Smallest still lifes with specific islands

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Saka
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Re: Smallest still lifes with specific islands

Post by Saka » April 16th, 2020, 1:55 am

yujh wrote:
April 16th, 2020, 1:45 am
Also, four cells of yours, Saka.

Code: Select all

x=10,y=8,rule=LifeHistory
4.2C$5.C$5.C.2A$A.2A.C.2A$2A.A.C$5.C$4.C$4.2C!
Wow, that's embarrassing :oops:
I've added that and the xs10_drz23 solution.
I have a feeling my solution for xs10_26hv isn't minimal.

EDIT:
Is using WLS allowed? (I mean, I dont see why not)
It found this 43 cell solution for xs10_xgc31z621 (I've very slightly modified it for bounding box), and it can't seem to find a 42 cell one.

Code: Select all

x = 13, y = 13, rule = LifeHistory
4.2A$4.A2.A$6.2A$7.A.2C$4.3A2.C$3.A2.A.C2.A$3.A4.C.2A$.A.2A2.C2.A$A.A
3.C3.A.A$A.A.2C5.2A$.2A.C$6.A$5.2A!
EDIT2:
I think this is minimal
xs10_4ara4

Code: Select all

x = 5, y = 17, rule = LifeHistory
2.A$.A.A$2.A2$5A$A3.A$2.C$.3C$C3.C$.3C$2.C$A3.A$5A2$2.A$.A.A$2.A!
EDIT3+:
This as well
xs10_311ui

Code: Select all

x = 9, y = 11, rule = LifeHistory
4.A$3.A.A$4.2A2.A$6.3A$2.3C$2.C2.2C$5.C$3.A.C$.3A.2C$A$2A!
This?
xs10_2js26

Code: Select all

x = 9, y = 8, rule = LifeHistory
7.2A$4.2A2.A$2A3.2A$A2.C$2.2C.2C$4.C.C$4.C$3.2C!
More:
xs9_32pm

Code: Select all

x = 7, y = 6, rule = LifeHistory
3.C.C$3.2C.C$6.C$.3A.C$A2.A.2C$2A!
xs9_23cic

Code: Select all

x = 7, y = 7, rule = LifeHistory
4.2A$2A3.A$A2.C$2.2C.C$4.C.C$4.C.C$5.C!
xs9_69p6

Code: Select all

x = 9, y = 8, rule = LifeHistory
3.2A$3.A3.2A$5.A2.A$4.3A$.2C$C2.2C$C2.C2.A$.2C2.2A!
xs9_17888o

Code: Select all

x = 7, y = 9, rule = LifeHistory
2C.A.2A$.C.2A.A$.C$2.4C$5.C$2.2A$2.A$3.A$2.2A!

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Re: Smallest still lifes with specific islands

Post by Ian07 » April 17th, 2020, 3:52 pm

Currently trying to get through all the xs8 ones now; I'm going through them alphanumerically rather than by commonness and the list I'm pretty sure now contains everything up to xs8_139e that's possible to stabilize: https://www.conwaylife.com/w/index.php? ... ldid=70793

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Re: Smallest still lifes with specific islands

Post by praosylen » April 17th, 2020, 4:49 pm

Nice! Reductions (most in population, a couple just in bounding box):

