Beluchenko's p13

Beluchenko's p13
x = 16, y = 16, rule = B3/S23 4b3o2$6bo$6b2o$5bo$8bo$4bo3bo$9b2o$2o2b3o5bo$2o5bo4b2obo$7bo3bo3bo$7bo bo5bo3$6b2o$6b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ AUTOSTART ]] #C [[ HEIGHT 600 THUMBSIZE 3 ZOOM 24 GPS 3 LOOP 13 ]]
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Pattern type	Oscillator
Number of cells	34
Bounding box	17 × 17
Period	13
Mod	13
Heat	30.2
Volatility	0.96
Strict volatility	0.96
Discovered by	Nicolay Beluchenko
Year of discovery	2009
Rules Outer-totalistic rules B3/S23 – B38/S238 # of rules 22 = 4 Isotropic rules B3-k/S23 – B34ceq5ej6ace7e8/S234ciqtwz5y6in7e8
Glider synthesis Fewest gliders 14 Catagolue-generated RLE synthesis Uploaded synthesis RLE 34p13_synth.rle
Pattern files Plaintext 34p13.cells RLE 34p13.rle
Identifiers apgcode xp13_gy1gr3zd5a64210g8c4066zy2kr6og Pentadecathlon ID 34P13.1

Beluchenko's p13 is a period-13 oscillator found by Nicolay Beluchenko on January 4, 2009. In terms of its 34 cells, it is the smallest known period 13 oscillator. It gives sparks, allowing for the construction of non-trivial higher-period oscillators as seen in a later section.

There are three ways in which two of these can share a common block, all of which are shown below. Jason Summers also discovered that four of these oscillators can be combined to create a statorless oscillator (i.e., where none of the cells are alive in all phases), making it the first such oscillator known with a prime period greater than two.

Beluchenko's p13 first appeared semi-naturally in March 2016, in a symmetric soup submitted to Catagolue.

Variants

x = 17, y = 31, rule = 23/3 4b3o10b2$6bo10b$6b2o9b$5bo11b$8bo8b$4bo3bo8b$9b2o6b$2o2b3o5bo4b$2o5bo 4b2obob$7bo3bo3bob$7bobo5bob3$6b2o9b$6b2o9b2$9bo2bo4b$8bo6bob$8bo7bo$ 2o6bo3b2obob$2o7b3o5b$4b3o10b$3bo3bo9b$7bo9b$7bo9b$3bo2bo10b$6bo10b2$ 4bobo10b$5bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ZOOM 8 LOOP 13 GPS 3 AUTOSTART ]]

Two copies of this oscillator sharing a block (click above to open LifeViewer) RLE: here Plaintext: here Catagolue: here

x = 25, y = 25, rule = 23/3 9b3o13b2$9bo15b$8b2o15b$10bo14b$7bo17b$7bo3bo13b$5b2o18b$3bo5b3o2b2o9b $ob2o4bo5b2o9b$o3bo3bo16b$o5bobo8bo2bo4b$16bo6bob$16bo7bo$8b2o6bo3b2ob ob$8b2o7b3o5b$12b3o10b$11bo3bo9b$15bo9b$15bo9b$11bo2bo10b$14bo10b2$12b obo10b$13bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ZOOM 8 LOOP 13 GPS 3 AUTOSTART ]]

Two copies of this oscillator sharing two blocks (click above to open LifeViewer) RLE: here Plaintext: here Catagolue: here

x = 19, y = 31, rule = 23/3 7b3o9b2$9bo9b$9b2o8b$8bo10b$11bo7b$7bo3bo7b$12b2o5b$3b2o2b3o5bo3b$3b2o 5bo4b2obo$10bo3bo3bo$10bobo5bo3$9b2o8b$9b2o8b2$4bo2bo11b$bo6bo10b$o7bo 10b$bob2o3bo6b2o2b$5b3o7b2o2b$10b3o6b$9bo3bo5b$9bo9b$9bo9b$10bo2bo5b$ 10bo8b2$10bobo6b$11bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ZOOM 8 LOOP 13 GPS 3 AUTOSTART ]]

Two copies of this oscillator sharing a block (click above to open LifeViewer) RLE: here Plaintext: here Catagolue: here

x = 36, y = 36, rule = 23/3 2$13bo8bo$12bobo7bo$22bo$12bo$12bo2bo7b2o$11bo11b2o$11bo11b3o$11bo3bo5b2obo$ 12b3o6b3o3bo$7b3o7b2o3bo3b4o$3bob2o3bo6b2o6bob3o$2bo7bo13b3o4b3o$3bo6bo14b2o$ 6bo2bo2$11b2o10b2o$11b2o10b2o2$26bo2bo$9b2o14bo6bo$2b3o4b3o13bo7bo$ 6b3obo6b2o6bo3b2obo$6b4o3bo3b2o7b3o$8bo3b3o6b3o$11bob2o5bo3bo$10b3o11bo$ 11b2o11bo$11b2o7bo2bo$23bo$13bo$13bo7bobo$13bo8bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ZOOM 8 LOOP 13 GPS 3 AUTOSTART ]]

Four copies of this oscillator sharing four blocks (click above to open LifeViewer) RLE: here Plaintext: here Catagolue: here

LCM oscillators

The LCM oscillators below are the smallest known ones of their period by population while satisfying the condition that at least one cell oscillates at the full period.

