Solitaire of Life

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AforAmpere
Posts: 1050
Joined: July 1st, 2016, 3:58 pm

Solitaire of Life

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) danny Posts: 969 Joined: October 27th, 2017, 3:43 pm Location: New Jersey, USA Contact: Re: Solitaire of Life 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
Posts: 1050
Joined: July 1st, 2016, 3:58 pm

Re: Solitaire of Life

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) danny Posts: 969 Joined: October 27th, 2017, 3:43 pm Location: New Jersey, USA Contact: Re: Solitaire of Life 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
Posts: 1050
Joined: July 1st, 2016, 3:58 pm

Re: Solitaire of Life

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)

Kazyan
Posts: 869
Joined: February 6th, 2014, 11:02 pm

Re: Solitaire of Life

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

dvgrn
Moderator
Posts: 5894
Joined: May 17th, 2009, 11:00 pm
Contact:

Re: Solitaire of Life

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$3.AC! Bullet51 Posts: 536 Joined: July 21st, 2014, 4:35 am Re: Solitaire of Life AforAmpere wrote:I hope this is original. The game's goal is to find the smallest still-life stabilization for a collection of cells, with all pre-placed cells having 3 or less neighbors. The game has been proposed by me in 2015, in our Chinese forum. Last edited by Bullet51 on January 11th, 2019, 1:26 am, edited 1 time in total. Still drifting. danny Posts: 969 Joined: October 27th, 2017, 3:43 pm Location: New Jersey, USA Contact: Re: Solitaire of Life Bullet51 wrote:{image that may show up strangely for some (it did the first time for me)} In case you see a weird, not-cgol image, here is the image: goly.png (155.77 KiB) Viewed 9900 times she/they // dani "I'm always on duty, even when I'm off duty." -Cody Kolodziejzyk, Ph.D. A for awesome Posts: 1904 Joined: September 13th, 2014, 5:36 pm Location: 0x-1 Contact: Re: Solitaire of Life For that particular one, this seems to be optimal: Code: Select all x = 5, y = 5, rule = LifeHistory 2.C$.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 Aidan F. Pierce Macbi Posts: 699 Joined: March 29th, 2009, 4:58 am Re: Solitaire of Life 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$2.CA!  Yes, I checked with a computer and that is the unique winner. danny Posts: 969 Joined: October 27th, 2017, 3:43 pm Location: New Jersey, USA Contact: Re: Solitaire of Life I think maybe we could use search programs to find the minimal *amount* of cells, just not post the actual pattern, which would make it fun to reach a goal. Just my 2 cents though. she/they // dani "I'm always on duty, even when I'm off duty." -Cody Kolodziejzyk, Ph.D. Macbi Posts: 699 Joined: March 29th, 2009, 4:58 am Re: Solitaire of Life Or don't even announce the number of cells, just when someone has won. For example I already cheated on the first one, so I can tell you that 34 isn't yet the minimal possible number of cells. AforAmpere Posts: 1050 Joined: July 1st, 2016, 3:58 pm Re: Solitaire of Life Macbi wrote:Or don't even announce the number of cells, just when someone has won. For example I already cheated on the first one, so I can tell you that 34 isn't yet the minimal possible number of cells. I agree, it would be good to know when there is the minimum, but not what the minimum is. EDIT, a different approach, getting 35: Code: Select all x = 17, y = 12, rule = LifeHistory .C$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)

Posts: 1908
Joined: November 8th, 2014, 8:48 pm
Location: Getting a snacker from R-Bee's

Re: Solitaire of Life

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
4.CA$4.2A!  LifeWiki: Like Wikipedia but with more spaceships. [citation needed] Macbi Posts: 699 Joined: March 29th, 2009, 4:58 am Re: Solitaire of Life BlinkerSpawn wrote: A for awesome wrote:Still not minimal. Ugh, if you insist... Code: Select all x = 16, y = 11, rule = LifeHistory 2A$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.

wildmyron
Posts: 1274
Joined: August 9th, 2013, 12:45 am

Re: Solitaire of Life

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
Posts: 475
Joined: April 13th, 2016, 9:40 am
Location: Ishikawa Prefecture, Japan

Re: Solitaire of Life

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).

Macbi
Posts: 699
Joined: March 29th, 2009, 4:58 am

Re: Solitaire of Life

Still nonoptimal.

AbhpzTa
Posts: 475
Joined: April 13th, 2016, 9:40 am
Location: Ishikawa Prefecture, Japan

Re: Solitaire of Life

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). Macbi Posts: 699 Joined: March 29th, 2009, 4:58 am Re: Solitaire of Life Not there yet. BlinkerSpawn Posts: 1908 Joined: November 8th, 2014, 8:48 pm Location: Getting a snacker from R-Bee's Re: Solitaire of Life 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]