Pentoad: Difference between revisions
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'''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. | '''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. | ||
[[goldenratio]] found a {{gliders|10}} [[synthesis]] of this oscillator on September 3, {{year|2020}}.<ref name="post103439" /> | [[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"/> | ||
== Variants == | == Variants == | ||
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==References== | ==References== | ||
<references> | <references> | ||
<ref name="j7184066944">{{CiteCatagolueJob|job=7184066944|date=June 25, 2024}}</ref> | |||
<ref name="post103439">{{LinkForumThread | <ref name="post103439">{{LinkForumThread | ||
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|author = Dongook Lee | |author = Dongook Lee | ||
|date = August 31, 2022 | |date = August 31, 2022 | ||
}}</ref> | |||
<ref name="post188470">{{LinkForumThread | |||
|format = ref | |||
|title = Re: Oscillator Discussion Thread | |||
|p = 188470 | |||
|author = Carson Cheng | |||
|date = June 25, 2024 | |||
}}</ref> | }}</ref> | ||
</references> | </references> | ||
Revision as of 14:10, 26 June 2024
| Pentoad | |||||||||
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| 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 | ||||||||
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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.
| 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]
| 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]
| pentoad 1H2 (click above to open LifeViewer) RLE: here Plaintext: here Catagolue: here |
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.[12]
| 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. The resulting oscillator has 42 alive cells.
| (click above to open LifeViewer) Catagolue: here |
See also
References
- ↑ "Eater-bound Z-hexomino". The Life Lexicon. Stephen Silver.
- ↑ goldenratio (September 3, 2020). Re: Synthesising Oscillators (discussion thread) at the ConwayLife.com forums
- ↑ Carson Cheng (June 25, 2024). Re: Oscillator Discussion Thread (discussion thread) at the ConwayLife.com forums
- ↑ shinjuku (#7184066944) (June 25, 2024). Job triggered by Adam P. Goucher at GitLab Catagolue project.
- ↑ Dean Hickerson's oscillator stamp collection. Retrieved on March 14, 2020.
- ↑ Jeremy Tan (March 19, 2019). Re: Synthesising Oscillators (discussion thread) at the ConwayLife.com forums
- ↑ Goldtiger997 (April 1, 2019). Re: Synthesising Oscillators (discussion thread) at the ConwayLife.com forums
- ↑ Apple Bottom (September 11, 2016). Re: Soup search results (discussion thread) at the ConwayLife.com forums
- ↑ https://conwaylife.com/w/index.php?title=Pentoad_1H2&oldid=14800
- ↑ Mark Niemiec (August 31, 2013). Re: Synthesising Oscillators (discussion thread) at the ConwayLife.com forums
- ↑ MathAndCode (January 17, 2021). Re: Synthesising Oscillators (discussion thread) at the ConwayLife.com forums
- ↑ Dongook Lee (August 31, 2022). Re: Oscillator Discussion Thread (discussion thread) at the ConwayLife.com forums
External links
- Pentoad at the Life Lexicon
- Pentoad at Adam P. Goucher's Catagolue
- 20P5.9 at Heinrich Koenig's Game of Life Object Catalogs
- Pentoad 2 at Adam P. Goucher's Catagolue
- Pentoad 2 at Heinrich Koenig's Game of Life Object Catalogs
- Pentoad 1H2 at Adam P. Goucher's Catagolue
- Pentoad 1H2 at Heinrich Koenig's Game of Life Object Catalogs
- Patterns
- Oscillators with 20 cells
- Periodic objects with minimum population 20
- Patterns with 20 cells
- Patterns found by Bill Gosper
- Patterns found in 1977
- Patterns that can be constructed with 9 gliders
- Oscillators
- Oscillators with period 5
- Oscillators with mod 5
- Oscillators with heat 8
- Oscillators with volatility 0.65
- Oscillators with strict volatility 0.65
- Patterns with 180-degree rotation symmetry
- Semi-natural periodic objects