Solitaire of Life

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Re: Solitaire of Life

dvgrn wrote:Huh. It looked pretty good. How about 49?

x = 13, y = 14, rule = LifeHistory10.2A$5.2A3.A$5.C2.C.C$6.CA.C$7.C$5.C2.2ACA$5.CA.A3.C$6.C.A2.2A$6.C.2A$3.AC.C.C$4.A.A2.C$.A2C2.C3.C$A2.C.A5.A$2A2.A5.CA! The top can be reduced, so 48: x = 13, y = 13, rule = LifeHistory5.2A2.2A$5.C2.C.C$6.CA.C$7.C$5.C2.2ACA$5.CA.A3.C$6.C.A2.2A$6.C.2A$3.AC.C.C$4.A.A2.C$.A2C2.C3.C$A2.C.A5.A$2A2.A5.CA! An alternative 48: x = 13, y = 13, rule = LifeHistory5.2A2.2A$5.C2.C.C$6.CA.C$7.C$5.C2.2ACA$5.CA.A3.C$6.C.A2.2A$6.C.2A$2A.AC.C.C$A3.A.A2.C$.A2C2.C3.C$3.C.A5.A$4.A5.CA! 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: 1003 Joined: July 1st, 2016, 3:58 pm Re: Solitaire of Life The previous problem has one 31-cell solution within a 16-by-16 bounding box (probably less). I found this out using WinLifeSearch. x = 81, y = 96, rule = LifeHistory58.2A$58.2A3$59.2A17.2A$59.2A17.2A3$79.2A$79.2A2$57.A$56.A$56.3A4$27.A$27.A.A$27.2A21$3.2A$3.2A2.2A$7.2A18$7.2A$7.2A2.2A$11.2A11$2A$2A2.2A$4.2A18$4.2A$4.2A2.2A$8.2A!
Gamedziner

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Re: Solitaire of Life

Gamedziner wrote:The previous problem has one 31-cell solution within a 16-by-16 bounding box (probably less). I found this out using WinLifeSearch.

31 cells? Yikes. It's good to have a target, but so far I can only get to 34:

x = 10, y = 12, rule = LifeHistory2A$C2.CA$2.2C.A$5.C$2.AC.A.C$2.A.C.A.C$6.A2.A$AC3AC2.AC$C2.C$8.2C$7.C.A$8.A! dvgrn Moderator Posts: 5634 Joined: May 17th, 2009, 11:00 pm Location: Madison, WI Re: Solitaire of Life dvgrn wrote: Gamedziner wrote:The previous problem has one 31-cell solution within a 16-by-16 bounding box (probably less). I found this out using WinLifeSearch. 31 cells? Yikes. What makes it worse is that there are no other 31-cell solutions. x = 81, y = 96, rule = LifeHistory58.2A$58.2A3$59.2A17.2A$59.2A17.2A3$79.2A$79.2A2$57.A$56.A$56.3A4$27.A$27.A.A$27.2A21$3.2A$3.2A2.2A$7.2A18$7.2A$7.2A2.2A$11.2A11$2A$2A2.2A$4.2A18$4.2A$4.2A2.2A$8.2A!
Gamedziner

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Re: Solitaire of Life

AforAmpere wrote:The top can be reduced, so 48:
x = 13, y = 13, rule = LifeHistory5.2A2.2A$5.C2.C.C$6.CA.C$7.C$5.C2.2ACA$5.CA.A3.C$6.C.A2.2A$6.C.2A$3.AC.C.C$4.A.A2.C$.A2C2.C3.C$A2.C.A5.A$2A2.A5.CA!

