Pentoad: Difference between revisions

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'''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|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.
'''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|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.


[[goldenratio]] found a {{gliders|10}} [[synthesis]] of this oscillator on September 3, {{year|2020}}.<ref name="post103439" />
== 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.
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.


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}}
}}


[[goldenratio]] found a {{gliders|10}} [[synthesis]] of this oscillator on September 3, {{year|2020}}.<ref name="post103439" />
=== 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.


== Variants ==
It is shown as the second pattern in the sixth row of Jason Summers' main period 5 collection.  It is extensible as well.
=== Pentoad 2 ===
'''Pentoad 2''' is a {{period|5}} [[oscillator]] that is shown as the second pattern in the sixth row of Jason Summers' main period 5 collection.  It is extensible.  The central part is the same as in pentoad.


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" />
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" />
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|position    = center
|position    = center
|viewerconfig = #C [[ THUMBSIZE 2 GPS 2 AUTOSTART ]]
|viewerconfig = #C [[ THUMBSIZE 2 GPS 2 AUTOSTART ]]
|caption      = An fairly common alternate stabilization of pentoad, named '''pentoad 2'''<br />
|caption      = '''pentoad 2'''
}}
}}


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|viewerconfig = #C [[ THUMBSIZE 2 GPS 2 AUTOSTART ]]
|viewerconfig = #C [[ THUMBSIZE 2 GPS 2 AUTOSTART ]]
|position    = center
|position    = center
|caption      = A hybrid version of the two stabilizations, named '''pentoad 1H2'''
|caption      = '''pentoad 1H2'''
}}
}}


Revision as of 03:03, 27 August 2022

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 Unspecified
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]

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.[3] 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 ]]
Pentoad with two Z-hexominoes

(click above to open LifeViewer)
RLE: here Plaintext: 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,[4] which was later improved to 12 gliders by Goldtiger997.[5]

This oscillator first appeared semi-naturally in September 2016.[6]

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

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]

Mark Niemiec found a 19-glider synthesis for this oscillator on August 29, 2013,[7] which MathAndCode improved to 13 gliders on January 17, 2021.[8]

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

See also

References

  1. ↑ Mark D. Niemiec. "Eater-bound Z-hexomino glider synthesis RLE file". Retrieved on April 28, 2009.
  2. ↑ goldenratio (September 3, 2020). Re: Synthesising Oscillators (discussion thread) at the ConwayLife.com forums
  3. ↑ Dean Hickerson's oscillator stamp collection. Retrieved on March 14, 2020.
  4. ↑ Jeremy Tan (March 19, 2019). Re: Synthesising Oscillators (discussion thread) at the ConwayLife.com forums
  5. ↑ Goldtiger997 (April 1, 2019). Re: Synthesising Oscillators (discussion thread) at the ConwayLife.com forums
  6. ↑ Apple Bottom (September 11, 2016). Re: Soup search results (discussion thread) at the ConwayLife.com forums
  7. ↑ Mark Niemiec (August 31, 2013). Re: Synthesising Oscillators (discussion thread) at the ConwayLife.com forums
  8. ↑ MathAndCode (January 17, 2021). Re: Synthesising Oscillators (discussion thread) at the ConwayLife.com forums
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