Difference between revisions of "Familiar fours"

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{{Glossary}}
{{Glossary}}
The '''familiar fours''' are common [[constellation]]s of four identical objects. The five most common (in decreasing order of frequency) are [[traffic light]] (four [[blinker]]s), [[honey farm]] (four [[beehive]]s), [[blockade]] (four [[block]]s), [[fleet]] (four [[ship]]s in the form of two [[ship-tie]]s), and [[bakery]] (four [[loaf|loaves]] in the form of two [[half-bakery|half-bakeries]]). [[Four skewed blocks]] is also occasionally included in the list.
The '''familiar fours''' are common [[constellation]]s of four identical objects. The five most common (in decreasing order of frequency) are [[traffic light]] (four [[blinker]]s), [[honey farm]] (four [[beehive]]s), [[blockade]] (four [[block]]s), [[fleet]] (four [[ship]]s in the form of two [[ship-tie]]s), and [[bakery]] (four [[loaf|loaves]] in the form of two [[half-bakery|half-bakeries]]). [[Four skewed blocks]] is also occasionally included in the list.
<center>
{{gallery top}}
{|
{{gallery item|{{EmbedViewer
|-
|pname        = trafficlight
|[[Image:trafficlight_small.png|framed|Traffic light<br />{{JavaRLE|trafficlight|brief}}]]
|viewerconfig = #C [[ HEIGHT 500 THUMBSIZE 3 ZOOM 24 ]]
|[[Image:honeyfarm_small.png|framed|Honey farm<br />{{JavaRLE|honeyfarm|brief}}]]
|position    = center
|[[Image:blockade_small.png|framed|Blockade<br />{{JavaRLE|blockade|brief}}]]
|caption      = Traffic light
|[[Image:fleet_small.png|framed|Fleet<br />{{JavaRLE|fleet|brief}}]]
|style        = width:100px;
|[[Image:bakery_small.png|framed|Bakery<br />{{JavaRLE|bakery|brief}}]]
}}}}
|}
{{gallery item|{{EmbedViewer
</center>
|pname        = honeyfarm
|viewerconfig = #C [[ HEIGHT 500 THUMBSIZE 3 ZOOM 24 ]]
|position    = center
|caption      = Honey farm
|style        = width:100px;
}}}}
{{gallery item|{{EmbedViewer
|pname        = blockade
|viewerconfig = #C [[ HEIGHT 500 THUMBSIZE 3 ZOOM 21 ]]
|position    = center
|caption      = Blockade
|style        = width:100px;
}}}}
{{gallery item|{{EmbedViewer
|pname        = fleet
|viewerconfig = #C [[ HEIGHT 500 THUMBSIZE 3 ZOOM 24 ]]
|position    = center
|caption      = Fleet
|style        = width:100px;
}}}}
{{gallery item|{{EmbedViewer
|pname        = bakery
|viewerconfig = #C [[ HEIGHT 500 THUMBSIZE 3 ZOOM 24 ]]
|position    = center
|caption      = Bakery
|style        = width:100px;
}}}}
{{gallery item|{{EmbedViewer
|pname        = 4skewedblocks
|viewerconfig = #C [[ HEIGHT 500 THUMBSIZE 3 ZOOM 24 ]]
|position    = center
|caption      = Four skewed blocks
|style        = width:100px;
}}}}
{{gallery bottom}}


Other "less familiar fours" include the [[land of lakes]] (four [[pond]]s in the form of two [[bi-pond]]s) and [[four eaters]] (four [[eater 1]]s) found in [[Dean Hickerson]]'s Life integer constructions,<ref>{{cite web|url=http://conwaylife.com/ref/DRH/digits.html|author=Dean Hickerson |title=Patterns formed from the digits of numbers |accessdate=March 15, 2019 }}</ref> but these do not have common enough random-[[ash]] predecessors to be counted as familiar fours.
Other '''less familiar fours''' include the [[land of lakes]] (four [[pond]]s in the form of two [[bi-pond]]s) and [[four eaters]] (four [[eater 1]]s) found in [[Dean Hickerson]]'s Life [[integer construction]]s,<ref>{{cite web|url=https://conwaylife.com/ref/DRH/digits.html|author=Dean Hickerson |title=Patterns formed from the digits of numbers |date=March 26, 2007 |accessdate=March 15, 2019 }}</ref> but these do not have common enough random-[[ash]] predecessors to be counted as familiar fours.
{{gallery top}}
{{gallery item|{{EmbedViewer
|pname        = landoflakes
|viewerconfig = #C [[ HEIGHT 500 THUMBSIZE 3 ZOOM 24 ]]
|position    = center
|caption      = Land of lakes
|style        = width:100px;
}}}}
{{gallery item|{{EmbedViewer
|pname        = 4eaters
|viewerconfig = #C [[ HEIGHT 500 THUMBSIZE 3 ZOOM 24 ]]
|position    = center
|caption      = Four eaters
|style        = width:100px;
}}}}
{{gallery bottom}}


==References==
An interesting thing to note is that several of the familiar fours can be formed from one of their constituent objects via the addition of a single cell:
* a traffic light can be formed by adding a single cell to a blinker in one of two ways: either forming a T-tetromino, or placing the extra cell one cell farther away such that it evolves into a Y in the next generation;
* a honey farm can be formed by adding a single cell to a beehive, either inside it, on one of the corners as to form a [[bun]], or one of the far tips as to give a spoon-like shape;
* a fleet can be formed by adding a single cell to a ship which is diagonally adjacent to it.
 
