Solitaire of Life

[AforAmpere]

I hope this is original. The game's goal is to find the smallest still-life stabilization for a collection of cells, with all pre-placed cells having 3 or less neighbors. If one answer can't be beaten, a new challenge is made. As an example, take these cells:

Code: Select all

x = 8, y = 8, rule = LifeHistory
3.C.C$.C3.C$C2.C.C$C2$6.2C$4.C2.C$2.C!


The goal is to find the smallest still-life (or constellation of them) that stabilizes all of the cells. IN this particular case, I believe the smallest stabilization is this, with 23 total cells:

Code: Select all

x = 8, y = 9, rule = LifeHistory
2.AC.CA$.C.A.C$C2.C.C$CA2.A2$6.2C$3.AC2.C$2.C2.2A$2.2A!


Answers will be ranked by the cell count of the stabilized constellation. As a first challenge, try this:

Code: Select all

x = 16, y = 10, rule = LifeHistory
C2$9.C$2.C$2.C2.C8.2C$3.C.C2.2C4.C$5.C$11.C$4.C$4.C!


Please don't use WLS, or JLS to find solutions.

[danny]

Answers will be ranked by the cell count of the stabilized constellation. As a first challenge, try this:

Code: Select all

x = 16, y = 10, rule = LifeHistory
C2$9.C$2.C$2.C2.C8.2C$3.C.C2.2C4.C$5.C$11.C$4.C$4.C!


Probably suboptimal,75 cells:

Code: Select all

x = 18, y = 14, rule = LifeHistory
9.2C$9.C2.2C$10.C.C$A2.C.2C2.2C.C$4C.C.C4.2C$5.C.C.AC.C$2.AC.C.C.C2.C
$2.A2.A.C2.C.C.2A$3.A.A.C2AC.C.A$4.CA6.C.C$7.4CAC.C.2C$4.AC.C6.2C.C$
4.A.C3.C.2C$10.2C.C!


[AforAmpere]

I don't know if this can be improved, but the block is nice, as less cells are needed, 55 total:

Code: Select all

x = 17, y = 12, rule = LifeHistory
2.2A$3.A2.A$.C2.3A$A.2A5.2A$.A2.A3.A.C$3.C.A2.A$2.AC2.C.A.A4.2C$.A2.C
.C2.2C4.CA$.A.2A.C$2.A2.A3.3AC$3.A.C.A2.A2.A$4.AC.2A3.2A!


[danny]

I don't know if this can be improved, but the block is nice, as less cells are needed, 55 total:

Code: Select all

x = 17, y = 12, rule = LifeHistory
2.2A$3.A2.A$.C2.3A$A.2A5.2A$.A2.A3.A.C$3.C.A2.A$2.AC2.C.A.A4.2C$.A2.C
.C2.2C4.CA$.A.2A.C$2.A2.A3.3AC$3.A.C.A2.A2.A$4.AC.2A3.2A!


My mistake: I thought it all had to be connected.

53 cell reduction:

Code: Select all

x = 17, y = 12, rule = LifeHistory
2.2A$3.A2.A$.C2.3A$A.2A5.2A$.A2.A3.A.C$3.C.A2.A$2.AC2.C.A.A4.2C$4.C.C
2.2C4.CA$4.A.C$2.2A.A3.3AC$2.A2.C.A2.A2.A$4.AC.2A3.2A!


EDIT: 50:

Code: Select all

x = 18, y = 12, rule = LifeHistory
2A$A.A$2.C$.A.2A5.2A$2.A2.A3.A.C$4.C.A2.A$3.AC2.C.A.A4.2C$5.C.C2.2C4.
CA$5.A.C$3.2A.A3.3AC$3.A2.C.A2.A2.A$5.AC.2A3.2A!


[AforAmpere]

Nice! 48:

Code: Select all

x = 17, y = 11, rule = LifeHistory
2A$AC$9.2A$2A2.A3.A.C$A2.C.A2.A$2.AC2.C.A.A4.2C$4.C.C2.2C4.CA$4.A.C$
2.2A.A3.3AC$2.A2.C.A2.A2.A$4.AC.2A3.2A!


