Beluchenko's p13: Difference between revisions

From LifeWiki
Jump to navigation Jump to search
← Older edit
WhiteHawk (talk | contribs)
Trusted users
2,600 edits
No edit summary
No edit summary
 
(5 intermediate revisions by 2 users not shown)
Line 1: Line 1:
{{Oscillator
{{Oscillator
|name            = Beluchenko's p13
|name            = Beluchenko's p13
|pname            = 34p13
|pname            = beluchenkosp13
|c                = 34
|c                = 34
|bx              = 17
|bx              = 17
Line 32: Line 32:
Beluchenko's p13 first appeared [[semi-natural]]ly in March {{year|2016}}, in a [[symmetric]] [[soup]] submitted to [[Catagolue]].<ref name="post29522" />
Beluchenko's p13 first appeared [[semi-natural]]ly in March {{year|2016}}, in a [[symmetric]] [[soup]] submitted to [[Catagolue]].<ref name="post29522" />


==Variants==
== Variants ==
{{gallery top}}
{{gallery top}}
{{gallery item|{{EmbedViewer
{{gallery item|{{EmbedViewer
Line 68: Line 68:
{{gallery bottom}}
{{gallery bottom}}


==LCM oscillators==
== LCM oscillators ==
The [[LCM oscillator]]s 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.
The [[LCM oscillator]]s 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.
{{gallery top}}
{{gallery top}}
Line 118: Line 118:
|style        = width:300px;
|style        = width:300px;
|apgcode      = xp117_wg8o696o8a6zg1aq1qr6wccz11074wgy1gr3zy3d5a64210g8c4066zy9kr6og
|apgcode      = xp117_wg8o696o8a6zg1aq1qr6wccz11074wgy1gr3zy3d5a64210g8c4066zy9kr6og
}}}}
{{gallery item|{{EmbedViewer
|pname        = 55p10onbeluchenkosp13
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 8 LOOP 130 GPS 26 ]]
|position    = center
|caption      = p130 with [[55P10]]
|style        = width:300px;
|apgcode      = xp130_og8o0u1eozy0mlgrzx1qa2my2meiz62460v0t60gg037fa60ggzy21x11y236fe5267zyc33
}}}}
}}}}
{{gallery item|{{EmbedViewer
{{gallery item|{{EmbedViewer
Line 137: Line 129:
|style        = width:300px;
|style        = width:300px;
|apgcode      = xp143_xgbb88gzy1cd3gv04aczc4530gy1gr3zy1d5a64210g8c4066zy7kr6og
|apgcode      = xp143_xgbb88gzy1cd3gv04aczc4530gy1gr3zy1d5a64210g8c4066zy7kr6og
}}}}
{{gallery item|{{EmbedViewer
|rle = x = 38, y = 33, rule = B3/S23
10b2o$9bo2bo4bo$16bobo$17bo2$7bobo$7bobo$7bo5b2o4bo$3b2o4bobo5bobo$3b
o6bo8bo$2obo6bo4bobo6bo$o2bob2o9bo6b2o$2b2obo10bo5b2o$3bobo15b3o3b2o$
2bo2b2o20b2o$3b2o2bo5b2o$4bob2o6bo4b2o9b2o$4bobo4b3o6bo9b2o$3b2obobo2b
o5b3o6bo$7b2o8bo7bo2bo$22bo6bo$21bo7bo$22bob2o3bo6b2o$26b3o7b2o$31b3o
$30bo3bo$30bo$30bo$31bo2bo$31bo2$31bobo$32bo!
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 8 LOOP 130 GPS 26 ]]
|position    = center
|caption      = p377 with p29 [[long boat spin]] <ref name="post201656" />
|style        = width:300px;
|apgcode      = xp377_y633y04a4zxo8y0757xsksz31kf0uiyaokndwoozx9f0eiowc453wo8a711y366zyi2ea07b960ggxcczyqj4m7zyq113
}}}}
{{gallery item|{{EmbedViewer
|rle = x = 35, y = 33, rule = B3/S23
18bo$2o14b3o$bo13bo$bobo11b2o$2b2o$10b2o$9b3o$9bo2bo$10b2o$25b2o$25bo
$2b2o19bobo$bobo19b2o$bo$2o$15b2o$14bo2bo3b2o$15b3o3b2o2b2o$15b2o8b2o
2$10b2o$11bo16b3o$8b3o16bob2ob3o$8bo10b2o6bo2bo2bo$19b2o7b2o2b2o$24b2o
$23bo2bo$23b2obo$23b3o2$24bobo$24b3o$24bo!
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 8 LOOP 130 GPS 26 ]]
|position    = center
|caption      = p481 with [[58P37]]
|style        = width:300px;
|apgcode      = xp481_2egoy7ca23zy56bb4y8ggzgs26yf643zya2dd6x66wcczy4c453y3ooy2cime0ks4zyjed96zyk723
}}}}
}}}}
{{gallery item|{{EmbedViewer
{{gallery item|{{EmbedViewer
Line 147: Line 164:
}}}}
}}}}
{{gallery bottom}}
{{gallery bottom}}


