Pentoad

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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 ]]
Pattern type Oscillator
Number of cells 20
Bounding box 13 × 12
Period 5
Mod 5
Heat 8.8
Volatility 0.65
Strict volatility 0.65
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
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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 = 12, y = 17, rule = B3/S23 b2o$b2o3$b3o$o$o$bo4b2o$3bo4bo$4b2o4bo$11bo$11bo$8b3o3$9b2o$9b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 GPS 2 AUTOSTART ]]
pentoad 2
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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][7]

Mark Niemiec found a 19-glider synthesis for this oscillator on August 29, 2013,[8] which MathAndCode improved to 13 gliders on January 17, 2021.[9]

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
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RLE: here Plaintext: 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.[10]

x = 18, y = 21, rule = B3/S23 9b2o$4b2obo4bob2o$4bo10bo$5b3o4b3o$2bo14bo$2b5ob4ob5o$8b4o$4bobo6bobo$ 4b2o8b2o2$8b2o$8b2obo$7b5o$5b3o$3b2o2b2o$4b3o$3b2o$2b2o$3bo$3o$o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ZOOM 12 GPS 2 AUTOSTART ]]
pentoad 1H2 supporting volcano
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Catagoluehere

Fumarole stabilisation

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

x = 8, y = 19, rule = B3/S23 2o4b2o$obo2bobo$2bo2bo$bo4bo$b2o2b2o$3b2o3$5bo$2b4o$2bo3$3b2o$b2o2b2o$bo4bo$2bo2bo$obo2bobo$2o4b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ZOOM 12 GPS 2 AUTOSTART ]]
(click above to open LifeViewer)
Catagoluehere

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. 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. https://conwaylife.com/w/index.php?title=Pentoad_1H2&oldid=14800
  8. Mark Niemiec (August 31, 2013). Re: Synthesising Oscillators (discussion thread) at the ConwayLife.com forums
  9. MathAndCode (January 17, 2021). Re: Synthesising Oscillators (discussion thread) at the ConwayLife.com forums
  10. Dongook Lee (August 31, 2022). Re: Oscillator Discussion Thread (discussion thread) at the ConwayLife.com forums

External links