[Kazyan]

I managed 34:

Code: Select all

x = 16, y = 11, rule = LifeHistory
2A$CA$9.2A$3.A5.CA$2.C.A$2.C2.C8.2C$3.C.C2.2C4.CA$2.2A.C.A2.A$4.A.A2.
A.C$4.C5.A$3.AC!

[dvgrn]

I managed 34...

"Smallest", eh? Is a smaller bounding box considered an improvement, at the same cell count?

Code: Select all

x = 16, y = 10, rule = LifeHistory
C$3A6.2A$3.A5.CA$2.C.A$2.C2.C8.2C$3.C.C2.2C4.CA$2.2A.C.A2.A$4.A.A2.A.
C$4.C5.A$3.AC!

[Bullet51]

I hope this is original. The game's goal is to find the smallest still-life stabilization for a collection of cells, with all pre-placed cells having 3 or less neighbors.

The game has been proposed by me in 2015, in our Chinese forum.

The Chinese sentence

Code: Select all

在左图中添加尽量少的格点，使得它成为稳态:
我的最好方案如右图，为9个格点。

means

Code: Select all

Add cells as less as possible to stabilize the pattern in the left into a still-life:
The best I can achieve is shown in the right, with 9 cells.

[danny]

{image that may show up strangely for some (it did the first time for me)}

In case you see a weird, not-cgol image, here is the image:

goly.png (155.77 KiB) Viewed 2374 times

[A for awesome]

For that particular one, this seems to be optimal:

Code: Select all

x = 5, y = 5, rule = LifeHistory
2.C$.A.A$C.A.C$.A2.A$2.CA!


[Macbi]

For that particular one, this seems to be optimal:

Code: Select all

x = 5, y = 5, rule = LifeHistory
2.C$.A.A$C.A.C$.A2.A$2.CA!


Yes, I checked with a computer and that is the unique winner.

[danny]

I think maybe we could use search programs to find the minimal *amount* of cells, just not post the actual pattern, which would make it fun to reach a goal. Just my 2 cents though.

[Macbi]

Or don't even announce the number of cells, just when someone has won. For example I already cheated on the first one, so I can tell you that 34 isn't yet the minimal possible number of cells.

[AforAmpere]

Or don't even announce the number of cells, just when someone has won. For example I already cheated on the first one, so I can tell you that 34 isn't yet the minimal possible number of cells.

I agree, it would be good to know when there is the minimum, but not what the minimum is.

EDIT, a different approach, getting 35:

Code: Select all

x = 17, y = 12, rule = LifeHistory
.C$A.A6.2A$.A.A5.AC$3.C$3.C.AC8.2C$4.C.C2.2C4.CA$6.C.A2.A$6.A2.A2.C$
5.CA3.2A$5.C$7.A$6.2A!


I have no idea of how to get under 34.

[BlinkerSpawn]

Two more related 34s:

Code: Select all

x = 16, y = 22, rule = LifeHistory
C$3A$3.A5.CA$2.C.A3.A.A$2.C2.C.A6.2C$3.C.C.A2C4.CA$2.2A.C4.A$2.A2.A3.
A.C$3.AC5.A5$C$3A$3.A4.AC$2.C.A3.2A$2.C2.C8.2C$3.C.C2.2C4.CA$2.2A.C.A
2.A$2.A2.A2.A2.C$4.CA3.2A!


EDIT: Ooh, don't forget this one:

Code: Select all

x = 16, y = 10, rule = LifeHistory
2A$CA$9.A$7.2AC$2.CA2.A$2.C2.C.A6.2C$3.C.C.A2C4.CA$2.2A.C4.A$2.A2.A3.
A.C$3.AC5.A!


Eureka!

