Beluchenko's p13 is a period -13 oscillator found by Nicolay Beluchenko [1] 2009 .[2] cells , it is the smallest known period 13 oscillator.[3] 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 .[4]
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 ]]
Please enable Javascript to view this LifeViewer.
Two copies of this oscillator sharing a blockLifeViewer )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 ]]
Please enable Javascript to view this LifeViewer.
Two copies of this oscillator sharing two blocksLifeViewer )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 ]]
Please enable Javascript to view this LifeViewer.
Two copies of this oscillator sharing a blockLifeViewer )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 ]]
Please enable Javascript to view this LifeViewer.
Four copies of this oscillator sharing four blocksLifeViewer )RLE :here Plaintext :here Catagolue here
The 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.
#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$13b2o!
#C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]]
#C [[ THUMBSIZE 2 ZOOM 12 LOOP 39 GPS 13 ]]
Please enable Javascript to view this LifeViewer.
p39 with caterer LifeViewer )RLE :here Plaintext :here Catagolue here
x = 18, y = 22, rule = B3/S23
2o4b2o$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 ]]
Please enable Javascript to view this LifeViewer.
p65 with fumarole 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 ]]
Please enable Javascript to view this LifeViewer.
p78 with p6 thumb LifeViewer )RLE :here Plaintext :here Catagolue here
x = 26, y = 19, rule = B3/S23
16b2o$16b2o2$20bo$19bob2obo$18bo4b3o$10b2o6bo2bo$10b2o7b2o2b2o$b2o4bo
7b2o$b3ob2obo5bo2bo$o7bo4bo3bo$5b2ob2o4bobo$2bo3bo2bo4bo$2bo5bo6bobo$b
o2bo3bo5b2obo$b2ob2o9bo$2bo7bo$2bob2ob3o$3bo4b2o!
#C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]]
#C [[ THUMBSIZE 2 ZOOM 12 LOOP 91 GPS 26 ]]
Please enable Javascript to view this LifeViewer.
p91 with meatball 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 ]]
Please enable Javascript to view this LifeViewer.
p104 with figure eight 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 ]]
Please enable Javascript to view this LifeViewer.
p130 with 55P10 LifeViewer )RLE :here Plaintext :here Catagolue here
See also References External links 34P13.1 at Heinrich Koenig's Game of Life Object Catalogs
