42P38: Difference between revisions

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|v            = 0.93
|v            = 0.93
|sv          = 0.87
|sv          = 0.87
|symmetry    = .c
|discoverer  = Mitchell Riley
|discoverer  = Mitchell Riley
|discoveryear = 2023
|discoveryear = 2023
|rulemin      = B3/S23
|rulemin      = B3/S23
|rulemax      = B38/S238
|rulemax      = B38/S238
|rulespecial  = [[Conway's Game of Life|Conway Life]]
|isorulemin  = B3/S23
|isorulemin  = B3/S23
|isorulemax  = B34e5ce6n7c8/S234cey5e6i7e8
|isorulemax  = B34e5ce6n7c8/S234cey5e6i7e8
|synthesis    = 22
|synthesis    = 18
|rle          = true
|rle          = true
|plaintext    = true
|apgcode      = xp38_y2178czy8s4cy1szsoyfesz01sy1ogszy9o8gzyb32
|apgcode      = xp38_y2178czy8s4cy1szsoyfesz01sy1ogszy9o8gzyb32
|viewerconfig = #C [[ HEIGHT 500 THUMBSIZE 3 ZOOM 18 GPS 19 LOOP 38 ]]
|viewerconfig = #C [[ HEIGHT 500 THUMBSIZE 3 ZOOM 18 GPS 19 LOOP 38 ]]
}}
}}
'''42P38''' is a small {{period|38}} [[oscillator]] found by [[Mitchell Riley]] on April 21, {{year|2023}}.<ref name="message1099006580030185472" /> With only 42 cells, it is the smallest known period-38 oscillator by population; surpassing [[44P38]]. It consists of an [[R-pentomino]] turning into an [[octomino II]] via [[fishhook]], then turning back into an R-pentomino via a combination of a [[transparent]] [[blinker]] plus [[toad]] catalyst and hitting a second copy of itself.
'''42P38''' is a small {{period|38}} [[oscillator]] found by [[Mitchell Riley]] on April 21, {{year|2023}}.<ref name="message1099006580030185472" /> With only 42 cells, it is the smallest known period-38 oscillator by population; surpassing [[44P38]]. It consists of an [[R-pentomino]] turning into an [[octomino II]] via [[fishhook]], then turning back into an R-pentomino via a combination of a [[transparent]] [[blinker]] plus [[toad]] [[catalyst]] and hitting a second copy of itself.


It is a delayed domino sparker, allowing for the construction of some [[LCM oscillator]]s and a period-38 [[honey farm hassler]]:
It is a delayed domino sparker, allowing for the construction of some [[LCM oscillator]]s and a period-38 [[honey farm hassler]]:
Line 28: Line 29:
{{EmbedViewer
{{EmbedViewer
|pname        = p38honeyfarmhassler3
|pname        = p38honeyfarmhassler3
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 10 HEIGHT 450 WIDTH 700 GPS 19 THEME Book AUTOSTART ]]
|viewerconfig = #C [[ THUMBSIZE 2 ZOOM 10 HEIGHT 450 WIDTH 700 GPS 19 AUTOSTART ]]
|position    = center
|position    = center
|caption      = p38 honey farm hassler found by [[David Raucci]] (base reaction), [[Mitchell Riley]] (sparker), and [[wwei23]] (combination) on April 21, 2023
|caption      = p38 honey farm hassler found by [[David Raucci]] (base reaction), [[Mitchell Riley]] (sparker), and [[Aleph]] (combination) on April 21, 2023
|style        = width:300px;
|style        = width:300px;
|apgcode      = xp38_y7178czyeg08oxszy1soy73221y0eszwggw1sxe917zwp4d2sgy6o8gz3ihehma1y04v1g06w3iw8gw253zw343y24u044oy01i2g72y1gs2sgzy3ca4x1w4s0g6w8f2y0ol687o4czye11y6g34bipzy6gy8e897x3ogzy637gxo44sy713zy83x11zyj31e8
}}
}}