Code: Select all

x = 101, y = 57, rule = B3/S23
3b2o$3bo13bo47b2o$4bo11bobo35b2o9bo$3b2o10bobo2bo11bob2o18bo3b2o7bo2b
2o$bo2bob2o6bo2bob2o11b2obo20bo2bo6b2o3bo$b2o3bo2bo5b3o2bob2obo24b2o3b
3o6bo2bobo$5bo2b2o9bo2bob2o6b3o16b3o10b2o3b2o13bo$4bo12b2o3bo10bobo2b
2o9bo4b2o12bo14bobo$4b2o9bo2bobobo8bo4bo2bo8bob3o2bo12bob3o10bo2bo$b2o
bo10b2o3b2o8bob3ob2o10bo3b2o13b2obo2bo6b2ob3obo$2bo3bo12bo11bo2bo12b2o
18bo2bobo5bo2bo4bo$obo2b2o13bobo9bobo34bobo6b2o2b3o$2o19b2o10bo36bo13b
2o12$54b2o28b2o$31b2o20bo2bo26bo2bo$9b2o20bo2b2o16bob3o26b3obo$10bo11b
2o9b2o2b2o14bo32bo$5b2obo9bo4bo12b2o12bo4b2o8b2o16b2o$6bob2o7bobo2bo10b
3o3bo9bobo2b2o2bo5bo2bo16b2o2b2o$4bobo2bo6bobo2bo9bo2bo2b2obo7bobo2bo
3b2o4bo2bo2bob2o9bo3bo2bo$2b3o2bo8bobob2obob2o4b2o3b2o2bo7bobob2o9b4o
b2obobo7bob2ob2o$bo3bob2o8b2obo2b2obo12bo9b2obo15bo2bobo7bo2bobo$bobo
bo2bo13bo17b3o11bo10bobo2bobo9b2o4bo$2b2ob2o14b2o19bo10b2o10b2o4bo15b
2o9$60b2o$61bo$59bo13b2o$59b2o13bo19b2o$3b2o12b2o13b2o22b2obo2bo9bo21b
o2b2o$2bo2bo10bo2bo12bo24bo3b2o7b4o22b2obo$2b3obo4b2o2bob3o14bob2o6b2o
b2o6bo2bo10bo5b2o5b2obo13bo$5bo5bo2bobo12bo3b2obobo6bobo7b2obo10bo2b2o
bo6bob2o10b2ob2o$2b2o8b3o3b2o8bobobo3bobo4bo3bo8bo2b2o9b3o2bo10b2obo5b
obo2bo$3b2o11bobo2bo5bobo3bobobo5b2o2b2o7bo3bo13bo8b2obob2o5bo2bo$bo3b
o8b2obo2b2o5bobob2o3bo8bobo2bo4b2obo13b2o7bo2bo11b2o$ob2obo6bo2bo12b2o
bo13bo3b2o5bob2o12bo8b2o2bo$o2bob2o5b2o3bo15bo12bo9bo17bo11bobo$b2o13b
2o14b2o11b2o8b2o16b2o12b2o!
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Re: Smallest still lifes with specific islands

Post by BlinkerSpawn » April 18th, 2020, 3:36 pm

If I made a DetLife variant that automatically detected forced supports, would anyone use it?
LifeWiki: Like Wikipedia but with more spaceships. [citation needed]

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ColorfulGalaxy
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Re: Smallest still lifes with specific islands

Post by ColorfulGalaxy » January 29th, 2021, 11:49 pm

I couldn't find them on the wiki article.
Any reduction?

Code: Select all

x = 10, y = 10, rule = LifeHistory
5.2A$5.2A2$2A.4C$2A.C2.C$3.C2.C.2A$3.4C.2A2$3.2A$3.2A!

Code: Select all

x = 18, y = 10, rule = LifeHistory
2.A$.A.A$2.A2$5A$A3.A$2.C$.3C$C3.C$2C.2C!

Code: Select all

x = 11, y = 5, rule = LifeHistory
$2A3.2C.2A$A.A.C.C.A$2.A.C.C.A.A$.2A.2C3.2A!

Code: Select all

x = 7, y = 8, rule = LifeHistory
2.2A$2.2A2$4C2.C$C2.4C2$3.2A$3.2A!

Code: Select all

x = 11, y = 11, rule = LifeHistory
4.2A$4.A$6.A$5.2A$2.2C3.2A$2.C.2C.A2.A$5.C3.2A$4A2.C$A2.A.2C$3.A$2.2A
!

Code: Select all

x = 7, y = 7, rule = LifeHistory
2.A$2.3A$5.A$4C.A$C2.C.2A$3.C$2.2C!

Code: Select all

x = 11, y = 10, rule = LifeHistory
9.2A$9.2A$3.2C$3.C.C.4A$5.C.A2.A$A2.A.C$4A.C.C$6.2C$2A$2A!