Code: Select all

x = 16, y = 10, rule = LifeHistory
2A$CA2$9.CA$2.CA6.A$2.C2.CA.A5.2C$3.C.C.A2C4.CA$2.2A.C4.A$2.A2.A3.A.C
$3.AC5.A!


EDIT 2: Another 33:

Code: Select all

x = 16, y = 10, rule = LifeHistory
2A$CA$9.2A$9.CA$2.CA$2.C2.CA7.2C$3.C.C2.2C4.CA$2.2A.C.2A2.A$2.A2.A4.A
C$4.CA!


32 looks even more doubtful.
EDIT 3: In the event that 33 is minimal for that, here's my proposal, on which I have 32:

Code: Select all

x = 10, y = 8, rule = LifeHistory
3.C3.C$3.C$5.C$2.C$2.C3.C2.C2$3.C$C3.2C!


[AforAmpere]

Is 33 the smallest? I have tried not to check with WLS.

[A for awesome]

Still not minimal.

[BlinkerSpawn]

Still not minimal.

Ugh, if you insist...

Code: Select all

x = 16, y = 11, rule = LifeHistory
2A$CA$8.A$7.A.C$2.CA2.A.A$2.C2.C.A6.2C$3.C.C2.2CA3.CA$4.AC5.A$10.AC$
4.CA$4.2A!


[Macbi]

Still not minimal.

Ugh, if you insist...

Code: Select all

x = 16, y = 11, rule = LifeHistory
2A$CA$8.A$7.A.C$2.CA2.A.A$2.C2.C.A6.2C$3.C.C2.2CA3.CA$4.AC5.A$10.AC$
4.CA$4.2A!


Winner! (By the way there's one of the required cells (at the bottom left) that you didn't highlight. If you don't need that cell you can get it in 31.)

If you wanted a smaller bounding box (from 16*11 = 176 to 17*10 = 170, which is optimal) you could move the block down like this:

Code: Select all

x = 17, y = 10, rule = B3/S23
2o$2o7bo$8bobo$3b2o2bobo$3bo2bobo6b2o$4bobo2b3o3b2o$5b2o5bo$11b2o$5b2o
$5b2o!

So I guess we accept your new puzzle as the next one to work on.

Code: Select all

x = 10, y = 8, rule = LifeHistory
3.C3.C$3.C$5.C$2.C$2.C3.C2.C2$3.C$C3.2C!


I gave it a go, but I couldn't make a still life at all! Does anyone have any tips?

For this one I've cheated again. It turns out that 32 cells is not optimum.

[wildmyron]

So I guess we accept your new puzzle as the next one to work on.

Code: Select all

x = 10, y = 8, rule = LifeHistory
3.C3.C$3.C$5.C$2.C$2.C3.C2.C2$3.C$C3.2C!

The best I can manage is 34 cells

Code: Select all

x = 10, y = 9, rule = LifeHistory
2.A4.2A$.A.C3.CA$.A.C$2A.A.C$2.C.A.A.2A$2.C.A.C.AC$.2A.A.A$A2.C2.A$CA
2.2C!

[AbhpzTa]

31 cells:

Code: Select all

x = 10, y = 9, rule = LifeHistory
2.2A2.2A$3.C3.C$3.C.A$.2A2.CA$2.C.A3.2A$2.C.2ACA.C$.2A$A2.C.A$CA2.2C!

[Macbi]

Still nonoptimal.

[AbhpzTa]

Still nonoptimal.

30 cells:

Code: Select all

x = 11, y = 10, rule = LifeHistory
7.2A$3.AC.A.C$4.C.A$3.A2.C$3.C.A$2.AC2.ACA.C$4.A.A2.2A$4.C2.A$AC3.2C$
2A!

[Macbi]

Not there yet.

[BlinkerSpawn]

Not there yet.

Well?

Code: Select all

x = 11, y = 8, rule = LifeHistory
4.CA.AC$4.C3.A$5.AC$3.C.A$.2AC.A.C.AC$A3.A2.2A.A$.A2.C.A$AC3.2C!