Merzenich's p31

Merzenich's p31
x = 24, y = 13, rule = B3/S23 7b2obo2bob2o$2o4bo2bo4bo2bo4b2o$2o5bobo4bobo5b2o$8bo6bo6$8bo6bo$2o5bob o4bobo5b2o$2o4bo2bo4bo2bo4b2o$7b2obo2bob2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ AUTOSTART ]] #C [[ THUMBSIZE 2 ZOOM 14 GPS 6 LOOP 31 ]]
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Pattern type	Oscillator
Number of cells	48
Bounding box	24 × 21
Period	31
Mod	31
Heat	59.6
Volatility	0.98
Strict volatility	0.98
Discovered by	Matthias Merzenich
Year of discovery	2010
Rules Outer-totalistic rules B3/S23 – B38/S238 # of rules 22 = 4 Isotropic rules B3/S23 – B34et5c6c8/S234c6cei8
Glider synthesis Fewest gliders 24† Catagolue-generated RLE synthesis Uploaded synthesis RLE 48p31_synth.rle †Can be constructed with 15 gliders using the reverse caber tosser universal constructor.
Pattern files Plaintext 48p31.cells RLE 48p31.rle
Identifiers apgcode xp31_ccy04ajaeweaja4y0cczz66y04apaeweapa4y066

Merzenich's p31 (or 48P31) is a period-31 oscillator found by Matthias Merzenich on November 5, 2010, being the first oscillator of this period to be discovered. In terms of its 48 cells, it is currently the smallest known period-31 oscillator. It first appeared semi-naturally on May 11, 2015.

It gives duoplet and domino sparks, the first of which can reflect gliders by 90 degrees, while the second allows for the construction of non-trivial higher-period oscillators as seen in a later section.

Approximately 1 in 4.2 billion D4_+2 soups form a Merzenich's p31.

A 72-glider synthesis was found by Mark Niemiec on August 11, 2013, which was reduced to 24 gliders by Chris Cain in March 2016.

Gallery

x = 35, y = 32, rule = B3/S23 33bo$32bo$32b3o6$26bo$24b2o$25b2o9$7b2obo2bob2o$2o4bo2bo4bo2bo4b2o$2o 5bobo4bobo5b2o$8bo6bo6$8bo6bo$2o5bobo4bobo5b2o$2o4bo2bo4bo2bo4b2o$7b2o bo2bob2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ZOOM 8 GPS 15 ]]

48P31 reflecting gliders 90° (click above to open LifeViewer) RLE: here Plaintext: here

x = 55, y = 26, rule = B3/S23 2b2o7b2o$2b2o7b2o$42b2o7b2o$42b2o7b2o3$2bo9bo$2obo7bob2o$2ob2o5b2ob2o 27bo9bo$3b2o5b2o28b2obo7bob2o$bobo7bobo26b2ob2o5b2ob2o$2bo9bo12bo17b2o 5b2o$2bo9bo10b3o4bo10bobo7bobo$bobo7bobo10bo4b3o10bo9bo$3b2o5b2o17bo 12bo9bo$2ob2o5b2ob2o26bobo7bobo$2obo7bob2o28b2o5b2o$2bo9bo27b2ob2o5b2o b2o$40b2obo7bob2o$42bo9bo3$2b2o7b2o$2b2o7b2o$42b2o7b2o$42b2o7b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ZOOM 8 GPS 15 ]]

Two 48P31s hassling two R-pentominoes, found by David Raucci on April 3, 2021 (click above to open LifeViewer) RLE: here Plaintext: here Catagolue: here

x = 24, y = 25, rule = B3/S23 7bob2o2b2obo$6bo3b4o3bo$2o4bob2ob2ob2obo4b2o$2o5b2o6b2o5b2o8$2o5b2o6b2o5b2o$ 2o4bob2ob2ob2obo4b2o$6bo3b4o3bo$7bob2o2b2obo6$9b6o$9bo4bo$10bo2bo$8bobo2bobo$ 8b2o4b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ZOOM 8 GPS 15 ]]

Merzenith's p31 rephasing a fumarole to form 66P62 – this appears to be a p155 oscillator, but it is not. (click above to open LifeViewer) RLE: here Plaintext: here Catagolue: here

LCM oscillators

The LCM oscillators below are listed due to being the smallest known ones by population, while also satisfying the condition that at least one cell oscillates at the full period.