Code: Select all

x = 7, y = 7, rule = LifeHistory
.2C$.C.C.2A$3.C.2A$3.C$2A.C$2A.C.C$4.2C!

Code: Select all

x = 7, y = 6, rule = LifeHistory
.2C$.C.C.2A$3.C.2A$3.C$2A.C$2A.2C!
(I'm not sure if it can eat gliders)

Code: Select all

x = 7, y = 7, rule = LifeHistory
2A.C$2A.3C$6.C$2C.3C$.C.C$.C.C$2.C!

Hunting
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Re: Smallest still lifes with specific islands

Post by Hunting » January 30th, 2021, 2:20 am

ColorfulGalaxy wrote:
January 29th, 2021, 11:49 pm

Code: Select all

x = 11, y = 10, rule = LifeHistory
9.2A$9.2A$3.2C$3.C.C.4A$5.C.A2.A$A2.A.C$4A.C.C$6.2C$2A$2A!
The table on blocks could be replaced with bookends.

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Re: Smallest still lifes with specific islands

Post by Ian07 » January 30th, 2021, 9:52 am

ColorfulGalaxy wrote:
January 29th, 2021, 11:49 pm
...
Added, with some reductions by Hunting and me.
ColorfulGalaxy wrote:
January 29th, 2021, 11:49 pm

Code: Select all

(I'm not sure if it can eat gliders)
Yep:

Code: Select all

x = 10, y = 9, rule = B3/S23
2bo$obo$b2o$4b2o$4bobob2o$6bob2o$6bo$3b2obo$3b2ob2o!
Hunting wrote:
January 30th, 2021, 2:20 am
The table on blocks could be replaced with bookends.
I presume you mean eaters?

Code: Select all

x = 11, y = 8, rule = B3/S23
9b2o$3b2o5bo$3bobob3o$5bobo$3bobo$b3obobo$o5b2o$2o!

Hunting
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Re: Smallest still lifes with specific islands

Post by Hunting » January 30th, 2021, 12:44 pm

Ian07 wrote:
January 30th, 2021, 9:52 am
ColorfulGalaxy wrote:
January 29th, 2021, 11:49 pm
...
Added, with some reductions by Hunting and me.
ColorfulGalaxy wrote:
January 29th, 2021, 11:49 pm

Code: Select all

(I'm not sure if it can eat gliders)
Yep:

Code: Select all

x = 10, y = 9, rule = B3/S23
2bo$obo$b2o$4b2o$4bobob2o$6bob2o$6bo$3b2obo$3b2ob2o!
Hunting wrote:
January 30th, 2021, 2:20 am
The table on blocks could be replaced with bookends.
I presume you mean eaters?

Code: Select all

x = 11, y = 8, rule = B3/S23
9b2o$3b2o5bo$3bobob3o$5bobo$3bobo$b3obobo$o5b2o$2o!
A bookend also works.

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praosylen
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Re: Smallest still lifes with specific islands

Post by praosylen » January 30th, 2021, 1:06 pm

One more reduction:

Code: Select all

x = 11, y = 5, rule = LifeHistory
$.2A2.2C.2A$.A2.C.C.A$2.A.C.C2.A$.2A.2C2.2A!
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Re: Smallest still lifes with specific islands

Post by Moosey » January 30th, 2021, 1:22 pm

Hunting wrote:
January 30th, 2021, 12:44 pm
Ian07 wrote:
January 30th, 2021, 9:52 am
ColorfulGalaxy wrote:
January 29th, 2021, 11:49 pm
...
Added, with some reductions by Hunting and me.
ColorfulGalaxy wrote:
January 29th, 2021, 11:49 pm

Code: Select all

(I'm not sure if it can eat gliders)
Yep:

Code: Select all

x = 10, y = 9, rule = B3/S23
2bo$obo$b2o$4b2o$4bobob2o$6bob2o$6bo$3b2obo$3b2ob2o!
Hunting wrote:
January 30th, 2021, 2:20 am
The table on blocks could be replaced with bookends.
I presume you mean eaters?

