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Solitaire of Life

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Solitaire of Life

Postby AforAmpere » January 19th, 2018, 8:51 pm

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:
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:
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:
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.
Things to work on:
- Find a (7,1)c/8 ship in a Non-totalistic rule (someone please search the rules)
- Find a C/10 in JustFriends
- Find a C/10 in Day and Night
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Re: Solitaire of Life

Postby danny » January 19th, 2018, 9:24 pm

AforAmpere wrote:Answers will be ranked by the cell count of the stabilized constellation. As a first challenge, try this:
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:
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!
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Re: Solitaire of Life

Postby AforAmpere » January 19th, 2018, 9:45 pm

I don't know if this can be improved, but the block is nice, as less cells are needed, 55 total:
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!
Things to work on:
- Find a (7,1)c/8 ship in a Non-totalistic rule (someone please search the rules)
- Find a C/10 in JustFriends
- Find a C/10 in Day and Night
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Re: Solitaire of Life

Postby danny » January 19th, 2018, 9:52 pm

AforAmpere wrote:I don't know if this can be improved, but the block is nice, as less cells are needed, 55 total:
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:
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:
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!
I prefer Dani now, but Danny is fine seeing as it's my username and I've already made 4 too many accounts.
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Re: Solitaire of Life

Postby AforAmpere » January 19th, 2018, 9:59 pm

Nice! 48:
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!
Things to work on:
- Find a (7,1)c/8 ship in a Non-totalistic rule (someone please search the rules)
- Find a C/10 in JustFriends
- Find a C/10 in Day and Night
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Re: Solitaire of Life

Postby Kazyan » January 19th, 2018, 10:09 pm

I managed 34:

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!
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Re: Solitaire of Life

Postby dvgrn » January 20th, 2018, 2:42 am

Kazyan wrote:I managed 34...

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

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!
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Re: Solitaire of Life

Postby Bullet51 » January 20th, 2018, 11:02 am

AforAmpere wrote: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
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
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.

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Re: Solitaire of Life

Postby danny » January 20th, 2018, 12:26 pm

Bullet51 wrote:{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
goly.png (155.77 KiB) Viewed 6254 times
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Re: Solitaire of Life

Postby A for awesome » January 20th, 2018, 12:31 pm

For that particular one, this seems to be optimal:
x = 5, y = 5, rule = LifeHistory
2.C$.A.A$C.A.C$.A2.A$2.CA!
x₁=ηx
V ⃰_η=c²√(Λη)
K=(Λu²)/2
Pₐ=1−1/(∫^∞_t₀(p(t)ˡ⁽ᵗ⁾)dt)

$$x_1=\eta x$$
$$V^*_\eta=c^2\sqrt{\Lambda\eta}$$
$$K=\frac{\Lambda u^2}2$$
$$P_a=1-\frac1{\int^\infty_{t_0}p(t)^{l(t)}dt}$$

http://conwaylife.com/wiki/A_for_all

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Re: Solitaire of Life

Postby Macbi » January 20th, 2018, 1:20 pm

A for awesome wrote:For that particular one, this seems to be optimal:
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.
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Re: Solitaire of Life

Postby danny » January 20th, 2018, 1:22 pm

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.
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Re: Solitaire of Life

Postby Macbi » January 20th, 2018, 1:29 pm

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.
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Re: Solitaire of Life

Postby AforAmpere » January 20th, 2018, 1:31 pm

Macbi wrote: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:
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.
Things to work on:
- Find a (7,1)c/8 ship in a Non-totalistic rule (someone please search the rules)
- Find a C/10 in JustFriends
- Find a C/10 in Day and Night
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Re: Solitaire of Life

Postby BlinkerSpawn » January 24th, 2018, 10:07 pm

Two more related 34s:
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:
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!
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:
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:
x = 10, y = 8, rule = LifeHistory
3.C3.C$3.C$5.C$2.C$2.C3.C2.C2$3.C$C3.2C!
Last edited by BlinkerSpawn on January 24th, 2018, 11:04 pm, edited 4 times in total.
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Re: Solitaire of Life

Postby AforAmpere » January 24th, 2018, 10:21 pm

Is 33 the smallest? I have tried not to check with WLS.
Things to work on:
- Find a (7,1)c/8 ship in a Non-totalistic rule (someone please search the rules)
- Find a C/10 in JustFriends
- Find a C/10 in Day and Night
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Re: Solitaire of Life

Postby A for awesome » January 24th, 2018, 11:23 pm

Still not minimal.
x₁=ηx
V ⃰_η=c²√(Λη)
K=(Λu²)/2
Pₐ=1−1/(∫^∞_t₀(p(t)ˡ⁽ᵗ⁾)dt)

$$x_1=\eta x$$
$$V^*_\eta=c^2\sqrt{\Lambda\eta}$$
$$K=\frac{\Lambda u^2}2$$
$$P_a=1-\frac1{\int^\infty_{t_0}p(t)^{l(t)}dt}$$

http://conwaylife.com/wiki/A_for_all

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Re: Solitaire of Life

Postby BlinkerSpawn » January 25th, 2018, 12:02 am

A for awesome wrote:Still not minimal.

Ugh, if you insist...
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!
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Re: Solitaire of Life

Postby Macbi » January 25th, 2018, 5:43 am

BlinkerSpawn wrote:
A for awesome wrote:Still not minimal.

Ugh, if you insist...
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:
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.

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.
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Re: Solitaire of Life

Postby wildmyron » January 25th, 2018, 6:13 am

Macbi wrote:So I guess we accept your new puzzle as the next one to work on.
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
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!
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Re: Solitaire of Life

Postby AbhpzTa » January 25th, 2018, 7:42 am

31 cells:
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!
Iteration of sigma(n)+tau(n)-n [sigma(n)+tau(n)-n : OEIS A163163] (e.g. 16,20,28,34,24,44,46,30,50,49,11,3,3, ...) :
965808 is period 336 (max = 207085118608).
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Re: Solitaire of Life

Postby Macbi » January 25th, 2018, 7:44 am

Still nonoptimal.
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Re: Solitaire of Life

Postby AbhpzTa » January 25th, 2018, 9:30 am

Macbi wrote:Still nonoptimal.


30 cells:
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!
Iteration of sigma(n)+tau(n)-n [sigma(n)+tau(n)-n : OEIS A163163] (e.g. 16,20,28,34,24,44,46,30,50,49,11,3,3, ...) :
965808 is period 336 (max = 207085118608).
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Re: Solitaire of Life

Postby Macbi » January 25th, 2018, 9:33 am

Not there yet.
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Re: Solitaire of Life

Postby BlinkerSpawn » January 25th, 2018, 10:05 am

Macbi wrote:Not there yet.

Well?
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!
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