#C Smallest known period-39 oscillator, found 6 January 2009 x = 23, y = 16, rule = B3/S23 5b2o4b3o$4bo$7bo5bo$3bo3bo5b2o$4o3bo4bo$5bo9bo$11bo3bo$16b2o$7b2o2b3o 5bo$7b2o5bo4b2obo$14bo3bo3bo$14bobo5bo3$13b2o$13b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ZOOM 12 LOOP 39 GPS 13 ]]

p39 with caterer (click above to open LifeViewer) RLE: here Plaintext: here Catagolue: here

x = 18, y = 22, rule = B3/S23 2o4b2o$obo2bobo$2bo2bo$bo4bo$b2o2b2o$3b2o5b2o$10b2o2$5bo2bo$2bo6bo$bo 7bo$2bob2o3bo6b2o$6b3o7b2o$11b3o$10bo3bo$10bo$10bo$11bo2bo$11bo2$11bob o$12bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ZOOM 12 LOOP 65 GPS 13 ]]

p65 with fumarole (click above to open LifeViewer) RLE: here Plaintext: here Catagolue: here

x = 25, y = 17, rule = B3/S23 9b2o$9b2o2$4bo2bo$bo6bo$o7bo$bob2o3bo6b2o$5b3o7b2o$10b3o6bo$9bo3bo5b3o $9bo7b2o3bo$9bo6bo3b2obo$10bo2bo3b3obobo$10bo7bo2bob2o$21bo$10bobo6bob o$11bo6b2ob2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ZOOM 12 LOOP 78 GPS 26 ]]

p78 with p6 thumb (click above to open LifeViewer) RLE: here Plaintext: here Catagolue: here

x = 31, y = 20, rule = B3/S23 20b2o$20b2o2$23bo2bo$22bo6bo$22bo7bo$14b2o6bo3b2obo$14b2o7b3o$18b3o$17b o3bo$21bo$7bo4b2o7bo$5bobo4bobo2bo2bo$3bo2bo6b3o4bo$2b3obobo5b2o$b2o3b 4o3b2o3bobo$2o5bobob3o5bo$3o6bo2bo$bobo4bobo$2b2o4bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ZOOM 12 LOOP 91 GPS 26 ]]

p91 with 34P7 (click above to open LifeViewer) RLE: here Plaintext: here Catagolue: here

x = 23, y = 17, rule = B3/S23 11bo$10bobo$4b2o$2bob2o6bo$bo7bo2bo$4bo8bo$2obo9bo$2o7bo3bo$10b3o$6b2o 7b3o$6b2o6bo3b2obo$14bo7bo$14bo6bo$15bo2bo2$12b2o$12b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ZOOM 12 LOOP 104 GPS 26 ]]

p104 with figure eight (click above to open LifeViewer) RLE: here Plaintext: here Catagolue: here

x = 27, y = 22, rule = B3/S23 9b2o$5bo4bo$4bobobo$3bo2bob5o$3b2obo5bo$b2o5b2o5bo$o2bob2ob2o4bobo$b2o 3bo$3b2o11bo$3bo9bo2bo$bobo3b2o8bo$b2o4b2o8bo$13bo3bo$14b3o$10b2o7b3o$ 10b2o6bo3b2obo$18bo7bo$18bo6bo$19bo2bo2$16b2o$16b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ZOOM 12 LOOP 117 GPS 26 ]]

p117 with 42P9 (click above to open LifeViewer) RLE: here Plaintext: here Catagolue: here

x = 26, y = 27, rule = B3/S23 6bo$5bobo$5bobo$ob2obob2o$2obobo2bo$5bobo$4bo2bo$4b2o$7bo$4b4o$3bo$4b 4o6b3o$7bo6b2o$4b2o9bo$4bo2bo6bobo$5bobo5b3o$2obobo2bo4b5o$ob2obob2o5b 2obo$5bobo7b2o$5bobo2b2o7b2o$6bo3b2o6bobobo2bo$18b4ob3o$19b4ob2o$20b2o 2$16b2o$16b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ZOOM 8 LOOP 130 GPS 26 ]]

p130 with 55P10 (click above to open LifeViewer) RLE: here Plaintext: here Catagolue: here

x = 42, y = 31, rule = B3/S23 31b2o$31b2o2$34bo2bo$33bo6bo$33bo7bo$25b2o6bo3b2obo$25b2o7b3o$o28b3o$ 3o25bo3bo$3bo28bo$2b2o28bo$28bo2bo$31bo2$19bo9bobo$b3o3b3o8b2o10bo$17b o$5bo12b2o$5bo13bo$5bo5$14b2o8b2o$14bo2b6o2bo$15b2o6b2o$12b3o10b3o$12b o2bobo4bobo2bo$13b2o4b2o4b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ ZOOM 12 HEIGHT 500 ]]

p988 with p76 pi-heptomino hassler (click above to open LifeViewer) RLE: here Plaintext: here Catagolue: here

See also

• p39 pi-heptomino hassler

External links

• Beluchenko's p13 at Adam P. Goucher's Catagolue
• 34P13.1 at Heinrich Koenig's Game of Life Object Catalogs