Code: Select all

x = 11, y = 8, rule = B3/S23
9b2o$3b2o5bo$3bobob3o$5bobo$3bobo$b3obobo$o5b2o$2o!
A bookend also works.
rle?
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bubblegum
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Re: Smallest still lifes with specific islands

Post by bubblegum » January 30th, 2021, 2:01 pm

Convoluted hybridisation:

Code: Select all

x = 10, y = 10, rule = B3/S23
5b2o$6bo$2b2o2bob2o$2bobob2obo$4bo$4bo$b2ob2o$2bo$obo$2o!
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Re: Smallest still lifes with specific islands

Post by MathAndCode » January 30th, 2021, 2:56 pm

ColorfulGalaxy wrote:
January 29th, 2021, 11:49 pm
Any reduction?
Here are a couple of population reductions:

Code: Select all

x = 23, y = 6, rule = LifeHistory
4.2C.2A8.2C$2A.C.C.A9.C.C$.A.C.C2.A10.C$A2.2C2.2A10.C.2A$2A14.2A.C2.A$16.2A.2C!
Here are two reductions by the population of the minimum covering polypet:

Code: Select all

x = 29, y = 11, rule = LifeHistory
5.A17.2A$5.3A15.A$8.A15.A$3.4C.A14.2A$3.C2.C.2A10.2C3.2A.A$2A.C2.C13.
C.2C.A.2A$.A.4C16.C$.A16.4A2.C$2.3A13.A2.A.2C$4.A16.A$20.2A!
I am tentatively considering myself back.

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Re: Smallest still lifes with specific islands

Post by ColorfulGalaxy » January 31st, 2021, 1:26 am

Ian07 wrote:
January 30th, 2021, 9:52 am
ColorfulGalaxy wrote:
January 29th, 2021, 11:49 pm
...
Added, with some reductions by Hunting and me.
ColorfulGalaxy wrote:
January 29th, 2021, 11:49 pm

Code: Select all

(I'm not sure if it can eat gliders)
Yep:

Code: Select all

x = 10, y = 9, rule = B3/S23
2bo$obo$b2o$4b2o$4bobob2o$6bob2o$6bo$3b2obo$3b2ob2o!
Hunting wrote:
January 30th, 2021, 2:20 am
The table on blocks could be replaced with bookends.
I presume you mean eaters?

Code: Select all

x = 11, y = 8, rule = B3/S23
9b2o$3b2o5bo$3bobob3o$5bobo$3bobo$b3obobo$o5b2o$2o!
Why not add your avatar to the list?

Code: Select all

x = 10, y = 5, rule = B3/S23History
.2C.2A.2C$C.C.2A.C.C$C8.C$.4C.3C$3.C.2C!

ColorfulGabrielsp138
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Re: Smallest still lifes with specific islands

Post by ColorfulGabrielsp138 » June 26th, 2021, 5:47 am

There are obviously fewer than 38 posts here but it says "38 posts".
Soup posted by JP21:

Code: Select all

x = 13, y = 10, rule = LifeHistory
.2A7.2A$A2.A5.A2.A$.3A5.3A$6.C$3.7C$2.C7.C$2.9C2$4.2A.2A$4.2A.2A!

Code: Select all

x = 21, y = 21, rule = LifeColorful
11.E$10.3E$10.E.2E$13.E4$2.2B$.2B$2B$.2B15.2D$19.2D$18.2D$17.2D4$7.C$
7.2C.C$8.3C$9.C!
I have reduced the glider cost of quadratic growth to eight and probably to seven. Looking for conduits...

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Re: Smallest still lifes with specific islands

Post by Ian07 » June 27th, 2021, 12:18 am

ColorfulGabrielsp138 wrote:
June 26th, 2021, 5:47 am
There are obviously fewer than 38 posts here but it says "38 posts".
You sure? Between the two pages it looks like the correct number to me.