[[Carson Cheng]] found a {{gliders|22}} synthesis of 42P38 on April 26, 2023.<ref name="message1100579873845690388" /><ref name="j4179541540" />
[[Carson Cheng]] found a {{gliders|22}} synthesis of 42P38 on April 26, 2023.<ref name="message1100579873845690388" /><ref name="j4179541540" /> This was reduced to {{gliders|18|text=18 gliders}} by [[Chris857]] on August 14, 2023.<ref name="post165064" /><ref name="j4866715643" />


== LCM oscillators ==
== LCM oscillators ==
The [[LCM oscillator]]s 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.
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 patterns are shown with visible [[envelope]] to highlight interactions between subpatterns.
{|style="margin:auto;width:300px;"
{{gallery top}}
|{{EmbedViewer
{{gallery item|{{EmbedViewer
|pname = moldon42p38
|pname       = catereron42p38
|viewerconfig = #C [[ THUMBSIZE 2 HEIGHT 400 ZOOM 12 GPS 24 THEME Book STARTFROM 114 ]]
|position    = center
|position    = center
|viewerconfig = #C [[ THUMBSIZE 2 HEIGHT 400 ZOOM 14 GPS 24 THEME Book STARTFROM 76 ]]
|caption      = 54P114 with [[caterer]]
|caption      = 54P76 with [[mold]]
|style        = width:300px;
|apgcode      = xp76_wo4an7y4o8zx11y4321z0g7y1317z73yfe7zy8746y17zy2gs26
|apgcode      = xp114_gggo211sy4c871zy1ty1c4szxseyfoszybsgoy1s1zy6g8ozy523
}}
}}}}
|-
{{gallery item|{{EmbedViewer
|{{EmbedViewer
|pname       = figureeighton42p38
|pname = figureeighton42p38
|viewerconfig = #C [[ THUMBSIZE 2 HEIGHT 400 ZOOM 14 GPS 24 THEME Book STARTFROM 152 ]]
|position    = center
|position    = center
|viewerconfig = #C [[ THUMBSIZE 2 HEIGHT 400 ZOOM 14 GPS 24 THEME Book STARTFROM 152 ]]
|caption      = 54P152 with [[figure eight]]
|caption      = 54P152 with [[figure eight]]
|style        = width:300px;
|apgcode      = xp152_y2178czy8s4cy1szsoyfesz01sy1ogszy9o8gzgggeeey532z333
|apgcode      = xp152_y2178czy8s4cy1szsoyfesz01sy1ogszy9o8gzgggeeey532z333
}}
}}}}
|-
{{gallery item|{{EmbedViewer
|{{EmbedViewer
|pname       = 34p14shuttleon42p38
|pname = 34p14shuttleon42p38
|viewerconfig = #C [[ THUMBSIZE 2 HEIGHT 400 ZOOM 12 GPS 24 THEME Book STARTFROM 266 ]]
|position    = center
|position    = center
|viewerconfig = #C [[ THUMBSIZE 2 HEIGHT 400 ZOOM 12 GPS 24 THEME Book STARTFROM 266 ]]
|caption      = 76P266 with [[34P14 shuttle]]
|caption      = 76P266 with [[34P14 shuttle]]
|style        = width:300px;
|apgcode      = xp266_033y133y544402331zo4maxam4oy4o8yaok46z1ppy1pp1x8ox111y34kszy8311zyk46620111
|apgcode      = xp266_033y133y544402331zo4maxam4oy4o8yaok46z1ppy1pp1x8ox111y34kszy8311zyk46620111
}}
}}}}
|-
{{gallery item|{{EmbedViewer
|{{EmbedViewer
|pname       = p9thumbon42p38
|pname = p18biblockhassleron42p38
|viewerconfig = #C [[ THUMBSIZE 2 HEIGHT 400 ZOOM 10 GPS 24 THEME Book STARTFROM 342 ]]
|position    = center
|position    = center
|viewerconfig = #C [[ THUMBSIZE 2 HEIGHT 400 ZOOM 12 GPS 24 THEME Book STARTFROM 342 ]]
|caption      = 78P342 with [[p9 thumb]]
|caption      = 85P342 with [[p18 bi-block hassler]]
|style        = width:300px;
|apgcode      = xp342_xcu5jzy1125ce53zy1ccx26062y1ggzcc08ki16y6643zy3ey162ezy1e7yfsezyde8cy1ezy8o4czy711
|apgcode      = xp342_xo487p8a6z330f840743156wggzy9643zwey162eze7yfsezy8e8cy1ezy3o4czy211
}}
}}}}
|}
{{gallery bottom}}


