Merzenich's p31

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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 | 0.98
Kinetic symmetry +e
Discovered by Matthias Merzenich
Year of discovery 2010

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.[1] In terms of its 48 cells, it is currently the smallest known period-31 oscillator. It first appeared semi-naturally on May 11, 2015.[2]

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,[3] which was reduced to 24 gliders by Chris Cain in March 2016.[4] On June 14, 2024, Carson Cheng found a 22-glider synthesis.[5][6]

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°
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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[7]
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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.
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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. The oscillators are shown with visible envelopes, to highlight interactions between subpatterns.

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
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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
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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
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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
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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
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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
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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
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RLE: here Plaintext: here
Catagolue: here


See also

References

  1. ↑ Matthias Merzenich (November 5, 2010). Re: Pattern of the Year 2010 competition (discussion thread) at the ConwayLife.com forums
  2. ↑ gameoflifeboy (May 11, 2015). Re: Soup search results (discussion thread) at the ConwayLife.com forums
  3. ↑ Mark Niemiec (August 13, 2013). Re: Synthesising Oscillators (discussion thread) at the ConwayLife.com forums
  4. ↑ Chris Cain (March 27, 2016). Re: Synthesising Oscillators (discussion thread) at the ConwayLife.com forums
  5. ↑ Carson Cheng (June 13, 2024). Re: Synthesising Oscillators (discussion thread) at the ConwayLife.com forums
  6. ↑ shinjuku (#7101611955) (June 14, 2024). Job triggered by Adam P. Goucher at GitLab Catagolue project.
  7. ↑ David Raucci (April 3, 2021). Re: Oscillator Discussion Thread (discussion thread) at the ConwayLife.com forums

External links


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