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Re: Smallest still lifes with specific islands

Post by ColorfulGabrielsp138 » August 7th, 2021, 5:57 am

Code: Select all

x = 116, y = 15, rule = LifeHistory
22.2A31.A17.A$4.A17.2A16.2A12.A.A15.A.A$2.3A35.2A13.A17.A21.2A$.A18.6C
70.A$.A2.3C13.C4.C12.4C11.5C13.5C18.C16.C$2A.C2.C10.2A.C.2A.C.2A8.C4.
C.2A6.C4.C2.A9.C5.C11.2A2.4C13.5C$3.C2.C.2A7.2A.C.2A.C.2A8.C.2A.C.2A3.
A2.C.2A.C.A.A5.A2.C2.A2.C2.A8.A2.C4.C11.C5.C$3.3C2.A11.C4.C8.2A.C.2A.
C5.A.A.C.2A.C2.A5.A.A.C.A.A.C.A.A9.2C.2A.C11.C2.A2.C$8.A11.6C8.2A.C4.
C6.A2.C4.C9.A2.C2.A2.C2.A11.C.2A.2C9.2C.A.A.2C$5.3A30.4C10.5C13.C5.C14.
C4.C2.A8.C2.A2.C$5.A16.2A47.5C16.4C2.2A8.C5.C$22.2A14.2A14.A38.C15.5C
$38.2A13.A.A17.A17.A19.C$54.A17.A.A16.2A$73.A!

Code: Select all

x = 21, y = 21, rule = LifeColorful
11.E$10.3E$10.E.2E$13.E4$2.2B$.2B$2B$.2B15.2D$19.2D$18.2D$17.2D4$7.C$
7.2C.C$8.3C$9.C!
I have reduced the glider cost of quadratic growth to eight and probably to seven. Looking for conduits...

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rattlesnake
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Re: Smallest still lifes with specific islands

Post by rattlesnake » October 2nd, 2022, 12:07 am

Reduction to https://catagolue.hatsya.com/object/xs8_1348o8/bs23

Code: Select all

x = 10, y = 12, rule = LifeHistory
4.2A$4.A$6.C.2A$5.2C.A$2A2.C4.A$A2.C2.3A$2.2C.2A$3.C$.A3.2A$.2A3.A$5.
A$5.2A!
I have discovered SKOP for 115, 188, 492 and gun_ and guntrue_ for 200, 226, 339, 752, 1944, 6624.

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breaker's glider gun
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Re: Smallest still lifes with specific islands

Post by breaker's glider gun » October 23rd, 2022, 1:53 pm

hmm... is this minimal?

Code: Select all

x = 7, y = 14, rule = LifeHistory
2.A$.C.A$C.A$C$.3CA.A$5.2A$.3A$2.A$A3.A$5A2$2.A$.A.A$2.A!
aaargh I'm horrible at this

Code: Select all

x = 25, y = 28, rule = LifeHistory
13.A$12.A.A$11.A.A.A$9.3A3.3A$8.A4.A4.A$9.4A.4A$13.A$11.A3.A$4.A6.5A$
3.A.A$3.A.A5.5A$2.2A.A.2A.A5.A$.A3.A2.A.A2.A2.A$A.A.A.A.A.A.A.A.A.A2.
A.2A$.A3.A2.A.A2.A2.A.4A.2A$2.2A.A.2A.A5.A$3.A.A5.5A.2C2.4A$3.A.A11.C
3.A2.A$4.A8.2A.C2.A.A$12.A.A.C.2A.2A$12.A3.C.A2.A$11.2A2.A.A2.A2.A$16.
A4.2A.A$23.A$21.2A$21.A$22.A$21.2A!
there go the sombreros:

Code: Select all

x = 14, y = 15, rule = LifeHistory
4.2A.A2.A.2A$5.A.4A.2A$2.A2.A$2.3A.2C2.4A$6.C3.A2.A$2.2A.C2.A.A$.A.A.
C.2A.2A$.A3.C.A2.A$2A2.A.A2.A2.A$5.A4.2A.A$12.A$10.2A$10.A$11.A$10.2A
!
:?: :?: . . . :!:
Give me a suggestion of something to draw here!

