Difference between revisions of "Beehive"

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(Added information about its commonness)
(32% of beehives form from honey farms)
 
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{{Stilllife|name=Beehive|pname=beehive|c=6|discoveryear=1970|discoverer=John Conway|life105=true|life106=true|plaintext=true|rle=true}}
{{Stilllife
'''Beehive''' is a [[:Category:Strict still lifes with 6 cells|6]]-[[cell]] [[still life]]. It is the second most common still life, being less common than [[block]] but over three times as common as [[loaf]].<ref>{{cite web|url=http://wwwhomes.uni-bielefeld.de/achim/freq_top_life.html |title=Most seen natural occurring ash objects in Game of Life |author=Achim Flammenkamp |date=September 7, 2004 |accessdate=January 15, 2009}}</ref>
|name             = Beehive
|pname           = beehive
|c               = 6
|bx              = 4
|by              = 3
|fc              = 0.9
|discoverer      = JHC group
|discoveryear     = 1969
|rulemin          = B/S2
|rulemax          = B34678/S012345678
|rulespecial      = [[Conway's Game of Life|Conway Life]], {{rl|HighLife}}
|isorulemin      = B/S2ck
|isorulemax      = B2-ae345-y678/S012345678
|synthesis        = 2
|synthesisRLE    = true
|plaintext       = true
|rle             = true
|apgcode          = xs6_696
|pentadecathlonid = 6.4
|viewerconfig    = [[ ZOOM 60 ]]
}}
'''Beehive''' is a {{slcells|6|text=6-cell}} [[still life]]. It can be seen as a [[weld]] of two [[tub]]s. As a tetromino descendant, it was one of the first objects found.


==See also==
It can be seen as containing a photonegative [[domino]].
*[[Beehive with tail]]
*[[Hivenudger]]
*[[List of common still lifes]]
*[[Pre-beehive]]


==External links==
== Behaviour ==
*[http://www.argentum.freeserve.co.uk/lex_b.htm#beehive Beehive] at the Life Lexicon
Beehives are frequently born in [[Familiar fours|a set of four]] called [[honey farm]].
*[http://home.interserv.com/~mniemiec/still.htm#6-bit%20still Six-bit still lifes] by Mark Niemiec
 
It is possible to turn a single beehive into one by adding a corner (turning it into a [[bun]]), adding a cell to the "tip" of it (the bit with one cell, adding it to the longer end will result in an R-pentomino grandson) or by adding one cell inside it. There are also formations of two beehives that also occur fairly commonly, evolving from [[seed]]s known as [[butterfly]] and [[teardrop]].
 
A beehive can be [[Eater|eaten]] with a [[block]], a reaction that allows the construction of the [[queen bee shuttle]] and further patterns based on it.
 
Some reactions push a beehive one cell. If space permits, the [[beehive push catalyst]] can push it back.
 
== Sequences that produce just a beehive ==
{|style="margin:auto;width:480px;"
|{{EmbedViewer
|pname = beehiveprocrastinator
|position    = center
|viewerconfig = #C [[ GPS 16 THUMBSIZE 2 ]]
|caption      = Procrastinator<ref>{{CiteLifeline|vol=4|pages=page 4}}</ref>
}}
|{{EmbedViewer
|pname = beehivegenerator
|position    = center
|viewerconfig = #C [[ GPS 16 THUMBSIZE 2 ]]
|caption      = Another beehive predecessor
}}
|}
The first pattern above is the "procrastinator", mentioned in [[Lifeline Volume 4]]. It is a [[list of common evolutionary sequences|fairly common sequence]]. It produces a single beehive after 76 generations.
 
The second pattern above is a [[phi spark]] predecessor hitting a block, which then becomes a traffic light hitting a block, which then becomes a single beehive. The beehive forms in generation 51, but it takes until generation 79 for the remaining active region to clear. It is semi-common, but not as common as the procrastinator. An example of a beehive being pushed one cell can be seen here.
 
== Commonness ==
{{main|List of common still lifes}}
{{CatagolueSLRarity
|population=6
|absrank=second
|abslesscommonthan=block
|absmorecommonthan=loaf
|popspecial=yes
|popmostcommon=yes
|popmorecommonthan=ship
}}
The beehive was also the second most common still life in [[Achim Flammenkamp's census]], again being less common than block but over three times as common as loaf.<ref>{{citeAchim|accessdate=January 15, 2009}}</ref>
 
One reason why beehives are so common compared to similarly-sized objects, such as the [[clock]] and [[snake]], is that they have an abundance of 4-cell predecessors.<ref>[[Lifeline Volume 4]]</ref>
{{EmbedViewer
|rle          = x = 16, y = 16, rule = B3/S23
8bo$b3o3b2o3b4o$bo5bo3$2bo4bo$12bo$b2o4b2o4b2o$bo5bo7bo4$obo5bo4bo$2bo
3bobo4bo$3bo5bo3bo$15bo!
|position    = center
|viewerconfig = #C [[ GPS 2 THUMBSIZE 2 ]]
|caption      = The nine 4-cell beehive predecessors
}}
 
Also, as mentioned above, simple [[Honey_farm#Predecessors|honey farm predecessors]] can often create groups of four beehives, given enough space. About 32% of beehives form from honey farms.<ref>https://conwaylife.com/forums/viewtopic.php?f=11&t=2030&start=850#p175341</ref>
 
== Glider synthesis ==
There is a perpendicular [[2-glider collision]] that produces a beehive via an intermediate [[tail]].
 