==References==
== References ==
<references>
<references>
<ref name="j4179541540">{{CiteCatagolueJob|job=4179541540|date=April 26, 2023}}</ref>
<ref name="j4179541540">{{CiteCatagolueJob|job=4179541540|date=April 26, 2023}}</ref>
<ref name="j4866715643">{{CiteCatagolueJob|job=4866715643|date=August 14, 2023}}</ref>
<ref name="message1099006580030185472">{{CiteDiscord
<ref name="message1099006580030185472">{{CiteDiscord
|author  = mvr
|author  = mvr
Line 87: Line 91:
|channel = cgol
|channel = cgol
|id      = 1100579873845690388
|id      = 1100579873845690388
}}</ref>
<ref name="post165064">{{LinkForumThread
|format = ref
|p      = 165064
|title  = Re: Synthesising Oscillators
|author = Chris857
|date  = August 14, 2023
}}</ref>
}}</ref>
</references>
</references>


==External links==
== External links ==
* {{LinkCatagolue|xp38_y2178czy8s4cy1szsoyfesz01sy1ogszy9o8gzyb32}}
* {{LinkCatagolue|xp38_y2178czy8s4cy1szsoyfesz01sy1ogszy9o8gzyb32}}


[[Category:R-pentomino hasslers|038]]
[[Category:R-pentomino hasslers|038]]
{{Symmetry|180deg}}
{{Sparker|p=38|type=domino|strength=strong}}
{{Sparker|p=38|type=domino|strength=strong}}
__NOTOC__
__NOTOC__

Latest revision as of 15:14, 6 August 2026

42P38
x = 27, y = 25, rule = B3/S23 13bo$12bo2bo$12bo2bo2bo$14bo3bo$18bo3$o$3o$3bo14bo$2b2o14b2o$17b2o2$8b 2o$7b2o14b2o$8bo14bo$24b3o$26bo3$8bo$8bo3bo$8bo2bo2bo$11bo2bo$13bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ AUTOSTART ]] #C [[ HEIGHT 500 THUMBSIZE 3 ZOOM 18 GPS 19 LOOP 38 ]]
View static image
Pattern type Oscillator
Number of cells 42
Bounding box 25 × 27
Period 38 (mod: 38)
Heat 45.5
Volatility 0.93 | 0.87
Kinetic symmetry .c
Discovered by Mitchell Riley
Year of discovery 2023

42P38 is a small period-38 oscillator found by Mitchell Riley on April 21, 2023.[1] With only 42 cells, it is the smallest known period-38 oscillator by population; surpassing 44P38. It consists of an R-pentomino turning into an octomino II via fishhook, then turning back into an R-pentomino via a combination of a transparent blinker plus toad catalyst and hitting a second copy of itself.

It is a delayed domino sparker, allowing for the construction of some LCM oscillators and a period-38 honey farm hassler:

x = 64, y = 38, rule = B3/S23 37b2o$34bo2bo$32b3o3b3o2b2o$31bo3b3o3bo2bo$32b3o3bob2obo$34bob2o4bo6b 3o$35bobob3o6b3o$25b2o11b2o4b3o$25bobo5b3o$26bo5bo3bo$12b3o16bo5bo$11b 3o17bo5bo11bo13bo$7b3o21bo5bo8bo2bo11b3o$32bo3bo8bo14bo$33b3o9bobo12b 2o$45b2o$12bo13bo$9bo2bo11b3o27b2o$8bo14bo15b2o12bobo$8bobo12b2o15bo 14bo$8b2o27b3o11bo2bo$37bo13bo$17b2o$2b2o12bobo9b3o$3bo14bo8bo3bo$3o 11bo2bo8bo5bo21b3o$o13bo11bo5bo17b3o$26bo5bo16b3o$27bo3bo5bo$28b3o5bob o$17b3o4b2o11b2o$13b3o6b3obobo$12b3o6bo4b2obo$20bob2obo3b3o$19bo2bo3b 3o3bo$19b2o2b3o3b3o$26bo2bo$25b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 ZOOM 10 HEIGHT 450 WIDTH 700 GPS 19 AUTOSTART ]]
p38 honey farm hassler found by David Raucci (base reaction), Mitchell Riley (sparker), and Aleph (combination) on April 21, 2023
(click above to open LifeViewer)
RLE: here Plaintext: here
Catagolue: here