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Wyirm
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Re: Smallest still lifes with specific islands

Post by Wyirm » October 23rd, 2022, 2:08 pm

breaker's glider gun wrote:
October 23rd, 2022, 1:53 pm
Stabilizations
Are cells allowed to touch the islands? If so, a lot of work previously done is suboptimal.

Code: Select all

x = 21, y = 9, rule = LifeSuper
7.A$.C.A2.A.A10.2A$C.2A2.A.A7.2A2.A$C6.A.2C5.A.2C$.3C5.C.A6.C$3.A4.C
2.A5.C2.A$8.C.A6.C.2A$6.A.C.2A2.2A.C$6.2A6.A.2A!
All of the islands being stabilized contain cells which die due to underpopulation, and can't be stabilized through non-adjacent cells.

Code: Select all

x = 36, y = 28, rule = TripleLife
17.G$17.3G$20.G$19.2G11$9.EF$8.FG.GD$8.DGAGF$10.DGD5$2.2G$3.G30.2G$3G
25.2G5.G$G27.G.G.3G$21.2G7.G.G$21.2G7.2G!
Bow down to the Herschel

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breaker's glider gun
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Location: the inside of a stuffed anaconda or maybe [click to not expand]

Re: Smallest still lifes with specific islands

Post by breaker's glider gun » October 23rd, 2022, 2:13 pm

Wyirm wrote:
October 23rd, 2022, 2:08 pm
breaker's glider gun wrote:
October 23rd, 2022, 1:53 pm
Stabilizations
Are cells allowed to touch the islands? If so, a lot of work previously done is suboptimal.

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x = 21, y = 9, rule = LifeSuper
7.A$.C.A2.A.A10.2A$C.2A2.A.A7.2A2.A$C6.A.2C5.A.2C$.3C5.C.A6.C$3.A4.C
2.A5.C2.A$8.C.A6.C.2A$6.A.C.2A2.2A.C$6.2A6.A.2A!
All of the islands being stabilized contain cells which die due to underpopulation, and can't be stabilized through non-adjacent cells.
hmm, good question. I had been assuming so, but they probably are not allowed.
is this stabalizible?

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x = 4, y = 7, rule = LifeHistory
2.2C$2.C$.C$C$C$C$2C!
:?: :?: . . . :!:
Give me a suggestion of something to draw here!

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Ian07
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Re: Smallest still lifes with specific islands

Post by Ian07 » October 23rd, 2022, 2:19 pm

Wyirm wrote:
October 23rd, 2022, 2:08 pm
Are cells allowed to touch the islands? If so, a lot of work previously done is suboptimal.
No, sorry. They're allowed in this thread by bubblegum though.

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squareroot12621
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Re: Smallest still lifes with specific islands

Post by squareroot12621 » October 23rd, 2022, 5:20 pm

breaker's glider gun wrote:
October 23rd, 2022, 2:13 pm
…is this stabalizible?

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x = 4, y = 7, rule = LifeHistory
2.2C$2.C$.C$C$C$C$2C!
No.