Easy reduction to 47:
x = 13, y = 13, rule = LifeHistory5.2A2.A$5.C2.C.C$6.CA.C$7.C$5.C2.2ACA$5.CA.A3.C$6.C.A2.2A$6.C.2A$3.AC.C.C$4.A.A2.C$.A2C2.C3.C$A2.C.A5.A$2A2.A5.CA!
x = 81, y = 96, rule = LifeHistory58.2A$58.2A3$59.2A17.2A$59.2A17.2A3$79.2A$79.2A2$57.A$56.A$56.3A4$27.A$27.A.A$27.2A21$3.2A$3.2A2.2A$7.2A18$7.2A$7.2A2.2A$11.2A11$2A$2A2.2A$4.2A18$4.2A$4.2A2.2A$8.2A! Gamedziner Posts: 723 Joined: May 30th, 2016, 8:47 pm Location: Milky Way Galaxy: Planet Earth Re: Solitaire of Life Gamedziner wrote: dvgrn wrote: Gamedziner wrote:The previous problem has one 31-cell solution within a 16-by-16 bounding box (probably less). I found this out using WinLifeSearch. 31 cells? Yikes. What makes it worse is that there are no other 31-cell solutions. ...which I wasn't actually expecting to find, given I couldn't get lower than 36 at first: x = 11, y = 11, rule = LifeHistory2A$C2.C$2.2C$3.A.C$3.C.2AC$4.C3.C$5.A2.A$AC.A.C3.CA$CA.CA5.A$7.A2C$7.C! Thanks for the inspiration, dvgrn. I'll hold off on submitting since people appear to still be working on the bump. For reference, I also have a 47-cell solution to that one, although Gamedeziner's looks much more conducive to reduction in the top right: x = 12, y = 15, rule = LifeHistory7.2A$6.A2.A$3.AC2.C.C$3.A.CA.C$6.C.A.A$4.CA3.C.A$4.C5.AC$5.C$3.A.C$.2AC.CAC$A7.C$.2C.AC.A.C$2.C.A3.A.A$2.A.A4.C$3.A! EDIT: Yup, there it is: x = 13, y = 13, rule = LifeHistory5.2A2.A$5.C2.C.C$6.CA.C$7.C.A.A$5.C4.C.A$5.CA4.AC$6.C$6.C.2A$3.AC.C.C$4.A.A2.C$.A2C2.C3.C$A2.C.A5.A$2A2.A5.CA! LifeWiki: Like Wikipedia but with more spaceships. [citation needed] BlinkerSpawn Posts: 1875 Joined: November 8th, 2014, 8:48 pm Location: Getting a snacker from R-Bee's Re: Solitaire of Life Gamedziner wrote: dvgrn wrote: Gamedziner wrote:The previous problem has one 31-cell solution within a 16-by-16 bounding box (probably less). I found this out using WinLifeSearch. 31 cells? Yikes. What makes it worse is that there are no other 31-cell solutions. A minor hint might be (select next line to see it). Think Aircraft Carriers. dvgrn Moderator Posts: 5634 Joined: May 17th, 2009, 11:00 pm Location: Madison, WI Re: Solitaire of Life Here's a much easier one. Don't use scripts, please! I already found the smallest solution (at least, to my knowledge). x = 6, y = 3, rule = LifeHistory5.C$4C.C$5.C! Life is hard. Deal with it. My favorite oscillator of all time: x = 7, y = 5, rule = B3/S2-i3-y4i4b3o$6bo$o3b3o$2o$bo! Hdjensofjfnen Posts: 1093 Joined: March 15th, 2016, 6:41 pm Location: r cis θ Re: Solitaire of Life I doubt there is any smaller solution than 16: x = 7, y = 5, rule = LifeHistoryA2.A.CA$4C.C$5.C$2A3.2A$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: 1003 Joined: July 1st, 2016, 3:58 pm Re: Solitaire of Life AforAmpere wrote:I doubt there is any smaller solution than 16: x = 7, y = 5, rule = LifeHistoryA2.A.CA$4C.C$5.C$2A3.2A$2A! There actually is, though. I'm hoping someone finds a 15-cell solution, because I couldn't come up with one. Didn't use a search program, though, as requested. dvgrn Moderator Posts: 5634 Joined: May 17th, 2009, 11:00 pm Location: Madison, WI Re: Solitaire of Life 14 cells: x = 7, y = 5, rule = LifeHistoryA2.A.CA$4C.C$5.C$2.3A$2.A! gmc_nxtman Posts: 1147 Joined: May 26th, 2015, 7:20 pm Re: Solitaire of Life gmc_nxtman wrote:14 cells: x = 7, y = 5, rule = LifeHistoryA2.A.CA$4C.C$5.C$2.3A$2.A! I won't ever say what exactly I get when using WLS for this, unless it is requested. Since Hdjensofjfnen requested that no one should use scripts, I will not reveal the patterns I found even upon others' request. With that caveat in mind, I can confirm that this is an optimal solution. There is one more optimal solution (excluding flipping along the x-axis). x = 81, y = 96, rule = LifeHistory58.2A$58.2A3$59.2A17.2A$59.2A17.2A3$79.2A$79.2A2$57.A$56.A$56.3A4$27.A$27.A.A$27.2A21$3.2A$3.2A2.2A$7.2A18$7.2A$7.2A2.2A$11.2A11$2A$2A2.2A$4.2A18$4.2A$4.2A2.2A$8.2A!
Gamedziner

