Pentoad: Difference between revisions

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Line 9: Line 9:
|h                = 8.8
|h                = 8.8
|v                = 0.65
|v                = 0.65
|symmetry        = .e
|discoverer      = Bill Gosper
|discoverer      = Bill Gosper
|discoveryear    = 1977
|discoveryear    = 1977
Line 16: Line 17:
|isorulemin      = B3aijqr/S2-in3ijnr
|isorulemin      = B3aijqr/S2-in3ijnr
|isorulemax      = B2i34-ajn5-ijq6-k78/S0234-jktw5-y678
|isorulemax      = B2i34-ajn5-ijq6-k78/S0234-jktw5-y678
|synthesis        = 12
|synthesis        = 9
|synthesisRLE    = true
|synthesisRLE    = true
|plaintext        = true
|plaintext        = true
Line 23: Line 24:
|apgcode          = xp5_y4ca23zwgg3226z6221
|apgcode          = xp5_y4ca23zwgg3226z6221
|pentadecathlonid = 20P5.9
|pentadecathlonid = 20P5.9
|viewerconfig    = #C [[ GPS 2 ZOOM 16 LOOP 5 ]]
}}
}}
'''Pentoad''' (or '''eater-bound Z-hexomino'''<ref>{{cite web|url=http://codercontest.com/mniemiec/20et2z.rle|title=Eater-bound Z-hexomino glider synthesis RLE file|author=Mark D. Niemiec|accessdate=April 28, 2009}}</ref>) is a [[period]] [[:Category:Oscillators with period 5|5]] [[oscillator]] that was found by [[:Category:Patterns found by Bill Gosper|Bill Gosper]] in June [[:Category:Patterns found in 1977|1977]]. It consists of a [[Z-hexomino]] that is stabilized by two [[eater 1]]s.
'''Pentoad''' (or '''eater-bound Z-hexomino'''<ref>{{CiteLexicon|file=lex_e.htm#eaterboundzhexomino|name=Eater-bound Z-hexomino}}</ref>) is a {{period|5}} [[oscillator]] that was found by [[Bill Gosper]] in June {{year|1977}}. It consists of a [[Z-hexomino]] that is stabilized by two [[eater 1]]s.


It was discovered by Scott Kim that this oscillator is extensible by moving one of the eaters diagonally away by four [[cell]]s and inserting another Z-hexomino in the gap. A pentoad constructed in this way with n Z-hexominoes has 14 + 6n cells and [[heat]] 8.8 + 6.4n. The pentoad with two Z-hexominoes is shown below.
[[goldenratio]] found a {{gliders|10}} [[synthesis]] of this oscillator on September 3, {{year|2020}}.<ref name="post103439" /> On June 25, {{year|2024}}, [[Carson Cheng]] reduced the cost to {{gliders|9|text=9 gliders}}.<ref name="post188470"/><ref name="j7184066944"/>


==Image gallery==
== Variants ==
{|
=== Extension ===
|-
It was discovered by Scott Kim that this oscillator is [[extensible]] by moving one of the eaters diagonally away by four [[cell]]s and inserting another Z-hexomino in the gap.<ref>{{CiteHickersonOscillators|accessdate=March 14, 2020}}</ref> A pentoad constructed in this way with n Z-hexominoes has 14 + 6n cells and [[heat]] 8.8 + 6.4n. The pentoad with two Z-hexominoes is shown below.
|[[File:Pentoad with two hexominoes.png|framed|left|The pentoad with two Z-hexominoes.<br />{{JavaRLE|pentoadwithtwohexominoes}}]]
|}


==See also==
{{EmbedViewer
*[[Biting off more than they can chew]]
|pname = pentoadwithtwohexominoes
*[[Toad]]
|position    = center
*[[Period_5_oscillators#Smallest|Smallest period five oscillators]]
|viewerconfig = #C [[ THUMBSIZE 2 GPS 2 AUTOSTART ]]
|caption      = Double Pentoad (with two Z-hexominoes)
|style        = width:320px;
|apgcode      = xp5_y8ca23zy0gx3226zw8o1113z311
}}
 
=== Pentoad 2 ===
'''Pentoad 2''' is a {{period|5}} [[oscillator]] that hassles a Z-hexomino with pairs of a [[block]] and a [[century]] predecessor instead of eaters.
 