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x = 53, y = 23, rule = LifeHistory
9.2C2.D5.D$8.BC4.D3.D$8.CDBE3.D.D$7.C2B2E4.D$7.C7.D.D$7.C6.D3.D$7.2C4.
D5.D2$2.2CB$2.CDB$.C2BA$C$C$C$2C2$9.2C6.2C6.2C6.2C6.2C3.D5.D$9.C2.A4.
C2.A4.C2.A4.C2.A3.BC2.A2.D3.D$8.C2.2A3.C2.2A3.C2.2A3.C2B2A3.CDB2A3.D.
D$7.C7.C2B5.C2BD4.CBDE4.C2BA6.D$7.C7.CDE5.CBFE4.CB2A4.C.2A5.D.D$7.C7.
C2B5.C2BD4.C2.F4.C2.F4.D3.D$7.2C6.2C6.2C6.2C6.2C5.D5.D!
[[ LABEL 0 8 8 "1" LABEL 7 0 8 "2" LABEL 7 16 8 "3" LABEL 15 16 8 "4" ]]
[[ LABEL 23 16 8 "5" LABEL 31 16 8 "6" LABEL 39 16 8 "7" ]]
  1. The red cell must be stabilized by overpopulation. We are not allowed to touch the white island; therefore, we cannot turn the blue cells on. The green cell is the only option.
  2. CASE 1: The option where the yellow cells are used populates the red cell to 3 neighbors. We can't use the blue cells. However, those are all of our options! Case 1 doesn't work.
  3. CASE 2: The option where the green cells are used avoids the problem in step 2.
  4. The red cell has 3 neighbors. We can't use the blue cells, so the only option is to use the yellow cell.
  5. To make the gray cell survive, at least one of the red cells must be on.
  6. The red cell currently has 3 neighbors, and the blue cells can't be used, so the yellow cell must be on. (The gray cell in steps 6 and 7 is optional.)
  7. The new red cell has 3 neighbors now! The blue cells are the only option, but they can't be used. Therefore, Case 2 doesn't work, either.
We've run out of cases! Therefore, it is impossible to stabilize this island.

Edit:
Here's an expansion of step 1.

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x = 47, y = 51, rule = LifeHistory
22.2CB$22.CDB$21.C2BA$20.C$20.C$20.C$20.2C3$16.2C4.2C.D5.D$16.C4.BC3.
D3.D$15.C5.CDB3.D.D$14.C2.A2.C2BA4.D$14.C5.C6.D.D$14.C5.C5.D3.D$14.2C
4.2C3.D5.D3$2.2C6.2C6.2C6.2C6.2C6.2C$2.C7.C7.C2.E4.C7.C2.E4.C2.E$.C2.
A4.C2.AE3.C2.A4.C2.AE3.C2.A4.C2.AE$C3.2E2.C3.E3.C3.E3.C4.E2.C4.E2.C$C
7.C7.C7.C7.C7.C$C7.C7.C7.C7.C7.C$2C6.2C6.2C6.2C6.2C6.2C2$D20.D2.D12.D
$22D2.14D2.D5.D$41.D3.D$6.2C2.D5.D12.2D2.D8.D.D$6.C2B2.D3.D12.D2.2D10.
D$5.CBDA3.D.D27.D.D$4.C.BFA4.D15.2D2.D7.D3.D$4.C7.D.D13.D2.2D7.D5.D$4.
C6.D3.D$4.2C4.D5.D13.2C$30.C2.E$29.C2.AE$28.C$28.C$28.C$28.2C3$28.D5.
D$29.D3.D$30.D.D$31.D$30.D.D$29.D3.D$28.D5.D!
[[ LABEL 20 0 8 "1" LABEL 14 9 8 "2" LABEL 0 18 8 "3A" LABEL 8 18 8 "3B" ]]
[[ LABEL 16 18 8 "3C" LABEL 24 18 8 "3D" LABEL 32 18 8 "3E" LABEL 40 18 8 "3F" ]]
  1. The red cell has 3 neighbors. The blue cells can't be used. Therefore, the green cell must be on.
  2. If the green cell is on, the red cell has 3 neighbors. The only remaining options (blue) can't be used.
  3. There are six remaining stabilizations that work.
    • A, B, and C don't work for the same reason each time. The red cell has 3 neighbors, but the gray cell can't be used (see step 2), and the blue cells can't be used because of the adjacent white cells.
    • D, E, and F are variations of the same theme. They don't work; this is covered in the first part of the post.

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4b8o$4b8o$4b8o$4b8o$4o8b4o$4o8b4o$4o8b4o$4o8b4o$4o8b4o$4o8b4o$4o8b4o$4o8b4o$4b8o$4b8o$4b8o$4b8o![[ THEME 0 AUTOSTART GPS 8 Z 16 T 1 T 1 Z 19.027 T 2 T 2 Z 22.627 T 3 T 3 Z 26.909 T 4 T 4 Z 32 T 5 T 5 Z 38.055 T 6 T 6 Z 45.255 T 7 T 7 Z 53.817 LOOP 8 ]]

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