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Re: Solitaire of Life

Gamedziner wrote:
gmc_nxtman wrote:14 cells:

x = 7, y = 5, rule = LifeHistoryA2.A.CA$4C.C$5.C$2.3A$2.A!
I won't ever say what exactly I get when using WLS for this, unless it is requested. Since Hdjensofjfnen requested that no one should use scripts, I will not reveal the patterns I found even upon others' request.
With that caveat in mind, I can confirm that this is an optimal solution. There is one more optimal solution (excluding flipping along the x-axis).

x = 7, y = 5, rule = LifeHistoryA2.A.CA$4C.C$5.C$2.A.A$2.2A!
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

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Re: Solitaire of Life

Gamedziner wrote:
gmc_nxtman wrote:14 cells:

x = 7, y = 5, rule = LifeHistoryA2.A.CA$4C.C$5.C$2.3A$2.A!
I won't ever say what exactly I get when using WLS for this, unless it is requested. Since Hdjensofjfnen requested that no one should use scripts, I will not reveal the patterns I found even upon others' request.
With that caveat in mind, I can confirm that this is an optimal solution. There is one more optimal solution (excluding flipping along the x-axis).

[Sniped by A for Awesome, whoops]
Yet Another Randomly-Generated Puzzle:
x = 12, y = 12, rule = LifeHistory7.C.3C$10.C$3.C.2C$2.C5.C$.C5.2C2.C$6.C$10.C2$C9.C$10.C$2.C$C.C!
LifeWiki: Like Wikipedia but with more spaceships. [citation needed]

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Re: Solitaire of Life

x = 12, y = 12, rule = LifeHistory7.C.3C$10.C$3.C.2C$2.C5.C$.C5.2C2.C$6.C$10.C2$C9.C$10.C$2.C$C.C!

My best so far is 49:
x = 16, y = 16, rule = LifeHistory9.2A$9.2A2$7.ACA3C$3.2A.A4.C.A$2.A.C.2CA5.A$.A.C5.C5.A$2.C5.2C2.C2A$7.C4.A$8.3AC2$.C8.AC$A.A7.AC$A2.C$.C.C$2.A! Things to work on: - Find a (7,1)c/8 ship in a Non-totalistic rule (someone please search the rules) - Find a C/10 in JustFriends - Find a C/10 in Day and Night AforAmpere Posts: 1003 Joined: July 1st, 2016, 3:58 pm Re: Solitaire of Life A new puzzle: x = 9, y = 13, rule = LifeHistory3.C.C2$C3.C3.C$2.C3.C3$.C2.C2.C3$2.C3.C$C3.C3.C2$3.C.C! 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: 1003 Joined: July 1st, 2016, 3:58 pm Re: Solitaire of Life 53 cells: x = 11, y = 15, rule = LifeHistory5.A$2A2.C.C$A2.A2.A$.C.A.C3.CA$2.AC.A.C2.A$5.A.2A$2.2A.A$2.CA.C.AC$5.A.2A$2.2A.A$A2.C.A.CA$AC3.C.A.C$4.A2.A2.A$4.C.C2.2A$5.A! EDIT: 51: x = 11, y = 15, rule = LifeHistory5.A$3.ACACA$2.A5.A$.C.A.CA2.C$.A.CA.ACA$2A$2.A.2A.2A$2.CA.C.AC3$3.CA.AC.2A$.C2.AC.A.CA$.2A$3.ACAC$3.A2.A! EDIT: 50: x = 10, y = 15, rule = LifeHistory2.A2.A$2.ACAC$2A$C2.AC.A.C$2.CA.ACA.A$9.A$.A.2A.A.A$.CA.C.AC3$2.CA.AC.2A$C2.AC.A.CA$2A$2.ACAC$2.A2.A! gmc_nxtman Posts: 1147 Joined: May 26th, 2015, 7:20 pm Re: Solitaire of Life 46? x = 9, y = 15, rule = LifeHistory4.A$2.ACACA$.A5.A$C2.AC.A.C$.AC.A.CA2$.2A.A.2A$.C.AC.AC3$.AC.A.CA$C2.AC.A.C$.A5.A$2.ACACA$4.A!
LifeWiki: Like Wikipedia but with more spaceships. [citation needed]

