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{{Stilllife
{{Stilllife
|name            = Table on table
|name            = Mirrored table
|pname            = tableontable
|pname            = mirroredtable
|c                = 12
|c                = 12
|bx              = 4
|bx              = 5
|by              = 5
|by              = 4
|fc              = 16.2
|fc              = 16.2
|symmetry        = +e
|rulemin          = B/S23
|rulemin          = B/S23
|rulemax          = B3578/S012345678
|rulemax          = B3578/S012345678
|rulespecial      = [[Conway's Game of Life|Conway Life]]
|rulespecial      = [[Conway's Game of Life|Conway Life]]
|isorulemin      = B/S2ae3r
|isorulemax      = B2-ac34-ai56-i78/S012345678
|synthesis        = 4
|synthesis        = 4
|synthesisRLE    = true
|synthesisRLE    = true
|life105          = true
|life106          = true
|plaintext        = true
|plaintext        = true
|rle              = true
|rle              = true
Line 18: Line 19:
|niemiecid        = 12.25
|niemiecid        = 12.25
|pentadecathlonid = 12.9
|pentadecathlonid = 12.9
|viewerconfig    = [[ ZOOM 57 ]]
}}
}}
'''Table on table''' is a 12-bit [[still life]]. It consists of two [[table]]s facing each other with one row of dead cells between them.
'''Mirrored table''' is a {{slcells|12|text=12-cell}} [[still life]]. It consists of two [[table]]s facing each other with one row of dead cells between them.


==[[List of common still lifes|Commonness]]==
One of the tables can be moved by two cells to the side, resulting in [[rotated table]].
Table on table is the thirtieth most common [[still life]] in [[Achim Flammenkamp's census]], being less common than [[very long ship]] but more common than [[canoe]].<ref>{{citeAchim|accessdate=January 15, 2009}}</ref> It is also the thirty-eighth most common object on [[Adam P. Goucher]]'s [[Catagolue]].<ref>{{citeCatagolueStats|June 24, 2016}}</ref>


==Image gallery==
It is the only 12-cell still life to fit within a {{times|5|4}} bounding box.
{|
 
|-
== Construction ==
|[[file:rotatedtable.png|framed|left|[[Rotated table|A variation of table on table]]<br/>{{JavaRLE|alternatetableontable|breif}}]]
{{EmbedViewer
|rle          = x = 92, y = 72, rule = B3/S23
81bo$25bo22bo31bo$24bo7bo14bo32b3o$24b3o6b2o12b3o$32b2o$70bobo$56bobo
12b2o$56b2o13bo$57bo$50bo$49b2o15b3o$49bobo16bo$67bo4$bo69b3o$b2o70bo$
obo10b2o57bo$13bobo5b2o$13bo6b2o$22bo2$5bo$6b2o$5b2o4$67b2o2b2o$66bobo
b2o$68bo3bo$46bobo$38bo7b2o$39b2o6bo$38b2o2$16bo$15bo$15b3o$19b3o$19bo
$20bo$35b2o$36b2o$35bo10b3o$46bo$47bo6$89b3o$89bo$5b2o83bo$6b2o$5bo12$
35b3o$37bo$36bo!
|viewerconfig = #C [[ THEME Book ZOOM 4 X 0 Y -6 AUTOSTART GPS 12 T 0 PAUSE 3 T 119 PAUSE 2 LOOP 120 ]]
|position    = center
|caption      = 4G syntheses<ref name="drh_syntheses" /><ref name="niemiec" />
|style        = width:300px;
}}
 
There are known {{gliders|4}} [[Glider synthesis|syntheses]] for a mirrored table; a number of known syntheses can be found in [[Mark Niemiec's database]].<ref name="niemiec" />
 
The [[octohash database]] contains a constellation of two [[long boat]]s which can serve as a [[one-glider seed]] for the mirrored table. The [[octo3obj database]] contains five other small constellations of common objects, each of which can also be used as a 1G seed for the mirrored table.
 
{| style="margin:auto;width:360px"
|{{EmbedViewer
|rle          = x = 10, y = 9, rule = B3/S23
bo$obo$bobo4b2o$2b2o3b2o$9bo$5bo$4bobo$3bobo$3b2o!
|viewerconfig = #C [[ THEME Book ZOOM 12 X 0 Y -2 AUTOSTART GPS 12 T 0 PAUSE 2 T 28 PAUSE 1 LOOP 29 ]]
|position    = center
|caption      = A 1G seed from the octohash database
}}
|{{EmbedViewer
|rle          = x = 59, y = 27, rule = B3/S23
4b2ob2o42bo$4b2ob2o16b2o23bobo$2o9b3o11b2o23bobo$2o9bo18bo13b3o4bo$6b
2o4bo17bo$5bo2bo15b2o4bo$6b2o16b2o27b3o$32b2o10b2ob2o4bo$32b2o10b2ob2o
5bo$24b2o$24bobo$24bo5$11b2o31bo$11b2o31bo$44bo$11b2o$5b3o3b2o35b2o$
48b2o$2b2o48b2o2b3o$2b2o6b2o40b2o2bo$10bobo34b2o8bo$10bo36b2o3b2o$52b
2o!
|viewerconfig = #C [[ THEME Book ZOOM 8 X 0 Y 0 AUTOSTART GPS 12 T 0 PAUSE 2 T 62 PAUSE 1 LOOP 63 ]]
|position    = center
|caption      = Five 1G seeds from the octo3obj database
}}
|}
|}


==See also==
== Occurrence ==
*[[Beehive and table]]
{{related|List of common still lifes}}
*[[Block on table]]
Mirrored table is the thirtieth most common [[still life]] in [[Achim Flammenkamp's census]], being less common than [[very long ship]] but more common than [[canoe]].<ref>{{citeAchim|accessdate=January 15, 2009}}</ref>
 
It is the 30th [[List of common still lifes|most common still life]] on [[Adam P. Goucher]]'s [[Catagolue]], being less common than [[tub with tail]] but more common than [[dead spark coil]]. It is the 2nd most common still life with 12 cells, being 392 times less common than [[ship-tie]] but 8 times as common as [[block on cap]].<ref>{{citeCatagolueStats|May 5, 2023}}</ref>
 
There are 12 results in the [[octohash database]] (including one collision with two occurrences{{refn|Headerless RLE: {{headerlessRLE|4bo$3bobo$2bobo$2b2o3$b2o$obo$2o2$bo$2o$obo!}}}}), 25 results in the octo3g database, and 191 results in the octo3obj database with this still life occurring in the ash.
 