It is shown as the second pattern in the sixth row of Jason Summers' main period 5 collection.  It is extensible as well.
 
A {{gliders|16}} [[Glider synthesis|synthesis]] was found by [[Jeremy Tan]] on March 19, {{year|2019}},<ref name="post73454" /> which was later improved to {{gliders|12|text=12 gliders}} by [[Goldtiger997]].<ref name="post74280" />
 
This oscillator first appeared [[semi-natural]]ly in September {{year|2016}}.<ref name="post35579" />
{{EmbedViewer
|pname        = pentoad2
|position    = center
|viewerconfig = #C [[ THUMBSIZE 2 GPS 2 AUTOSTART ]]
|caption      = '''Pentoad 2'''
|apgcode      = xp5_0jrz3210o88czy5e53zy533
}}
 
=== Pentoad 1H2 ===
'''Pentoad 1H2''' is a period-5 [[oscillator]] that is a hybrid of pentoad and pentoad 2.  It is extensible in a similar manner.  The '1' and '2' in the name refer to the types of pentoad ends in the pattern.  The 'H' refers to the one hexomino in middle.{{citation needed}}<!-- Not "hybrid"? --><ref>https://conwaylife.com/w/index.php?title=Pentoad_1H2&oldid=14800 </ref>
 
[[Mark Niemiec]] found a {{gliders|19}} [[synthesis]] for this oscillator on August 29, {{year|2013}},<ref name="post8907" /> which [[MathAndCode]] improved to {{gliders|13|text=13 gliders}} on January 17, {{year|2021}}.<ref name="post119427" />
{{EmbedViewer
|pname = pentoad1h2
|viewerconfig = #C [[ THUMBSIZE 2 GPS 2 AUTOSTART ]]
|position    = center
|caption      = '''Pentoad 1H2'''
|apgcode      = xp5_0jrz3210o88czy46a8o
}}
On May 15, {{year|2024}}, Carson Cheng found a 7-glider synthesis for a 'fast component' containing the Z-hexomino and one eater, enabling the double pentoad to be synthesised in {{gliders|14|text=14 gliders}} and the 1H2 in {{gliders|12|text=12 gliders}}.<ref name="post185252" />
 
==== Use as component ====
The pentoad 1H2 reaction can also support an oscillator in place of its block, which is the basis of an unnamed 61-cell low-clearance [[heavyweight volcano]] variant by [[Dongook Lee]].<ref name="post150403" />
{{EmbedViewer
|rle          = x = 20, y = 18, rule = B3/S23
15b2o$15bo$12b2obo2b2o$12bo2bobobo$14b2obo$17bo$8b2o4bob2o$8bobo2bo2b2o$9b3obo2b2o$14bob2o$5b2o10bo$6bo7b2obo$6bo5bo2bobobo$6b2o4b2obo2b2o$2b2o11bo$bobo11b2o$bo$2o!
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 12 GPS 2 AUTOSTART ]]
|position    = center
|caption      = Pentoad 1H2 supporting volcano
|apgcode      = xp5_32aczy07147gg8ozy0c4og5w4go4czw31pl5cpttpc5lp13
|style = width:320px;
}}
 
=== Fumarole stabilisation ===
A [[heavyweight volcano]] is not necessary; the [[fumarole]]'s domino spark suffices to stabilise the Z-hexomino.
{{EmbedViewer
|rle          = x = 19, y = 8, rule = B3/S23
2o15b2o$o2b2o9b2o2bo$b2obo3b2o4bob2o$5bo3bo3bo$5bo3bo3bo$b2obo4b2o3bob2o$o2b2o9b2o2bo$2o15b2o!
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 12 GPS 2 AUTOSTART ]]
|position    = center
|caption      = The resulting oscillator has {{cells|42|text=42 alive cells}}.
|apgcode      = xp5_3pmwmp3zwghhoz0gh88ggzc96w69c
|style = width:320px;
}}
 