== See also ==
* [[Beehive with tail]]
* [[Hivenudger]]
* [[Loaf]]
* [[Mango]]
* [[Pond]]
* [[Pre-beehive]]
* [[Honeycomb]]
* [[SW-2]]
 
== References ==
<references />
 
== External links ==
* {{LinkLexicon|lex_b.htm#beehive}}
* {{LinkCatagolue|xs6_696}}
* {{LinkNiemiec|p1.htm#p1-6|The 5 six-bit still-lifes|rle=0/6hv.rle}}
* {{LinkPentadecathlonObject|id=6.4|patternname=Beehive}}
 
{{Symmetry|orthogonal4}}

Latest revision as of 14:49, 17 January 2024

Beehive
x = 4, y = 3, rule = B3/S23 b2o$o2bo$b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 3 ZOOM 21 HEIGHT 400 SUPPRESS ]] [[ ZOOM 60 ]]
View static image
Pattern type Strict still life
Number of cells 6
Bounding box 4 × 3
Frequency class 0.9
Discovered by JHC group
Year of discovery 1969

Beehive is a 6-cell still life. It can be seen as a weld of two tubs. As a tetromino descendant, it was one of the first objects found.

It can be seen as containing a photonegative domino.

Behaviour

Beehives are frequently born in a set of four called honey farm.

It is possible to turn a single beehive into one by adding a corner (turning it into a bun), adding a cell to the "tip" of it (the bit with one cell, adding it to the longer end will result in an R-pentomino grandson) or by adding one cell inside it. There are also formations of two beehives that also occur fairly commonly, evolving from seeds known as butterfly and teardrop.

A beehive can be eaten with a block, a reaction that allows the construction of the queen bee shuttle and further patterns based on it.

Some reactions push a beehive one cell. If space permits, the beehive push catalyst can push it back.

Sequences that produce just a beehive

x = 5, y = 3, rule = B3/S23 3bo$b4o$2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ GPS 16 THUMBSIZE 2 ]]
Procrastinator[1]
(click above to open LifeViewer)
RLE: here Plaintext: here
x = 9, y = 4, rule = B3/S23 b2o$o2bo3b2o$obo4b2o$2bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ GPS 16 THUMBSIZE 2 ]]
Another beehive predecessor
(click above to open LifeViewer)
RLE: here Plaintext: here

The first pattern above is the "procrastinator", mentioned in Lifeline Volume 4. It is a fairly common sequence. It produces a single beehive after 76 generations.

The second pattern above is a phi spark predecessor hitting a block, which then becomes a traffic light hitting a block, which then becomes a single beehive. The beehive forms in generation 51, but it takes until generation 79 for the remaining active region to clear. It is semi-common, but not as common as the procrastinator. An example of a beehive being pushed one cell can be seen here.

Commonness

Main article: List of common still lifes

Beehive is the second most common still life on Adam P. Goucher's Catagolue, being less common than block but more common than loaf. Among all still lifes with 6 cells, it is the absolute most common, followed by ship.[2] The beehive was also the second most common still life in Achim Flammenkamp's census, again being less common than block but over three times as common as loaf.[3]

One reason why beehives are so common compared to similarly-sized objects, such as the clock and snake, is that they have an abundance of 4-cell predecessors.[4]

x = 16, y = 16, rule = B3/S23 8bo$b3o3b2o3b4o$bo5bo3$2bo4bo$12bo$b2o4b2o4b2o$bo5bo7bo4$obo5bo4bo$2bo 3bobo4bo$3bo5bo3bo$15bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ GPS 2 THUMBSIZE 2 ]]
The nine 4-cell beehive predecessors
(click above to open LifeViewer)

Also, as mentioned above, simple honey farm predecessors can often create groups of four beehives, given enough space. About 32% of beehives form from honey farms.[5]

Glider synthesis

There is a perpendicular 2-glider collision that produces a beehive via an intermediate tail.

See also

References

  1. ↑ Robert Wainwright (December 1971). Lifeline, vol 4, page 4.
  2. ↑ Adam P. Goucher. "Statistics". Catagolue. Retrieved on June 24, 2016.
  3. ↑ Achim Flammenkamp (September 7, 2004). "Most seen natural occurring ash objects in Game of Life". Retrieved on January 15, 2009.
  4. ↑ Lifeline Volume 4
  5. ↑ https://conwaylife.com/forums/viewtopic.php?f=11&t=2030&start=850#p175341

External links

Retrieved from "https://conwaylife.com/w/index.php?title=Beehive&oldid=144604"