Search found 1992 matches
- November 10th, 2019, 11:55 am
- Forum: Patterns
- Topic: Oscillator Discussion Thread
- Replies: 4542
- Views: 1700116
Re: Oscillator Discussion Thread
Edit 3: Here's another "Trivial p6", just for amusement. Right is new. x = 24, y = 14, rule = LifeHistory 11.A.2A$.2A6.2A3.A$A2.A9.A4.A$.2A2.2A4.A5.A.A2.2A$3.2A2.A4.A4.A2.A2.A $.2A3.A3.A.3A.2A.2A.A$A2.2A2.6A4.A4.2A$A.A3.3A6.2A2.A.A$.A.2A.A7.2A.A 4.2A$3.A2.A.A2.4A2.A.2A.A$3.A.A4.A4.A.A.A2.A$2.2A.A.2...
- November 9th, 2019, 9:34 pm
- Forum: Patterns
- Topic: 19-bit still life syntheses
- Replies: 99
- Views: 41548
Re: 19-bit still life syntheses
Found with Chris's script. Seems pretty elementary as a transformation. x = 33, y = 35, rule = B3/S23 bo$2bo$3o5$28bo$27bo$27b3o11$25bo$24bo$24b3o3$12bo$10bobo$11b2o4bo$17b obo$17b2o10bo2bo$27b6o$26bo$27b2obo$25bobob2o$25b2o! Two seconds in Seeds of Destruction: x = 23, y = 33, rule = B3/S23 21bo$2...
- November 4th, 2019, 6:29 pm
- Forum: The Sandbox
- Topic: Thread for Non-CA Academic Questions
- Replies: 347
- Views: 158193
Re: Thread for Non-CA Academic Questions
Any computable function suffices.gameoflifemaniac wrote: ↑November 4th, 2019, 11:24 amIs there any lower bound on how quickly the Busy Beaver function grows?
- November 4th, 2019, 6:28 pm
- Forum: The Sandbox
- Topic: Ordinals in googology
- Replies: 186
- Views: 53877
Re: Ordinals in googology
no. Probably gamma_1 = sup{gamma_0+1,phi_gamma_0+1(0),phi_phi_gamma_0+1(0)(0),etc.} Probably? Yes. Remember, phi(1,0,a) enumerates fixed points of phi(0,a,0). Then phi(1,1,a) enumerates fixed points of phi(1,0,a), phi(1,2,a) the fixed points of phi(1,1,a), and so on until phi(2,0,a) enumerates the ...
- November 1st, 2019, 4:49 pm
- Forum: Patterns
- Topic: Spaceship Eaters
- Replies: 344
- Views: 128253
Re: Spaceship Eaters
Another promising catalysis:
Code: Select all
x = 28, y = 28, rule = B3/S23
9b2o$b2o7bo$b2o4b3o$7bo2$b2o$b2o$o2bo$o2bob2o$o11b2o$o2bo3b2o3b2o$bo5b
2o$b5obo$6bo$17b2o$17b2o$7b3o$9bo16b2o$10b2o13bobo$11bo4b2o7bo$11bo3b
3o6b2o$14bo4bo$15bo3bo$15bo$15bobob2o$15bo5b2o2b2o$15b2o4b2o2b2o$17b4o
!
- October 31st, 2019, 9:49 pm
- Forum: The Sandbox
- Topic: Ordinals in googology
- Replies: 186
- Views: 53877
Re: Ordinals in googology
Epsilon numbers are the fixed points of w^, so e_a = w^(e_a) for any a.toroidalet wrote: ↑October 31st, 2019, 8:32 pmThis is sort of a stupid question, but why isn't ε_1=ε_0^ω?
w^(e_0^w) = w^(e_0+e_0^w) = e_0^e_0^w > e_0^w, so e_1 cannot be e_0^w.
- October 28th, 2019, 4:43 pm
- Forum: Patterns
- Topic: Small Spaceship Syntheses
- Replies: 731
- Views: 566356
Re: Small Spaceship Syntheses
Great work, Goldtiger! And now for the obligatory round of improvements from the community. :wink: The fuse could be shortened with an activation like this: rle EDIT: Optimizing out the LWSS coming from the right: rle Another four cells off the boat, and one fewer cleanup glider: x = 62, y = 67, ru...
- October 24th, 2019, 9:48 pm
- Forum: The Sandbox
- Topic: Thread for Non-CA Academic Questions
- Replies: 347
- Views: 158193
Re: Thread for Non-CA Academic Questions
Can someone explain bashicu matrix systems? I think I understand what this file is trying to say, but not much else: https://googology.wikia.org/wiki/File:BMS_expansion.png I'll try my best to paraphrase what goes on for BM2.3: If your last column is all zeroes, your matrix is a successor, and you ...
