## Solitaire of Life

A forum where anything goes. Introduce yourselves to other members of the forums, discuss how your name evolves when written out in the Game of Life, or just tell us how you found it. This is the forum for "non-academic" content.

### 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: 734 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!
get down with the sickness.

danny

Posts: 619
Joined: October 27th, 2017, 3:43 pm
Location: i love to eat bees

### 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: 734 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!
get down with the sickness.

danny

Posts: 619
Joined: October 27th, 2017, 3:43 pm
Location: i love to eat bees

### 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: 734
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: 748
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$3.AC! dvgrn Moderator Posts: 4783 Joined: May 17th, 2009, 11:00 pm Location: Madison, WI ### Re: Solitaire of Life AforAmpere wrote:I hope this is original. The game's goal is to find the smallest still-life stabilization for a collection of cells, with all pre-placed cells having 3 or less neighbors. The game has been proposed by me in 2015, in our Chinese forum. The Chinese sentence 在左图中添加尽量少的格点，使得它成为稳态:我的最好方案如右图，为9个格点。 means Add cells as less as possible to stabilize the pattern in the left into a still-life:The best I can achieve is shown in the right, with 9 cells. Still drifting. Bullet51 Posts: 483 Joined: July 21st, 2014, 4:35 am ### Re: Solitaire of Life Bullet51 wrote:{image that may show up strangely for some (it did the first time for me)} In case you see a weird, not-cgol image, here is the image: goly.png (155.77 KiB) Viewed 3959 times get down with the sickness. danny Posts: 619 Joined: October 27th, 2017, 3:43 pm Location: i love to eat bees ### Re: Solitaire of Life For that particular one, this seems to be optimal: x = 5, y = 5, rule = LifeHistory2.C$.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: 1633 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$2.CA! Yes, I checked with a computer and that is the unique winner. Macbi Posts: 481 Joined: March 29th, 2009, 4:58 am ### Re: Solitaire of Life I think maybe we could use search programs to find the minimal *amount* of cells, just not post the actual pattern, which would make it fun to reach a goal. Just my 2 cents though. get down with the sickness. danny Posts: 619 Joined: October 27th, 2017, 3:43 pm Location: i love to eat bees ### Re: Solitaire of Life Or don't even announce the number of cells, just when someone has won. For example I already cheated on the first one, so I can tell you that 34 isn't yet the minimal possible number of cells. Macbi Posts: 481 Joined: March 29th, 2009, 4:58 am ### Re: Solitaire of Life Macbi wrote:Or don't even announce the number of cells, just when someone has won. For example I already cheated on the first one, so I can tell you that 34 isn't yet the minimal possible number of cells. I agree, it would be good to know when there is the minimum, but not what the minimum is. EDIT, a different approach, getting 35: x = 17, y = 12, rule = LifeHistory.C$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: 734
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: 1753 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: 734 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: 1633 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$4.2A! LifeWiki: Like Wikipedia but with more spaceships. [citation needed] BlinkerSpawn Posts: 1753 Joined: November 8th, 2014, 8:48 pm Location: Getting a snacker from R-Bee's ### Re: Solitaire of Life BlinkerSpawn wrote: A for awesome wrote:Still not minimal. Ugh, if you insist... x = 16, y = 11, rule = LifeHistory2A$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: 481
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: 821
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: 440
Joined: April 13th, 2016, 9:40 am
Location: Ishikawa Prefecture, Japan

### Re: Solitaire of Life

Still nonoptimal.

Macbi

Posts: 481
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: 440 Joined: April 13th, 2016, 9:40 am Location: Ishikawa Prefecture, Japan ### Re: Solitaire of Life Not there yet. Macbi Posts: 481 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]