=== Two pentoads [[Biting off more than they can chew|hassling pond]] ===
This variant occurred seminaturally, in {{cata|attribute/xp5_178cwggzy147wo8k8zy611o88czyc6a8o/b3s23/D4_x1|a D4_x1 soup}} submitted by [[Charity Engine]] on March 29, 2024.<ref>{{cata|attribute/xp5_178cwggzy147wo8k8zy611o88czyc6a8o/b3s23/D4_x1|the attribute page}}</ref>
{{EmbedViewer
|rle          = x = 20, y = 20, rule = B3/S23
19bo$17b3o$16bo$16b2o2$12bo$12b4o$15bo2$10b2o$9bobo$9b2obo$5b2o4bo$6bo$6bo$6b2o$2b2o$bobo$bo$2o!
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 12 GPS 2 AUTOSTART ]]
|position    = center
|caption      =
|apgcode      = xp5_178cwggzy147wo8k8zy611o88czyc6a8o
|style = width:320px;
}}
 
== See also ==
* [[Biting off more than they can chew]]
* [[Toad]]
* [[p6 shuttle]]
* [[Smallest period 5 oscillators]]


==References==
== References ==
<references />
<references>
<ref name="j7184066944">{{CiteCatagolueJob|job=7184066944|date=June 25, 2024}}</ref>
<ref name="post103439">{{LinkForumThread
|format = ref
|title  = Re: Synthesising Oscillators
|p      = 103439
|author = goldenratio
|date  = September 3, 2020
}}</ref>
<ref name="post35579">{{LinkForumThread
|format = ref
|title  = Re: Soup search results
|p      = 35579
|author = Apple Bottom
|date  = September 11, 2016
}}</ref>
<ref name="post73454">{{LinkForumThread
|format = ref
|title  = Re: Synthesising Oscillators
|p      = 73454
|author = Jeremy Tan
|date  = March 19, 2019
}}</ref>
<ref name="post74280">{{LinkForumThread
|format = ref
|title  = Re: Synthesising Oscillators
|p      = 74280
|author = Goldtiger997
|date  = April 1, 2019
}}</ref>
<ref name="post8907">{{LinkForumThread
|format = ref
|title  = Re: Synthesising Oscillators
|p      = 8907
|author = Mark Niemiec
|date  = August 31, 2013
}}</ref>
<ref name="post119427">{{LinkForumThread
|format = ref
|title  = Re: Synthesising Oscillators
|p      = 119427
|author = MathAndCode
|date  = January 17, 2021
}}</ref>
<ref name="post150403">{{LinkForumThread
|format = ref
|title  = Re: Oscillator Discussion Thread
|p      = 150403
|author = Dongook Lee
|date  = August 31, 2022
}}</ref>
<ref name="post185252">{{LinkForumThread
|format = ref
|p      = 185252
|title  = Re: Synthesising oscillators
|author = Carson Cheng
|date  = May 18, 2024
}}</ref>
<ref name="post188470">{{LinkForumThread
|format = ref
|title  = Re: Oscillator Discussion Thread
|p      = 188470
|author = Carson Cheng
|date  = June 25, 2024
}}</ref>
</references>