== See also ==
* [[Composer]]
 
== References ==
<references />
<references />


==External links==
== External links ==
{{LinkWeisstein|FamiliarFours.html}}
* {{LinkLexicon|lex_f.htm#familiarfours}}
{{LinkLexicon|lex_f.htm#familiarfours}}


[[Category:Constellations]]
[[Category:Constellations]]

Latest revision as of 13:51, 9 May 2023

The familiar fours are common constellations of four identical objects. The five most common (in decreasing order of frequency) are traffic light (four blinkers), honey farm (four beehives), blockade (four blocks), fleet (four ships in the form of two ship-ties), and bakery (four loaves in the form of two half-bakeries). Four skewed blocks is also occasionally included in the list.

2b3o2$o5bo$o5bo$o5bo2$2b3o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ HEIGHT 500 THUMBSIZE 3 ZOOM 24 ]]
Traffic light
(click above to open LifeViewer)
RLE: here Plaintext: here
x = 13, y = 13, rule = B3/S23 6bo$5bobo$5bobo$6bo2$b2o7b2o$o2bo5bo2bo$b2o7b2o2$6bo$5bobo$5bobo$6bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ HEIGHT 500 THUMBSIZE 3 ZOOM 24 ]]
Honey farm
(click above to open LifeViewer)
RLE: here Plaintext: here
x = 23, y = 10, rule = B3/S23 2o$2o3$b2o17b2o$b2o17b2o3$21b2o$21b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ HEIGHT 500 THUMBSIZE 3 ZOOM 21 ]]
Blockade
(click above to open LifeViewer)
RLE: here Plaintext: here
x = 10, y = 10, rule = B3/S23 4b2o$3bobo$3b2o$b2o$obo5b2o$2o5bobo$7b2o$5b2o$4bobo$4b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ HEIGHT 500 THUMBSIZE 3 ZOOM 24 ]]
Fleet
(click above to open LifeViewer)
RLE: here Plaintext: here
x = 10, y = 10, rule = B3/S23 4b2o$3bo2bo$3bobo$b2obo3bo$o2bo3bobo$obo3bo2bo$bo3bob2o$4bobo$3bo2bo$ 4b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ HEIGHT 500 THUMBSIZE 3 ZOOM 24 ]]
Bakery
(click above to open LifeViewer)
RLE: here Plaintext: here
x = 10, y = 13, rule = B3/S23 3b2o$3b2o4$8b2o$2o6b2o$2o4$5b2o$5b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ HEIGHT 500 THUMBSIZE 3 ZOOM 24 ]]
Four skewed blocks
(click above to open LifeViewer)
RLE: here Plaintext: here


Other less familiar fours include the land of lakes (four ponds in the form of two bi-ponds) and four eaters (four eater 1s) found in Dean Hickerson's Life integer constructions,[1] but these do not have common enough random-ash predecessors to be counted as familiar fours.

x = 14, y = 14, rule = B3/S23 8b2o$7bo2bo$7bo2bo$8b2ob2o$10bo2bo$10bo2bo$11b2o$b2o$o2bo$o2bo$b2ob2o$ 3bo2bo$3bo2bo$4b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ HEIGHT 500 THUMBSIZE 3 ZOOM 24 ]]
Land of lakes
(click above to open LifeViewer)
RLE: here Plaintext: here
x = 15, y = 15, rule = B3/S23 3bo7bo$b3o7b3o$o13bo$2o11b2o8$2o11b2o$o13bo$b3o7b3o$3bo7bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ HEIGHT 500 THUMBSIZE 3 ZOOM 24 ]]
Four eaters
(click above to open LifeViewer)
RLE: here Plaintext: here


An interesting thing to note is that several of the familiar fours can be formed from one of their constituent objects via the addition of a single cell:

  • a traffic light can be formed by adding a single cell to a blinker in one of two ways: either forming a T-tetromino, or placing the extra cell one cell farther away such that it evolves into a Y in the next generation;
  • a honey farm can be formed by adding a single cell to a beehive, either inside it, on one of the corners as to form a bun, or one of the far tips as to give a spoon-like shape;
  • a fleet can be formed by adding a single cell to a ship which is diagonally adjacent to it.

See also

References

  1. Dean Hickerson (March 26, 2007). "Patterns formed from the digits of numbers". Retrieved on March 15, 2019.

External links