Pentoad: Difference between revisions

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restore removed information from redirected pages https://conwaylife.com/w/index.php?title=Pentoad_2&oldid=114372 https://conwaylife.com/w/index.php?title=Pentoad_1H2&curid=5749&oldid=114371
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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.


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


==Pentoad 2==
[[goldenratio]] found a {{gliders|10}} [[synthesis]] of this oscillator on September 3, {{year|2020}}.<ref name="post103439" />
'''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]].
 
== Variants ==
=== 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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}}
}}


==Pentoad 1H2==
=== 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.
'''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"? -->


[[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" />
[[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" />
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* [[Biting off more than they can chew]]
* [[Biting off more than they can chew]]
* [[Toad]]
* [[Toad]]
* [[Pentoad 1H2]]
* [[p6 shuttle]]
* [[Smallest period 5 oscillators]]
* [[Smallest period 5 oscillators]]


Revision as of 02:51, 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.

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.[2] 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

goldenratio found a 10-glider synthesis of this oscillator on September 3, 2020.[3]

Variants

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 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 ]]
An fairly common alternate stabilization of pentoad, named 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 ]]
A hybrid version of the two stabilizations, named 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. ↑ Dean Hickerson's oscillator stamp collection. Retrieved on March 14, 2020.
  3. ↑ goldenratio (September 3, 2020). Re: Synthesising Oscillators (discussion thread) at the ConwayLife.com forums
  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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