Solitaire of Life

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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:
x = 8, y = 8, rule = LifeHistory3.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 = LifeHistory2.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 = LifeHistoryC2$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 AforAmpere Posts: 960 Joined: July 1st, 2016, 3:58 pm Re: Solitaire of Life 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 = LifeHistoryC2$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 = LifeHistory9.2C$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 // Please stop using my full name. Refer to me as dani.

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

danny

Posts: 927
Joined: October 27th, 2017, 3:43 pm
Location: New Jersey, USA

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:
x = 17, y = 12, rule = LifeHistory2.2A$3.A2.A$.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 AforAmpere Posts: 960 Joined: July 1st, 2016, 3:58 pm 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: x = 17, y = 12, rule = LifeHistory2.2A$3.A2.A$.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 = LifeHistory2.2A$3.A2.A$.C2.3A$A.2A5.2A$.A2.A3.A.C$3.C.A2.A$2.AC2.C.A.A4.2C$4.C.C2.2C4.CA$4.A.C$2.2A.A3.3AC$2.A2.C.A2.A2.A$4.AC.2A3.2A! EDIT: 50: x = 18, y = 12, rule = LifeHistory2A$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 // Please stop using my full name. Refer to me as dani.

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

danny

Posts: 927
Joined: October 27th, 2017, 3:43 pm
Location: New Jersey, USA

Re: Solitaire of Life

Nice! 48:
x = 17, y = 11, rule = LifeHistory2A$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
AforAmpere

Posts: 960
Joined: July 1st, 2016, 3:58 pm

Re: Solitaire of Life

I managed 34:

x = 16, y = 11, rule = LifeHistory2A$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

Kazyan

Posts: 789
Joined: February 6th, 2014, 11:02 pm

Re: Solitaire of Life

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 = LifeHistoryC$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$3.AC! dvgrn Moderator Posts: 5455 Joined: May 17th, 2009, 11:00 pm Location: Madison, WI Re: Solitaire of Life AforAmpere wrote:I hope this is original. The game's goal is to find the smallest still-life stabilization for a collection of cells, with all pre-placed cells having 3 or less neighbors. The game has been proposed by me in 2015, in our Chinese forum. Last edited by Bullet51 on January 11th, 2019, 1:26 am, edited 1 time in total. Still drifting. Bullet51 Posts: 518 Joined: July 21st, 2014, 4:35 am Re: Solitaire of Life Bullet51 wrote:{image that may show up strangely for some (it did the first time for me)} In case you see a weird, not-cgol image, here is the image: goly.png (155.77 KiB) Viewed 8604 times she/they // Please stop using my full name. Refer to me as dani. "I'm always on duty, even when I'm off duty." -Cody Kolodziejzyk, Ph.D. danny Posts: 927 Joined: October 27th, 2017, 3:43 pm Location: New Jersey, USA Re: Solitaire of Life For that particular one, this seems to be optimal: x = 5, y = 5, rule = LifeHistory2.C$.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 A for awesome Posts: 1751 Joined: September 13th, 2014, 5:36 pm Location: 0x-1 Re: Solitaire of Life A for awesome wrote:For that particular one, this seems to be optimal: x = 5, y = 5, rule = LifeHistory2.C$.A.A$C.A.C$.A2.A$2.CA! Yes, I checked with a computer and that is the unique winner. Macbi Posts: 629 Joined: March 29th, 2009, 4:58 am Re: Solitaire of Life I think maybe we could use search programs to find the minimal *amount* of cells, just not post the actual pattern, which would make it fun to reach a goal. Just my 2 cents though. she/they // Please stop using my full name. Refer to me as dani. "I'm always on duty, even when I'm off duty." -Cody Kolodziejzyk, Ph.D. danny Posts: 927 Joined: October 27th, 2017, 3:43 pm Location: New Jersey, USA Re: Solitaire of Life Or don't even announce the number of cells, just when someone has won. For example I already cheated on the first one, so I can tell you that 34 isn't yet the minimal possible number of cells. Macbi Posts: 629 Joined: March 29th, 2009, 4:58 am Re: Solitaire of Life Macbi wrote:Or don't even announce the number of cells, just when someone has won. For example I already cheated on the first one, so I can tell you that 34 isn't yet the minimal possible number of cells. I agree, it would be good to know when there is the minimum, but not what the minimum is. EDIT, a different approach, getting 35: x = 17, y = 12, rule = LifeHistory.C$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
AforAmpere

Posts: 960
Joined: July 1st, 2016, 3:58 pm

Re: Solitaire of Life

Two more related 34s:
x = 16, y = 22, rule = LifeHistoryC$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.A2.A$2.A2.A2.A2.C$4.CA3.2A! EDIT: Ooh, don't forget this one: x = 16, y = 10, rule = LifeHistory2A$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 = LifeHistory2A$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 = LifeHistory2A$CA$9.2A$9.CA$2.CA$2.C2.CA7.2C$3.C.C2.2C4.CA$2.2A.C.2A2.A$2.A2.A4.AC$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 = LifeHistory3.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] BlinkerSpawn Posts: 1845 Joined: November 8th, 2014, 8:48 pm Location: Getting a snacker from R-Bee's Re: Solitaire of Life 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 AforAmpere Posts: 960 Joined: July 1st, 2016, 3:58 pm Re: Solitaire of Life 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 Aidan F. Pierce A for awesome Posts: 1751 Joined: September 13th, 2014, 5:36 pm Location: 0x-1 Re: Solitaire of Life A for awesome wrote:Still not minimal. Ugh, if you insist... x = 16, y = 11, rule = LifeHistory2A$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$4.2A! LifeWiki: Like Wikipedia but with more spaceships. [citation needed] BlinkerSpawn Posts: 1845 Joined: November 8th, 2014, 8:48 pm Location: Getting a snacker from R-Bee's Re: Solitaire of Life BlinkerSpawn wrote: A for awesome wrote:Still not minimal. Ugh, if you insist... x = 16, y = 11, rule = LifeHistory2A$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/S232o$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 = LifeHistory3.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.

Macbi

Posts: 629
Joined: March 29th, 2009, 4:58 am

Re: Solitaire of Life

Macbi wrote:So I guess we accept your new puzzle as the next one to work on.
x = 10, y = 8, rule = LifeHistory3.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 = LifeHistory2.A4.2A$.A.C3.CA$.A.C$2A.A.C$2.C.A.A.2A$2.C.A.C.AC$.2A.A.A$A2.C2.A$CA2.2C!
wildmyron

Posts: 1058
Joined: August 9th, 2013, 12:45 am

Re: Solitaire of Life

31 cells:
x = 10, y = 9, rule = LifeHistory2.2A2.2A$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).
AbhpzTa

Posts: 457
Joined: April 13th, 2016, 9:40 am
Location: Ishikawa Prefecture, Japan

Re: Solitaire of Life

Still nonoptimal.

Macbi

Posts: 629
Joined: March 29th, 2009, 4:58 am

Re: Solitaire of Life

Macbi wrote:Still nonoptimal.

30 cells:
x = 11, y = 10, rule = LifeHistory7.2A$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). AbhpzTa Posts: 457 Joined: April 13th, 2016, 9:40 am Location: Ishikawa Prefecture, Japan Re: Solitaire of Life Not there yet. Macbi Posts: 629 Joined: March 29th, 2009, 4:58 am Re: Solitaire of Life Macbi wrote:Not there yet. Well? x = 11, y = 8, rule = LifeHistory4.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]