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Re: Solitaire of Life

x = 9, y = 15, rule = LifeHistory4.A$2.ACACA$.A5.A$C2.AC.A.C$.AC.A.CA2$.2A.A.2A$.C.AC.AC3$.AC.A.CA$C2.AC.A.C$.A5.A$2.ACACA$4.A! Not an optimal solution. x = 81, y = 96, rule = LifeHistory58.2A$58.2A3$59.2A17.2A$59.2A17.2A3$79.2A$79.2A2$57.A$56.A$56.3A4$27.A$27.A.A$27.2A21$3.2A$3.2A2.2A$7.2A18$7.2A$7.2A2.2A$11.2A11$2A$2A2.2A$4.2A18$4.2A$4.2A2.2A$8.2A!
Gamedziner

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Re: Solitaire of Life

Since it has been a full week, I'll give a hint: an optimal solution exists with 43 cells.
x = 81, y = 96, rule = LifeHistory58.2A$58.2A3$59.2A17.2A$59.2A17.2A3$79.2A$79.2A2$57.A$56.A$56.3A4$27.A$27.A.A$27.2A21$3.2A$3.2A2.2A$7.2A18$7.2A$7.2A2.2A$11.2A11$2A$2A2.2A$4.2A18$4.2A$4.2A2.2A$8.2A! Gamedziner Posts: 723 Joined: May 30th, 2016, 8:47 pm Location: Milky Way Galaxy: Planet Earth Re: Solitaire of Life gmc_nxtman wrote:14 cells: x = 7, y = 5, rule = LifeHistoryA2.A.CA$4C.C$5.C$2.3A$2.A! Correct, that was my solution. Life is hard. Deal with it. My favorite oscillator of all time: x = 7, y = 5, rule = B3/S2-i3-y4i4b3o$6bo$o3b3o$2o$bo! Hdjensofjfnen Posts: 1093 Joined: March 15th, 2016, 6:41 pm Location: r cis θ Re: Solitaire of Life Here's a new puzzle, if anyone wants one: x = 12, y = 10, rule = LifeHistory2C3.C$4.C.C$3.C.C$3.C.C.C$2.C3.C$2.C5.C$3.C6.C$.C3.C5.C$6.C4.C$5.C!

77topaz

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43 cells:

x = 13, y = 10, rule = LifeHistory.2C3.C$2.A2.C.C$2.A.C.C$.2A.C.C.C$3.C.A.C.A$3.C.A.A.C$.2A.C.A.A.AC$2.C3.C3.A.C$A.A2.A.C2.A.C$2A4.C4.A! EDIT: 40: x = 12, y = 13, rule = LifeHistory2A$2C3.C$4.C.C$3.C.C$3.C.C.C$.AC.A.C.A$A.C.A3.C$A2.C.A2.2AC$.C.A.C5.C$2.A2.AC3.AC$5.C$7.A$6.2A! gmc_nxtman Posts: 1147 Joined: May 26th, 2015, 7:20 pm Re: Solitaire of Life Alternative 40 x = 12, y = 12, rule = LifeHistory2C3.C$.A2.C.C$.A.C.C$2A.C.C.C$2.C.A.C.A$2.C.A3.C$3.C.A2.2AC$.C.A.C5.C$.2A2.AC3.AC$5.C$7.A$6.2A!
Sarp

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Re: Solitaire of Life

38:
x = 12, y = 11, rule = LifeHistory2A$2C3.C$4.C.C$3.C.C$3.C.C.C$.AC3.C.A$A.C.2A2.C$A2.C2.3A.C$.CA2.C3.A.C$6.C2.A.C$5.CA3.A!
LifeWiki: Like Wikipedia but with more spaceships. [citation needed]