7b2obo2bob2o$2o4bo2bo4bo2bo4b2o$2o5bobo4bobo5b2o$8bo6bo6$8bo6bo$2o5bob o4bobo5b2o$2o4bo2bo4bo2bo4b2o$7b2obo2bob2o7$12b3o$10bo$10bo4bo$11bo$ 13b2o$14bo$14bo$14bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ HEIGHT 450 THUMBSIZE 2 ZOOM 12 GPS 31 THEME BOOK STARTFROM 93 ]]

p93 with caterer (click above to open LifeViewer) RLE: here Plaintext: here Catagolue: here

10b2o$9bo2bo$8bobobo$8bo2bo$7bo$8bobo6$7b2obo2bob2o$2o4bo2bo4bo2bo4b2o $2o5bobo4bobo5b2o$8bo6bo6$8bo6bo$2o5bobo4bobo5b2o$2o4bo2bo4bo2bo4b2o$ 7b2obo2bob2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ HEIGHT 450 THUMBSIZE 2 ZOOM 12 GPS 31 THEME BOOK STARTFROM 124 ]]

p124 with mold (click above to open LifeViewer) RLE: here Plaintext: here Catagolue: here

x = 24, y = 26, rule = B3/S23 8bo6bo$7b4o2b4o$2o4bo3bo2bo3bo4b2o$2o5bob2o2b2obo5b2o$8bo6bo6$8bo6bo$ 2o5bob2o2b2obo5b2o$2o4bo3bo2bo3bo4b2o$7b4o2b4o$8bo6bo6$7bo2bo$6bob2ob o$7bo2bo$7bo2bo$6bob2obo$7bo2bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ HEIGHT 450 THUMBSIZE 2 ZOOM 12 GPS 31 THEME BOOK STARTFROM 155 ]]

p155 with Octagon 2 (click above to open LifeViewer) Catagolue: here

x = 24, y = 28, rule = B3/S23 8bo6bo$7b4o2b4o$2o4bo3bo2bo3bo4b2o$2o5bob2o2b2obo5b2o$8bo6bo6$8bo6bo$2o5bob2o 2b2obo5b2o$2o4bo3bo2bo3bo4b2o$7b4o2b4o$8bo6bo6$6b2o$6b2o2b2o$4b2obo2b2o$4b3o 3$5b2o$5b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ HEIGHT 450 THUMBSIZE 2 ZOOM 12 GPS 31 THEME BOOK STARTFROM 186 ]]

p186 with unix (click above to open LifeViewer) RLE: here Plaintext: here Catagolue: here

x = 24, y = 24, rule = B3/S23 8bo4bo$6b2ob4ob2o$8bo4bo9$7b2obo2bob2o$2o4bo2bo4bo2bo4b2o$2o5bobo4bobo 5b2o$8bo6bo6$8bo6bo$2o5bobo4bobo5b2o$2o4bo2bo4bo2bo4b2o$7b2obo2bob2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ HEIGHT 450 THUMBSIZE 2 ZOOM 12 GPS 31 THEME BOOK STARTFROM 465 ]]

p465 with pentadecathlon (click above to open LifeViewer) RLE: here Plaintext: here Catagolue: here

x = 24, y = 30, rule = B3/S23 8bo6bo$7b4o2b4o$2o4bo3bo2bo3bo4b2o$2o5bob2o2b2obo5b2o$8bo6bo6$8bo6bo$2o5bob2o 2b2obo5b2o$2o4bo3bo2bo3bo4b2o$7b4o2b4o$8bo6bo7$11b3o2$6b2ob2o$6b2obobo$12bo$ 7bo4bo$7bo4bo$8bo2b2o$11b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ HEIGHT 450 THUMBSIZE 2 ZOOM 12 GPS 31 THEME BOOK STARTFROM 496 ]]

p496 with Rob's p16 (click above to open LifeViewer) RLE: here Plaintext: here Catagolue: here

x = 45, y = 28, rule = B3/S23 33b2o7b2o$33b2o7b2o4$o$3o30bo9bo$3bo28bobo7bobo$2b2o28bo2bo5bo2bo$33b 2o7b2o$32bo11bo2$19bo$b3o3b3o8b2o12bo11bo$17bo15b2o7b2o$5bo12b2o12bo2b o5bo2bo$5bo13bo12bobo7bobo$5bo27bo9bo5$14b2o8b2o7b2o7b2o$14bo2b6o2bo7b 2o7b2o$15b2o6b2o$12b3o10b3o$12bo2bobo4bobo2bo$13b2o4b2o4b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ ZOOM 12 HEIGHT 500 THUMBSIZE 2 THEME BOOK STARTFROM 2356 ]]

p2356 with p76 pi-heptomino hassler (click above to open LifeViewer) RLE: here Plaintext: here Catagolue: here

See also

• 110P62
• 66P62
• p124 lumps of muck hassler
• Raucci's p217

External links

• Merzenich's p31 at Adam P. Goucher's Catagolue