Carson Cheng found a 22-glider synthesis of 42P38 on April 26, 2023.[2][3] This was reduced to 18 gliders by Chris857 on August 14, 2023.[4][5]

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. The patterns are shown with visible envelope to highlight interactions between subpatterns.

x = 27, y = 26, rule = B3/S23 21b3o$13bo7b2o$12bo2bo6b2o$12bo2bo2bo3bo$14bo3bo6b2o$18bo3b2obo$23bo$ 23bo$o$3o$3bo14bo$2b2o14b2o$17b2o2$8b2o$7b2o14b2o$8bo14bo$24b3o$26bo3$ 8bo$8bo3bo$8bo2bo2bo$11bo2bo$13bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 HEIGHT 400 ZOOM 12 GPS 24 THEME Book STARTFROM 114 ]]
54P114 with caterer
(click above to open LifeViewer)
RLE: here Plaintext: here
Catagolue: here
x = 32, y = 25, rule = B3/S23 13bo$12bo2bo14b2o$12bo2bo2bo9bob2o$14bo3bo8bo$18bo11bo$26b2obo$26b2o$o $3o$3bo14bo$2b2o14b2o$17b2o2$8b2o$7b2o14b2o$8bo14bo$24b3o$26bo3$8bo$8b o3bo$8bo2bo2bo$11bo2bo$13bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 HEIGHT 400 ZOOM 14 GPS 24 THEME Book STARTFROM 152 ]]
54P152 with figure eight
(click above to open LifeViewer)
RLE: here Plaintext: here
Catagolue: here
x = 39, y = 25, rule = B3/S23 13bo$12bo2bo13b2o5b2o$12bo2bo2bo10b2o5b2o$14bo3bo$18bo2$28b3o5b3o$o27b o2bo3bo2bo$3o26bo7bo$3bo14bo11bobobobo$2b2o14b2o$17b2o12b2ob2o2$8b2o$ 7b2o14b2o5bo5bo$8bo14bo5b2o5b2o$24b3o$26bo3$8bo$8bo3bo$8bo2bo2bo$11bo 2bo$13bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 HEIGHT 400 ZOOM 12 GPS 24 THEME Book STARTFROM 266 ]]
76P266 with 34P14 shuttle
(click above to open LifeViewer)
RLE: here Plaintext: here
Catagolue: here
x = 25, y = 36, rule = B3/S23 16b2o$16bo$14bobo$14b2o4$10bo$2b3o4b3o$11bo2$b2o$3bo18b2o$o23bo$b2o18b o$22b2o2$13bo$13b3o4b3o$14bo4$9b2o$8bobo$8bo$7b2o$15bo3b2o$11b2o7bo$11b o3bob2obob2o$12b3o2b2obob2o$18bobo$14b3obobo$13bo3bobo$13b2o2bo$16b2o ! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 2 HEIGHT 400 ZOOM 10 GPS 24 THEME Book STARTFROM 342 ]]
78P342 with p9 thumb
(click above to open LifeViewer)
RLE: here Plaintext: here
Catagolue: here


References

  1. ↑ mvr (April 21, 2023). Message in #cgol on the Conwaylife Lounge Discord server
  2. ↑ carsoncheng (April 26, 2023). Message in #cgol on the Conwaylife Lounge Discord server
  3. ↑ shinjuku (#4179541540) (April 26, 2023). Job triggered by Adam P. Goucher at GitLab Catagolue project.
  4. ↑ Chris857 (August 14, 2023). Re: Synthesising Oscillators (discussion thread) at the ConwayLife.com forums
  5. ↑ shinjuku (#4866715643) (August 14, 2023). Job triggered by Adam P. Goucher at GitLab Catagolue project.


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