==External links==
== External links ==
{{LinkWeisstein|filename=Pentoad.html}}
* {{LinkLexicon|filename=lex_p.htm#pentoad}}
{{LinkLexicon|filename=lex_p.htm#pentoad}}
* {{LinkCatagolue|xp5_y4ca23zwgg3226z6221}}
{{LinkCatagolue|xp5_y4ca23zwgg3226z6221}}
* {{LinkPentadecathlonObject|20P5.9}}
{{LinkPentadecathlonObject|20P5.9}}
* {{LinkCatagolue|xp5_0jrz3210o88czy5e53zy533|patternname=Pentoad 2}}
* {{LinkPentadecathlonObject|26P5.2|patternname=Pentoad 2}}
* {{LinkCatagolue|xp5_0jrz3210o88czy46a8o|patternname=Pentoad 1H2}}
* {{LinkPentadecathlonObject|23P5.1|patternname=Pentoad 1H2}}


{{Symmetry|180degree}}
{{seminatural}}
{{seminatural}}
__NOTOC__
__NOTOC__

Latest revision as of 18:47, 6 August 2024

Pentoad
x = 13, y = 12, rule = B3/S23 11b2o$11bo$9bobo$9b2o$5b2o$6bo$6bo$6b2o$2b2o$bobo$bo$2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ AUTOSTART ]] #C [[ GPS 2 ZOOM 16 LOOP 5 ]]
View animated image
View static image
Pattern type Oscillator
Number of cells 20
Bounding box 13 × 12
Period 5 (mod: 5)
Heat 8.8
Volatility 0.65 | 0.65
Kinetic symmetry .e
Discovered by Bill Gosper
Year of discovery 1977

Pentoad (or eater-bound Z-hexomino[1]) is a period-5 oscillator that was found by Bill Gosper in June 1977. It consists of a Z-hexomino that is stabilized by two eater 1s.

goldenratio found a 10-glider synthesis of this oscillator on September 3, 2020.[2] On June 25, 2024, Carson Cheng reduced the cost to 9 gliders.[3][4]

Variants

Extension

It was discovered by Scott Kim that this oscillator is extensible by moving one of the eaters diagonally away by four cells and inserting another Z-hexomino in the gap.[5] A pentoad constructed in this way with n Z-hexominoes has 14 + 6n cells and heat 8.8 + 6.4n. The pentoad with two Z-hexominoes is shown below.

x = 17, y = 16, rule = b3/s23 15b2o$15bob$13bobob$13b2o2b$9b2o6b$10bo6b$10bo6b$10b2o5b$5b2o10b$6bo 10b$6bo10b$6b2o9b$2b2o13b$bobo13b$bo15b$2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 GPS 2 AUTOSTART ]]
Double Pentoad (with two Z-hexominoes)
(click above to open LifeViewer)
RLE: here Plaintext: here
Catagolue: here

Pentoad 2

Pentoad 2 is a period-5 oscillator that hassles a Z-hexomino with pairs of a block and a century predecessor instead of eaters.

It is shown as the second pattern in the sixth row of Jason Summers' main period 5 collection. It is extensible as well.

A 16-glider synthesis was found by Jeremy Tan on March 19, 2019,[6] which was later improved to 12 gliders by Goldtiger997.[7]

This oscillator first appeared semi-naturally in September 2016.[8]

x = 17, y = 12, rule = B3/S23 10b2o$10bobo2b2o$11b3ob2o2$7b2o$8bo$8bo$8b2o2$2ob3o$2o2bobo$5b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 GPS 2 AUTOSTART ]]
Pentoad 2
(click above to open LifeViewer)
RLE: here Plaintext: here
Catagolue: here

Pentoad 1H2

Pentoad 1H2 is a period-5 oscillator that is a hybrid of pentoad and pentoad 2. It is extensible in a similar manner. The '1' and '2' in the name refer to the types of pentoad ends in the pattern. The 'H' refers to the one hexomino in middle.[citation needed][9]

Mark Niemiec found a 19-glider synthesis for this oscillator on August 29, 2013,[10] which MathAndCode improved to 13 gliders on January 17, 2021.[11]

x = 15, y = 12, rule = B3/S23 8b2o$8bobo2b2o$9b3ob2o2$5b2o$6bo$6bo$6b2o$2b2o$bobo$bo$2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 GPS 2 AUTOSTART ]]
Pentoad 1H2
(click above to open LifeViewer)
RLE: here Plaintext: here
Catagolue: here

