Beluchenko's p51

Beluchenko's p51
x = 31, y = 31, rule = B3/S23 3b2o21b2o$3b2o21b2o2$2o27b2o$2o5bo2b3o5b3o2bo5b2o$6b3ob3o5b3ob3o$5bo2bo13bo2b o$4b2o19b2o$5b2o17b2o2$4b2o19b2o$4b2o19b2o$4b2o19b2o6$4b2o19b2o$4b2o19b2o$4b 2o19b2o2$5b2o17b2o$4b2o19b2o$5bo2bo13bo2bo$6b3ob3o5b3ob3o$2o5bo2b3o5b3o2bo5b 2o$2o27b2o2$3b2o21b2o$3b2o21b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ AUTOSTART ]] #C [[ LOOP 51 GPS 25 THUMBSIZE 2 ZOOM 10 HEIGHT 480 ]]
View animated image
View static image
Pattern type	Oscillator
Number of cells	112
Bounding box	41 × 41
Period	51 (mod: 51)
Heat	154.0
Volatility	0.98 | 0.98
Kinetic symmetry	*c
Discovered by	Nicolay Beluchenko
Year of discovery	2009
Rules Outer-totalistic rules B3/S23 – B38/S23 # of rules 21 = 2 Isotropic rules B3/S23 – B38/S234c6i
Glider synthesis Fewest gliders 43† Catagolue-generated RLE synthesis Uploaded synthesis RLE beluchenkosp51_synth.rle †Can be constructed with 15 gliders using the reverse caber tosser universal constructor.
Pattern files Plaintext beluchenkosp51.cells RLE beluchenkosp51.rle
Identifiers apgcode xp51_oo033wgwgggy1gggwgw330oozy04e9130111y11110319e4zy077yf77zy0ooyfoozy09t40gy9g04t9z660gg01310333y133301310gg066zx11yh11 Niemiec ID 112p51-1 Pentadecathlon ID 112P51.1

Beluchenko's p51 (or 112P51) is a period-51 oscillator that was discovered by Nicolay Beluchenko on February 17, 2009. It was the first non-trivial period 51 oscillator to be found, all previously known period 51 oscillators being made up of disjoint period-3 and period-17 oscillators. It can be extended diagonally by making copies of itself share two blocks as shown below.

Beluchenko's p51 first appeared on Catagolue in March 2015. About 1 in 2.9 billion eightfold symmetric soups with odd symmetry (D8_1) form a Beluchenko's p51.

A 76-glider synthesis of this oscillator was found by Jason Summers and Matthias Merzenich on April 20, 2010. This was improved to 43 gliders by Chris Cain on January 5, 2020.

On November 8, 2018, 2718281828 found that two p51s can hassle a beehive, creating a p102.

Gallery

x = 64, y = 64, rule = B3/S23 15b2o3b2o3$6b2o21b2o$6b2o21b2o2$3b2o27b2o$3b2o9b2o5b2o9b2o$9b3ob2o7b2o b3o$8bobo15bobo$8b2o17b2o$8bo19bo2$8bo19bo$7b2o19b2o$o6bo21bo6bo$o35bo 4$o35bo$o6bo21bo6bo$7b2o19b2o$8bo19bo2$8bo19bo10bo9bo$8b2o17b2o10b2o7b 2o$8bobo15bobo8b5o5b5o$9b3ob2o7b2ob3o14bo3bo$3b2o9b2o5b2o9b2o7b3ob3o7b 2o$3b2o27b2o2b2o3b2o3b2o3b2o2b2o$38bo2b3ob3o2bo$6b2o21b2o6b2o2bo5bo2b 2o6b2o$6b2o21b2o8b2o7b2o8b2o$39b3o5b3o$40bo7bo$15b2o3b2o8bo8b2ob2ob2ob 2o8bo$27bo2bobo6b2ob2ob2ob2o6bobo2bo$27bo3b2o8bo5bo8b2o3bo$25b3o5b2ob 2o13b2ob2o5b3o$26b2o5b5o13b5o5b2o$27bob4obo3bo11bo3bob4obo$28b4o4b2o 13b2o4b4o$29bobo4b2o13b2o4bobo2$29bobo4b2o13b2o4bobo$28b4o4b2o13b2o4b 4o$27bob4obo3bo11bo3bob4obo$26b2o5b5o13b5o5b2o$25b3o5b2ob2o13b2ob2o5b 3o$27bo3b2o8bo5bo8b2o3bo$27bo2bobo6b2ob2ob2ob2o6bobo2bo$30bo8b2ob2ob2o b2o8bo$40bo7bo$39b3o5b3o$29b2o8b2o7b2o8b2o$29b2o6b2o2bo5bo2b2o6b2o$38b o2b3ob3o2bo$32b2o2b2o3b2o3b2o3b2o2b2o$32b2o7b3ob3o7b2o$42bo3bo$37b5o5b 5o$39b2o7b2o$39bo9bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 AUTOSTART GPS 25 ZOOM 5 HEIGHT 400 ]] An extension of this oscillator (click above to open LifeViewer) RLE: here Plaintext: here Catagolue: here

x = 87, y = 55, rule = B3/S23 5$58bo11bo$52b2o3bob2o7b2obo3b2o$52b2o5b2o7b2o5b2o$57bob2o7b2obo$49b2o 6b2o11b2o6b2o$49b2o6b2o3bo3bo3b2o6b2o$61b3ob3o$63bobo2$49bob3o21b3obo$ 12bo11bo23bo3b2o21b2o3bo$6b2o3bob2o7b2obo3b2o18b3o25b3o$6b2o5b2o7b2o5b 2o18b3o25b3o$11bob2o7b2obo28bo19bo$3b2o6b2o11b2o6b2o19b2o19b2o$3b2o6b 2o3bo3bo3b2o6b2o20b2o17b2o$15b3ob3o$17bobo34b2o17b2o$53b2o19b2o$3bob3o 21b3obo20bo19bo$2bo3b2o21b2o3bo6bo7b3o25b3o$3b3o25b3o6bobo6b3o25b3o$3b 3o25b3o6bobo5bo3b2o21b2o3bo$8bo19bo12bo7bob3o21b3obo$7b2o19b2o$8b2o17b 2o34bobo$61b3ob3o$8b2o17b2o20b2o6b2o3bo3bo3b2o6b2o$7b2o19b2o19b2o6b2o 11b2o6b2o$8bo19bo28bob2o7b2obo$3b3o25b3o18b2o5b2o7b2o5b2o$3b3o25b3o18b 2o3bob2o7b2obo3b2o$2bo3b2o21b2o3bo23bo11bo$3bob3o21b3obo2$17bobo$15b3o b3o$3b2o6b2o3bo3bo3b2o6b2o$3b2o6b2o11b2o6b2o$11bob2o7b2obo$6b2o5b2o7b 2o5b2o$6b2o3bob2o7b2obo3b2o$12bo11bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 AUTOSTART GPS 25 ZOOM 5 HEIGHT 400 ]] Two of these oscillators hassling a beehive (click above to open LifeViewer) RLE: here Plaintext: here Catagolue: here

See also

• Beluchenko's p37

External links

• Beluchenko's p51 at the Life Lexicon
• Beluchenko's p51 at Adam P. Goucher's Catagolue
• 112P51.1 at Heinrich Koenig's Game of Life Object Catalogs
• New Oscillators at Game of Life News. Posted by Heinrich Koenig on March 16, 2009.