Beluchenko's p13

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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 [[ GPS 3 ZOOM 14 LOOP 13 ]]
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

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 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.[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
Catagoluehere
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
Catagoluehere
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
Catagoluehere
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
Catagoluehere

LCM oscillators

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$13b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ZOOM 12 LOOP 39 GPS 13 ]]
p39 with caterer
(click above to open LifeViewer)
RLE: here Plaintext: here
Catagoluehere
x = 18, y = 22, rule = B3/S23 2o4b2o$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
Catagoluehere
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
Catagoluehere
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 ]]
p91 with meatball
(click above to open LifeViewer)
RLE: here Plaintext: here
Catagoluehere
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
Catagoluehere
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
Catagoluehere

See also

References

  1. New Oscillators at Game of Life News. Posted by Heinrich Koenig on January 08, 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

External links

  • 34P13.1 at Heinrich Koenig's Game of Life Object Catalogs