Trans-very long hook with nine: Difference between revisions

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{{Stilllife
{{Stilllife
|name            = Integral with very long hook
|name            = Trans-very long hook with nine
|pname            = integralwithverylonghook
|pname            = transverylonghookwithnine
|c                = 12
|c                = 12
|bx              = 8
|bx              = 8
|by              = 5
|by              = 5
|fc              = 29.5
|fc              = 29.5
|symmetry        = n
|discoverer      = Robert Wainwright
|discoverer2      = Everett Boyer
|discoveryear    = 1973
|rulemin          = B/S23
|rulemin          = B/S23
|rulemax          = B3678/S012345678
|rulemax          = B3678/S012345678
|rulespecial      = [[Conway's Game of Life|Conway Life]], [[HighLife]]
|rulespecial      = [[Conway's Game of Life|Conway Life]], {{rl|HighLife}}
|isorulemin      = B/S23n
|isorulemin      = B/S23n
|isorulemax      = B2ikn34-jnr5-q678/S012345678
|isorulemax      = B2ikn34-jnr5-q678/S012345678
|synthesis        = 6
|synthesis        = 5
|plaintext        = true
|plaintext        = true
|rle              = true
|rle              = true
Line 18: Line 22:
|pentadecathlonid = 12.39
|pentadecathlonid = 12.39
}}
}}
The '''integral with very long hook''' is a {{slcells|12}}-[[cell]] [[still life]].
'''Trans-very long hook with nine''' or '''integral with very long hook'''<ref name="catagolue_object" /> is a {{slcells|12|text=12-cell}} [[still life]].


== [[List of common still lifes|Commonness]] ==
== Construction ==
Among still lifes with 12 cells, this is the 60th most common still life according to [[Catagolue]]. Its position among all still lifes of all populations as a whole, however, is currently unknown.[[Category:Natural periodic objects with commonness requiring clarification]]
A {{gliders|6}} [[Glider synthesis|synthesis]] of this still life was found in March {{year|2021}}.<ref name="post125234" />
A {{gliders|5}} synthesis was found in March 2023.<ref name="j4011864005" />
Several known syntheses can be found in [[Mark Niemiec's database]].<ref name="niemiec" />


== [[Glider synthesis]] ==
{| style="margin:auto;width:300px"
A {{gliders|6}} [[synthesis]] of this still life was found in March {{year|2021}}.<ref name="post125234" />
|{{EmbedViewer
|rle          = x = 39, y = 38, rule = B3/S23
32bo$31bo$31b3o10$7bo$8bo$6b3o6$31b2o$31bobo3b2o$33bo2bobo$33bobo$34bo
3$6b2o$b2o2bobo$obo4bo$2bo5$8b3o$10bo$9bo!
|viewerconfig = #C [[ HEIGHT 430 THEME Book ZOOM 10 AUTOSTART GPS 12 T 0 PAUSE 1 T 20 PAUSE 3 T 77 PAUSE 2 LOOP 78 ]]
|position    = center
|caption      = A 5G synthesis<ref name="j4011864005" />
}}
|-
|{{EmbedViewer
|rle          = x = 84, y = 61, rule = B3/S23
59bo$59bobo$59b2o2$34bo$32bobo$33b2o6$43bo$41bobo$42b2o13bo$56bo$56b3o
15$63b2o$63bobo3b2o$65bo2bobo$65bobo$66bo11$2o$b2o$o10$81b3o$81bo$82bo
!
|viewerconfig = #C [[ HEIGHT 430 THEME Book ZOOM 8 X 0 Y -8 AUTOSTART GPS 12 T 0 PAUSE 1 T 20 PAUSE 3 T 48 PAUSE 1 T 57 PAUSE 1 T 189 PAUSE 1 T 190 PAUSE 2 LOOP 191 ]]
|position    = center
|caption      = A 6G synthesis<ref name="post125234" />
}}
|-
|{{EmbedViewer
|rle          = x = 42, y = 38, rule = B3/S23
2bo$obo$b2o2$26bobo$26b2o$27bo2$bo$2b2o7bo$b2o9bo$10b3o14bobo$27b2o$
28bo5$34b2o$34bobo3b2o$36bo2bobo$36bobo$37bo3$30b3o$30bo$9b3o19bo$11bo
$10bo6$26b2o$26bobo$26bo!
|viewerconfig = #C [[ HEIGHT 430 THEME Book ZOOM 10 AUTOSTART GPS 12 T 0 PAUSE 1 T 20 PAUSE 3 T 29 PAUSE 1 T 51 PAUSE 2 LOOP 52 ]]
|position    = center
|caption      = A 8G synthesis<ref name="niemiec" />
}}
|}
 
== Occurrence ==
{{related|List of common still lifes}}
Among the 121 still lifes with 12 cells, this is the 60th most common still life according to [[Catagolue]].
 
There are no occurrences of this still life in final patterns of collisions in [[Octohash database|octohash]], octo3obj or octo3g databases.
 
== Isomers ==
This still life is comprised of the normally unstable [[very long hook]] with a normally unstable [[nine]] attached. This is one of two possible [[isomer]]s, named [[trans]] due to the corner part of the hook being farther from the nine; the other isomer, [[cis-very long hook with nine]], has this corner part slightly closer.


== See also ==
Unlike the cis-version, the trans-very long hook with nine can be shrunk down to two smaller still lifes: the [[long hook with nine]] and [[hooked integral]]. Due to the trans version being the only one which can be shrunk, these two do not have cis-trans prefixes.
* [[Integral with cis-hook]]
 
It can be [[Substitutive nomenclature|substitutively]] referred to as the ''integral with trans-very long hook'', with one [[pre-block]] of the [[integral sign]] replaced with a very long hook, however "trans-very long hook with nine" is usually preferred for this object.