== See also ==
* [[Beehive on table]]
* [[Block on table]]
 
== 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=12/12-25.rle|nobullet=nobullet}}</ref>


==References==
</references>
<references />


==External links==
== External links ==
{{LinkWeisstein|filename=TableonTable.html}}
* {{LinkCatagolue|xs12_raar}}
{{LinkLexicon|filename=lex_t.htm#tableontable}}
* {{LinkLexicon|filename=lex_t.htm#tableontable}}
{{LinkCatagolue|xs12_raar}}
* {{LinkPentadecathlonObject|12.9}}
{{LinkNiemiec|p1-12.htm|patternname=The 121 twelve-bit still-lifes}}


{{Symmetry|orthogonal4}}
__NOTOC__
__NOTOC__

Latest revision as of 14:34, 9 August 2024

Mirrored table
x = 5, y = 4, rule = B3/S23 2ob2o$bobo$bobo$2ob2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 3 ZOOM 21 HEIGHT 400 SUPPRESS ]] [[ ZOOM 57 ]]
View static image
Pattern type Strict still life
Number of cells 12
Bounding box 5 × 4
Frequency class 16.2
Static symmetry +e (D4_+2)
Discovered by Unknown
Year of discovery Unknown

Mirrored table is a 12-cell still life. It consists of two tables facing each other with one row of dead cells between them.

One of the tables can be moved by two cells to the side, resulting in rotated table.

It is the only 12-cell still life to fit within a 5 × 4 bounding box.

Construction

x = 92, y = 72, rule = B3/S23 81bo$25bo22bo31bo$24bo7bo14bo32b3o$24b3o6b2o12b3o$32b2o$70bobo$56bobo 12b2o$56b2o13bo$57bo$50bo$49b2o15b3o$49bobo16bo$67bo4$bo69b3o$b2o70bo$ obo10b2o57bo$13bobo5b2o$13bo6b2o$22bo2$5bo$6b2o$5b2o4$67b2o2b2o$66bobo b2o$68bo3bo$46bobo$38bo7b2o$39b2o6bo$38b2o2$16bo$15bo$15b3o$19b3o$19bo $20bo$35b2o$36b2o$35bo10b3o$46bo$47bo6$89b3o$89bo$5b2o83bo$6b2o$5bo12$ 35b3o$37bo$36bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THEME Book ZOOM 4 X 0 Y -6 AUTOSTART GPS 12 T 0 PAUSE 3 T 119 PAUSE 2 LOOP 120 ]]
4G syntheses[1][2]
(click above to open LifeViewer)

There are known 4-glider syntheses for a mirrored table; a number of known syntheses can be found in Mark Niemiec's database.[2]

The octohash database contains a constellation of two long boats which can serve as a one-glider seed for the mirrored table. The octo3obj database contains five other small constellations of common objects, each of which can also be used as a 1G seed for the mirrored table.

x = 10, y = 9, rule = B3/S23 bo$obo$bobo4b2o$2b2o3b2o$9bo$5bo$4bobo$3bobo$3b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THEME Book ZOOM 12 X 0 Y -2 AUTOSTART GPS 12 T 0 PAUSE 2 T 28 PAUSE 1 LOOP 29 ]]
A 1G seed from the octohash database
(click above to open LifeViewer)
x = 59, y = 27, rule = B3/S23 4b2ob2o42bo$4b2ob2o16b2o23bobo$2o9b3o11b2o23bobo$2o9bo18bo13b3o4bo$6b 2o4bo17bo$5bo2bo15b2o4bo$6b2o16b2o27b3o$32b2o10b2ob2o4bo$32b2o10b2ob2o 5bo$24b2o$24bobo$24bo5$11b2o31bo$11b2o31bo$44bo$11b2o$5b3o3b2o35b2o$ 48b2o$2b2o48b2o2b3o$2b2o6b2o40b2o2bo$10bobo34b2o8bo$10bo36b2o3b2o$52b 2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THEME Book ZOOM 8 X 0 Y 0 AUTOSTART GPS 12 T 0 PAUSE 2 T 62 PAUSE 1 LOOP 63 ]]
Five 1G seeds from the octo3obj database
(click above to open LifeViewer)

Occurrence

See also: List of common still lifes

Mirrored table is the thirtieth most common still life in Achim Flammenkamp's census, being less common than very long ship but more common than canoe.[3]

It is the 30th most common still life on Adam P. Goucher's Catagolue, being less common than tub with tail but more common than dead spark coil. It is the 2nd most common still life with 12 cells, being 392 times less common than ship-tie but 8 times as common as block on cap.[4]

There are 12 results in the octohash database (including one collision with two occurrences[5]), 25 results in the octo3g database, and 191 results in the octo3obj database with this still life occurring in the ash.

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: 12/12-25.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. ↑ Headerless RLE: 4bo$3bobo$2bobo$2b2o3$b2o$obo$2o2$bo$2o$obo!


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