Pentoad

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 ]]
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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	.e
Discovered by	Bill Gosper
Year of discovery	1977
Rules Outer-totalistic rules B3/S23 – B378/S023678 # of rules 26 = 64 Isotropic rules B3aijqr/S2-in3ijnr – B2i34-ajn5-ijq6-k78/S0234-jktw5-y678
Glider synthesis Fewest gliders 9 Catagolue-generated RLE synthesis Uploaded synthesis RLE pentoad_synth.rle
Pattern files Plaintext pentoad.cells RLE pentoad.rle
Identifiers apgcode xp5_y4ca23zwgg3226z6221 Pentadecathlon ID 20P5.9

Pentoad (or eater-bound Z-hexomino) 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. On June 25, 2024, Carson Cheng reduced the cost to 9 gliders.

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. 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, which was later improved to 12 gliders by Goldtiger997.

This oscillator first appeared semi-naturally in September 2016.

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]}

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

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.

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.

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.

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

• Biting off more than they can chew
• Toad
• p6 shuttle
• Smallest period 5 oscillators

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