== References ==
== References ==
<references>
<references>
<ref name="catagolue_object">{{LinkCatagolue|xs12_31eg8426|style=nobullet}}</ref>
<ref name="j4011864005">{{CiteCatagolueJob|job=4011864005|date=March 27, 2023}}</ref>
<ref name="niemiec">{{LinkNiemiec|p1-12.htm|The 121 twelve-bit still-lifes|rle=12/12-40.rle|nobullet=nobullet}}</ref>
<ref name="post125234">{{LinkForumThread
<ref name="post125234">{{LinkForumThread
|format = ref
|format = ref
|p      = 125234
|title  = Re: Still Life Synthesis Thread
|title  = Re: Still Life Synthesis Thread
|p      = 125234
|author = bubblegum
|author = bubblegum
|date  = March 11, 2021
|date  = March 11, 2021
Line 41: Line 88:


== External links ==
== External links ==
{{LinkCatagolue|xs12_31eg8426}}
* {{LinkCatagolue|xs12_31eg8426|patternname=Integral with very long hook}}
{{LinkNiemiec|12/12-40.rle|patternname=12.40}}
* {{LinkPentadecathlonObject|id=12.39|archivedate=20221027111717}}
{{LinkPentadecathlonObject|12.39}}
 
__NOTOC__

Latest revision as of 14:54, 9 August 2024

Trans-very long hook with nine
x = 8, y = 5, rule = B3/S23 4bo$3bobo$obo2bo$2o3bobo$6b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 3 ZOOM 21 HEIGHT 400 SUPPRESS ]]
View static image
Pattern type Strict still life
Number of cells 12
Bounding box 8 × 5
Frequency class 29.5
Static symmetry n (C1)
Discovered by Robert Wainwright
Everett Boyer
Year of discovery 1973

Trans-very long hook with nine or integral with very long hook[1] is a 12-cell still life.

Construction

A 6-glider synthesis of this still life was found in March 2021.[2] A 5-glider synthesis was found in March 2023.[3] Several known syntheses can be found in Mark Niemiec's database.[4]

x = 39, y = 38, rule = B3/S23 32bo$31bo$31b3o10$7bo$8bo$6b3o6$31b2o$31bobo3b2o$33bo2bobo$33bobo$34bo 3$6b2o$b2o2bobo$obo4bo$2bo5$8b3o$10bo$9bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ HEIGHT 430 THEME Book ZOOM 10 AUTOSTART GPS 12 T 0 PAUSE 1 T 20 PAUSE 3 T 77 PAUSE 2 LOOP 78 ]]
A 5G synthesis[3]
(click above to open LifeViewer)
x = 84, y = 61, rule = B3/S23 59bo$59bobo$59b2o2$34bo$32bobo$33b2o6$43bo$41bobo$42b2o13bo$56bo$56b3o 15$63b2o$63bobo3b2o$65bo2bobo$65bobo$66bo11$2o$b2o$o10$81b3o$81bo$82bo ! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ HEIGHT 430 THEME Book ZOOM 8 X 0 Y -8 AUTOSTART GPS 12 T 0 PAUSE 1 T 20 PAUSE 3 T 48 PAUSE 1 T 57 PAUSE 1 T 189 PAUSE 1 T 190 PAUSE 2 LOOP 191 ]]
A 6G synthesis[2]
(click above to open LifeViewer)
x = 42, y = 38, rule = B3/S23 2bo$obo$b2o2$26bobo$26b2o$27bo2$bo$2b2o7bo$b2o9bo$10b3o14bobo$27b2o$ 28bo5$34b2o$34bobo3b2o$36bo2bobo$36bobo$37bo3$30b3o$30bo$9b3o19bo$11bo $10bo6$26b2o$26bobo$26bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ HEIGHT 430 THEME Book ZOOM 10 AUTOSTART GPS 12 T 0 PAUSE 1 T 20 PAUSE 3 T 29 PAUSE 1 T 51 PAUSE 2 LOOP 52 ]]
A 8G synthesis[4]
(click above to open LifeViewer)

Occurrence

See also: List of common still lifes

Among the 121 still lifes with 12 cells, this is the 60th most common still life according to Catagolue.

There are no occurrences of this still life in final patterns of collisions in octohash, octo3obj or octo3g databases.

Isomers

This still life is comprised of the normally unstable very long hook with a normally unstable nine attached. This is one of two possible isomers, named trans due to the corner part of the hook being farther from the nine; the other isomer, cis-very long hook with nine, has this corner part slightly closer.

Unlike the cis-version, the trans-very long hook with nine can be shrunk down to two smaller still lifes: the long hook with nine and hooked integral. Due to the trans version being the only one which can be shrunk, these two do not have cis-trans prefixes.

It can be substitutively referred to as the integral with trans-very long hook, with one pre-block of the integral sign replaced with a very long hook, however "trans-very long hook with nine" is usually preferred for this object.

References

  1. ↑ xs12_31eg8426 at Adam P. Goucher's Catagolue
  2. ↑ 2.0 2.1 bubblegum (March 11, 2021). Re: Still Life Synthesis Thread (discussion thread) at the ConwayLife.com forums
  3. ↑ 3.0 3.1 shinjuku (#4011864005) (March 27, 2023). Job triggered by Adam P. Goucher at GitLab Catagolue project.
  4. ↑ 4.0 4.1 The 121 twelve-bit still-lifes at Mark D. Niemiec's Life Page (download pattern file: 12/12-40.rle)


Retrieved from "https://conwaylife.com/w/index.php?title=Trans-very_long_hook_with_nine&oldid=152912"