Solitaire of Life

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AforAmpere
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Solitaire of Life

Post by 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:

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.
I and wildmyron manage the 5S project, which collects all known spaceship speeds in Isotropic Non-totalistic rules.

Things to work on:
- Find a (7,1)c/8 ship in a Non-totalistic rule
- Finish a rule with ships with period >= f_e_0(n) (in progress)

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danny
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Re: Solitaire of Life

Post by 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:

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!
she/they // dani

"I'm always on duty, even when I'm off duty." -Cody Kolodziejzyk, Ph.D.

AforAmpere
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Re: Solitaire of Life

Post by 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:

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!
I and wildmyron manage the 5S project, which collects all known spaceship speeds in Isotropic Non-totalistic rules.

Things to work on:
- Find a (7,1)c/8 ship in a Non-totalistic rule
- Finish a rule with ships with period >= f_e_0(n) (in progress)

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danny
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Re: Solitaire of Life

Post by 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:

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!
she/they // dani

"I'm always on duty, even when I'm off duty." -Cody Kolodziejzyk, Ph.D.

AforAmpere
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Re: Solitaire of Life

Post by AforAmpere » January 19th, 2018, 9:59 pm

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!
I and wildmyron manage the 5S project, which collects all known spaceship speeds in Isotropic Non-totalistic rules.

Things to work on:
- Find a (7,1)c/8 ship in a Non-totalistic rule
- Finish a rule with ships with period >= f_e_0(n) (in progress)

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Kazyan
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Re: Solitaire of Life

Post by Kazyan » January 19th, 2018, 10:09 pm

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!
Tanner Jacobi

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dvgrn
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Re: Solitaire of Life

Post by 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?

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
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Re: Solitaire of Life

Post by 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.
Last edited by Bullet51 on January 11th, 2019, 1:26 am, edited 1 time in total.
Still drifting.

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danny
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Re: Solitaire of Life

Post by 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 9900 times
she/they // dani

"I'm always on duty, even when I'm off duty." -Cody Kolodziejzyk, Ph.D.

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A for awesome
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Re: Solitaire of Life

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

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!
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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Macbi
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Re: Solitaire of Life

Post by Macbi » January 20th, 2018, 1:20 pm

A for awesome wrote: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.

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danny
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Re: Solitaire of Life

Post by 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.
she/they // dani

"I'm always on duty, even when I'm off duty." -Cody Kolodziejzyk, Ph.D.

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Macbi
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Re: Solitaire of Life

Post by 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.

AforAmpere
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Re: Solitaire of Life

Post by 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:

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.
I and wildmyron manage the 5S project, which collects all known spaceship speeds in Isotropic Non-totalistic rules.

Things to work on:
- Find a (7,1)c/8 ship in a Non-totalistic rule
- Finish a rule with ships with period >= f_e_0(n) (in progress)

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BlinkerSpawn
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Re: Solitaire of Life

Post by BlinkerSpawn » January 24th, 2018, 10:07 pm

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!
Last edited by BlinkerSpawn on January 24th, 2018, 11:04 pm, edited 4 times in total.
LifeWiki: Like Wikipedia but with more spaceships. [citation needed]

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AforAmpere
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Re: Solitaire of Life

Post by AforAmpere » January 24th, 2018, 10:21 pm

Is 33 the smallest? I have tried not to check with WLS.
I and wildmyron manage the 5S project, which collects all known spaceship speeds in Isotropic Non-totalistic rules.

Things to work on:
- Find a (7,1)c/8 ship in a Non-totalistic rule
- Finish a rule with ships with period >= f_e_0(n) (in progress)

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A for awesome
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Re: Solitaire of Life

Post by 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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BlinkerSpawn
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Re: Solitaire of Life

Post by BlinkerSpawn » January 25th, 2018, 12:02 am

A for awesome wrote: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!
LifeWiki: Like Wikipedia but with more spaceships. [citation needed]

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Macbi
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Re: Solitaire of Life

Post by Macbi » January 25th, 2018, 5:43 am

BlinkerSpawn wrote:
A for awesome wrote: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.

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Re: Solitaire of Life

Post by wildmyron » January 25th, 2018, 6:13 am

Macbi wrote: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!
The latest version of the 5S Project contains over 221,000 spaceships. Tabulated pages up to period 160 are available on the LifeWiki.

AbhpzTa
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Re: Solitaire of Life

Post by AbhpzTa » January 25th, 2018, 7:42 am

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!
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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Macbi
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Re: Solitaire of Life

Post by Macbi » January 25th, 2018, 7:44 am

Still nonoptimal.

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Re: Solitaire of Life

Post by AbhpzTa » January 25th, 2018, 9:30 am

Macbi wrote: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!
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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Macbi
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Re: Solitaire of Life

Post by Macbi » January 25th, 2018, 9:33 am

Not there yet.

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Re: Solitaire of Life

Post by BlinkerSpawn » January 25th, 2018, 10:05 am

Macbi wrote: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!
LifeWiki: Like Wikipedia but with more spaceships. [citation needed]

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