Beluchenko's p13

From LifeWiki
Revision as of 20:09, 21 January 2022 by HotdogPi (talk | contribs) (more LCMs)
Jump to navigation Jump to search
Beluchenko's p13
Beluchenko's p13 image
View animated image
View static image
Pattern type Oscillator
Number of cells 34
Bounding box 17 × 17
Period 13 (mod: 13)
Heat 30.2
Volatility 0.96 | 0.96
Kinetic symmetry Unspecified
Discovered by Nicolay Beluchenko
Year of discovery 2009

Beluchenko's p13 is a period-13 oscillator found by Nicolay Beluchenko[1] on January 4, 2009.[2] In terms of its 34 cells, it is the smallest known period 13 oscillator.[3]

It can be combined with itself and with other oscillators to produce larger oscillators with periods that are multiples of 13. 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 pure rotor 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 ]]
Two copies of this oscillator sharing a block

(click above to open LifeViewer)
RLE: here Plaintext: 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
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
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

LCM oscillators

#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 8 LOOP 39 GPS 13 ]]
Caterer on Beluchenko's p13, the smallest known p39 oscillator by population

(click above to open LifeViewer)
RLE: here Plaintext: 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 8 LOOP 65 GPS 13 ]]
Fumarole on Beluchenko's p13, the smallest known p65 oscillator by population

(click above to open LifeViewer)
RLE: here Plaintext: 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 8 LOOP 78 GPS 26 ]]
p6 thumb on Beluchenko's p13, the smallest known p78 oscillator by population

(click above to open LifeViewer)
RLE: here Plaintext: here
x = 25, y = 25, rule = B3/S23 9b2o$9b2o2$4bo2bo$bo6bo$o7bo$bob2o3bo6b2o$5b3o7b2o2b2o$10b3o6bo$9bo3bo 6bo$9bo7b3obo$9bo7bo3bo$10bo2bo5b2ob2o$10bo6bo2bobobo$17b3o4bo$10bobo 6bob3o$11bo7bobo$17b3o$17bo2bo$19b2o$17bo$17b4o$20bo$19bo$19b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ZOOM 8 LOOP 91 GPS 26 ]]
p7 thumb on Beluchenko's p13, the smallest known p91 oscillator by population

(click above to open LifeViewer)
RLE: here Plaintext: 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 8 LOOP 104 GPS 26 ]]
Figure eight on Beluchenko's p13, the smallest known p104 oscillator by population

(click above to open LifeViewer)
RLE: here Plaintext: here

References

  1. ↑ "New Oscillators at Game of Life News" (January 8, 2009). Retrieved on April 11, 2009.
  2. ↑ Jason Summers' all-osc pattern collection. Retrieved on June 28, 2009.
  3. ↑ "Class 2 Objects Catalog". Retrieved on April 11, 2009.
  4. ↑ praosylen (March 31, 2016). Re: Soup search results (discussion thread) at the ConwayLife.com forums


Retrieved from "https://conwaylife.com/w/index.php?title=Beluchenko%27s_p13&oldid=95983"