On May 15, 2024, Carson Cheng found a 7-glider synthesis for a 'fast component' containing the Z-hexomino and one eater, enabling the double pentoad to be synthesised in 14 gliders and the 1H2 in 12 gliders.[12]

Use as component

The pentoad 1H2 reaction can also support an oscillator in place of its block, which is the basis of an unnamed 61-cell low-clearance heavyweight volcano variant by Dongook Lee.[13]

x = 20, y = 18, rule = B3/S23 15b2o$15bo$12b2obo2b2o$12bo2bobobo$14b2obo$17bo$8b2o4bob2o$8bobo2bo2b2o$9b3obo2b2o$14bob2o$5b2o10bo$6bo7b2obo$6bo5bo2bobobo$6b2o4b2obo2b2o$2b2o11bo$bobo11b2o$bo$2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ZOOM 12 GPS 2 AUTOSTART ]]
Pentoad 1H2 supporting volcano
(click above to open LifeViewer)
Catagolue: here

Fumarole stabilisation

A heavyweight volcano is not necessary; the fumarole's domino spark suffices to stabilise the Z-hexomino.

x = 19, y = 8, rule = B3/S23 2o15b2o$o2b2o9b2o2bo$b2obo3b2o4bob2o$5bo3bo3bo$5bo3bo3bo$b2obo4b2o3bob2o$o2b2o9b2o2bo$2o15b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ZOOM 12 GPS 2 AUTOSTART ]]
The resulting oscillator has 42 alive cells.
(click above to open LifeViewer)
Catagolue: here

Two pentoads hassling pond

This variant occurred seminaturally, in a D4_x1 soup submitted by Charity Engine on March 29, 2024.[14]

x = 20, y = 20, rule = B3/S23 19bo$17b3o$16bo$16b2o2$12bo$12b4o$15bo2$10b2o$9bobo$9b2obo$5b2o4bo$6bo$6bo$6b2o$2b2o$bobo$bo$2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ZOOM 12 GPS 2 AUTOSTART ]]
(click above to open LifeViewer)
Catagolue: here

See also

References

  1. ↑ "Eater-bound Z-hexomino". The Life Lexicon. Stephen Silver.
  2. ↑ goldenratio (September 3, 2020). Re: Synthesising Oscillators (discussion thread) at the ConwayLife.com forums
  3. ↑ Carson Cheng (June 25, 2024). Re: Oscillator Discussion Thread (discussion thread) at the ConwayLife.com forums
  4. ↑ shinjuku (#7184066944) (June 25, 2024). Job triggered by Adam P. Goucher at GitLab Catagolue project.
  5. ↑ Dean Hickerson's oscillator stamp collection. Retrieved on March 14, 2020.
  6. ↑ Jeremy Tan (March 19, 2019). Re: Synthesising Oscillators (discussion thread) at the ConwayLife.com forums
  7. ↑ Goldtiger997 (April 1, 2019). Re: Synthesising Oscillators (discussion thread) at the ConwayLife.com forums
  8. ↑ Apple Bottom (September 11, 2016). Re: Soup search results (discussion thread) at the ConwayLife.com forums
  9. ↑ https://conwaylife.com/w/index.php?title=Pentoad_1H2&oldid=14800
  10. ↑ Mark Niemiec (August 31, 2013). Re: Synthesising Oscillators (discussion thread) at the ConwayLife.com forums
  11. ↑ MathAndCode (January 17, 2021). Re: Synthesising Oscillators (discussion thread) at the ConwayLife.com forums
  12. ↑ Carson Cheng (May 18, 2024). Re: Synthesising oscillators (discussion thread) at the ConwayLife.com forums
  13. ↑ Dongook Lee (August 31, 2022). Re: Oscillator Discussion Thread (discussion thread) at the ConwayLife.com forums
  14. ↑ the attribute page
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