36, rule = B3/S23 8b2o$7bo2bo$7b4o2$7b2o$7b2o8$obo27bobo27bobo$b2o15bo12b2o15bo12b2o15bo $bo16bobo10bo16bobo10bo16bobo$18b2o28b2o28b2o6$14bobo$14b2o$15bo5$31b 2o39b2o$32b2o37b2o$31bo7bo25bo7bo$38b2o25b2o$2o36bobo23bobo$b2o$o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THEME Book ZOOM 6 AUTOSTART GPS 12 T 0 PAUSE 3 T 32 PAUSE 2 LOOP 33 ]]
4G syntheses[1][2]
(click above to open LifeViewer)

The block on cap can be constructed with 4 gliders. A number of known alternate syntheses can be found in Mark Niemiec's database.[2]

Commonness

Main article: List of common still lifes

Block on cap is the forty-eighth most common still life in Achim Flammenkamp's census, being less common than elevener but more common than trans-loaf with tail.[3]

It is the 49th most common still life on Adam P. Goucher's Catagolue, being less common than mirrored dock but more common than trans-loaf with tail. It is the 3rd most common still life with 12 cells, being less common than mirrored table but more common than trans-block on long bookend.[4]

There are 3 collisions in the octohash database[5] and 35 collisions in the octo3obj database where the final pattern contains a block on cap along with other junk.

See also

References

  1. ↑ 2, 3, and 4-glider syntheses at Dean Hickerson's Life page
  2. ↑ 2.0 2.1 The 121 twelve-bit still-lifes at Mark D. Niemiec's Life Page (download pattern file: 12/12-27.rle)
  3. ↑ Achim Flammenkamp (September 7, 2004). "Most seen natural occurring ash objects in Game of Life". Retrieved on January 15, 2009.
  4. ↑ Adam P. Goucher. "Statistics". Catagolue. Retrieved on May 5, 2023.
  5. ↑ Two out of three collisions converge to the same sequence after 9 ticks; the headerless RLEs are b2o$obo$bo3$2b2o$bo2bo2b2o$2bobob2o$3bo4bo! and b2o$obo$bo3$3bo$2bobo2b2o$bo2bob2o$2b2o4bo! Third collision is 8b2o$7bobo$7b2o6$b2o$o2bo$o2bo$b2o2b2o$5bobo$5bo!


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