== See also ==
== See also ==
* [[p39 pi-heptomino hassler]]
* [[p39 pi-heptomino hassler]]


==References==
== References ==
<references>
<references>
<ref name="post29522">{{LinkForumThread
<ref name="post29522">{{LinkForumThread
Line 159: Line 177:
|author = praosylen
|author = praosylen
|date  = March 31, 2016
|date  = March 31, 2016
}}</ref>
<ref name="post201656">{{LinkForumThread
|format = ref
|p      = 201656
|title  = Re: Smallest Known Oscillators to p106 (and Beyond)
|author = Period1GliderGun
|date  = January 13, 2025
}}</ref>
}}</ref>
</references>
</references>
Line 166: Line 191:
* {{LinkPentadecathlonObject|34P13.1}}
* {{LinkPentadecathlonObject|34P13.1}}


{{Symmetry|diagonal2}}
{{Sparker|p=13|type=dot|strength=strong}}
{{Sparker|p=13|type=dot|strength=strong}}
{{seminatural}}
{{seminatural}}


__NOTOC__
__NOTOC__

Latest revision as of 13:22, 27 March 2025

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 ]]
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 /
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
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 = 20, y = 25, rule = B3/S23 4b2o$4b2o2$4b4o$3bo4bo$6b2obo$7bobo2bo$5b2o2bobobo$5b2o2bo2b2o$8b2o$2b2o8b2o$ 3bo8b2o$3o$o11bo$5bo5b2o$5b2o4bo$7b2obo7b2o$5b2ob2o5b2ob2o$5bobo6b2o$13bo$12b o$12b2o$11bobo$12bobo$11b2ob2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ZOOM 8 LOOP 130 GPS 26 ]]
p143 with p11 thumb
(click above to open LifeViewer)
Catagolue: here
x = 38, y = 33, rule = B3/S23 10b2o$9bo2bo4bo$16bobo$17bo2$7bobo$7bobo$7bo5b2o4bo$3b2o4bobo5bobo$3b o6bo8bo$2obo6bo4bobo6bo$o2bob2o9bo6b2o$2b2obo10bo5b2o$3bobo15b3o3b2o$ 2bo2b2o20b2o$3b2o2bo5b2o$4bob2o6bo4b2o9b2o$4bobo4b3o6bo9b2o$3b2obobo2b o5b3o6bo$7b2o8bo7bo2bo$22bo6bo$21bo7bo$22bob2o3bo6b2o$26b3o7b2o$31b3o $30bo3bo$30bo$30bo$31bo2bo$31bo2$31bobo$32bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ZOOM 8 LOOP 130 GPS 26 ]]
p377 with p29 long boat spin [5]
(click above to open LifeViewer)
Catagolue: here
x = 35, y = 33, rule = B3/S23 18bo$2o14b3o$bo13bo$bobo11b2o$2b2o$10b2o$9b3o$9bo2bo$10b2o$25b2o$25bo $2b2o19bobo$bobo19b2o$bo$2o$15b2o$14bo2bo3b2o$15b3o3b2o2b2o$15b2o8b2o 2$10b2o$11bo16b3o$8b3o16bob2ob3o$8bo10b2o6bo2bo2bo$19b2o7b2o2b2o$24b2o $23bo2bo$23b2obo$23b3o2$24bobo$24b3o$24bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ZOOM 8 LOOP 130 GPS 26 ]]
p481 with 58P37
(click above to open LifeViewer)
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

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
  5. ↑ Period1GliderGun (January 13, 2025). Re: Smallest Known Oscillators to p106 (and Beyond) (discussion thread) at the ConwayLife.com forums


Retrieved from "https://conwaylife.com/w/index.php?title=Beluchenko%27s_p13&oldid=159897"