- October 23rd, 2019, 5:21 pm
- Forum: The Sandbox
- Topic: Ordinals in googology
- Replies: 186
- Views: 53877
Re: Ordinals in googology
By most definitions, w ^{n} w is phi(n-1,0).testitemqlstudop wrote: ↑October 13th, 2019, 11:39 pmIs the diagonalization omega, epsilon, delta, gamma, etc. literally just w^^...n times...^w?
Gamma_0 is then w ^{w ^{w^{ ... } w} w} w, in keeping with the "standard" result f_(w+1) = s_(G0)
- October 19th, 2019, 8:39 pm
- Forum: Patterns
- Topic: 19-bit still life syntheses
- Replies: 99
- Views: 41548
Re: 19-bit still life syntheses
Feather to carrier: rle This will probably find a few things during the next transfer.py run. Stumbled upon a way to save four gliders in the middle of trying something more complicated: x = 46, y = 32, rule = Life 8bo$6bobo31bo$7b2o19bo9b2o$26b2o11b2o$4bo22b2o$5b2o$4b2o2$29bobo$29b2o $30bo3$24bo$2...
- October 18th, 2019, 4:40 pm
- Forum: Patterns
- Topic: 19-bit still life syntheses
- Replies: 99
- Views: 41548
Re: 19-bit still life syntheses
Here's a synthesis of xs19_03p6853z3543: x = 93, y = 19, rule = B3/S23 7b2o2b2o34b2o2b2o34b2o2b2o$7bobo2bo34bobo2bo34bobo2bo$9bobo37bobo23bob o11bobo$8bobo37bobo5bo19b2o10bobo$8bo39bo6bo20bo11bo$6b2obo36b2obo5b3o 28b2obo$5bo2bo36bo2bo36bo2b2o$5b2o37bobo37bobo$obo7bobo32bo39bo$b2o7b 2o$bo9bo2$78bo$9...
- October 15th, 2019, 3:04 pm
- Forum: Patterns
- Topic: 19-bit still life syntheses
- Replies: 99
- Views: 41548
Re: 19-bit still life syntheses
This should help with the various Chop Suey still lifes, though I'm not sure what an efficient way to build the scaffolding would be: x = 42, y = 40, rule = B3/S23 3bo$4bo12bobo4bobo$2b3o15bo3b2o$20bo4bo$17bo2bo$18b3o3$16bo$2bo12bo$3b o11b3o$b3o17bo3bobo$20bo4b2o$20b3o3bo3$9b2o$9b2o2$9b2o$9bobo2b2o...
- October 9th, 2019, 5:11 pm
- Forum: The Sandbox
- Topic: Stabilise [GAME]
- Replies: 60
- Views: 17708
Re: Stabilise [GAME]
Now that one was tough , but 90: x = 13, y = 14, rule = LifeHistory 3.E$.3E$E6.2E$.A.3A2.E$EA.A2.2E$.A.EDE$E.DA.A3.2E.E$E.A2.2A2.A.2E$.A. EA2.A.A$3.A2.A.2A$3.E.2A$4.A2.3A$6.E2.E$7.2E! EDIT: 88 x = 13, y = 14, rule = LifeHistory 2.2E$3.E$2.E4.2E$.A.3A2.E$.A.A2.2E$EA.EDE$E.DA.A3.2E.E$2.A2.2A2.A.2E$ .A...
- October 8th, 2019, 9:45 pm
- Forum: The Sandbox
- Topic: Ordinals in googology
- Replies: 186
- Views: 53877
Re: Ordinals in googology
Testitem's variant is very close to Hardy, which is related to FGH as I stated above, so dco's relation to Hardy is essentially dco's relation with that variant. dco(G0+n) is certainly weaker than f_(G0+1)(n), probably between H_(G0) and H_(G0+w). so dco(G0+n) would be between f_G0(n) and f_(G0+1)(...
- October 8th, 2019, 9:43 pm
- Forum: The Sandbox
- Topic: Stabilise [GAME]
- Replies: 60
- Views: 17708
Re: Stabilise [GAME]
I would certainly be inclined to agree, since I specifically designed it to be impossible with two OFFs, well done!A for awesome wrote: ↑October 8th, 2019, 5:32 pm103:I'd be surprised if this wasn't minimal.Code: Select all
x = 6, y = 10, rule = LifeHistory 3.2E$.3A.E$A2.D.E$.4A$2.A$E2.D$E4A$2.D2.A$2.3A$2.E!
Next puzzle is yours.
- October 8th, 2019, 3:52 pm
- Forum: The Sandbox
- Topic: Stabilise [GAME]
- Replies: 60
- Views: 17708
Re: Stabilise [GAME]
85, as promised:
New puzzle:
Code: Select all
x = 15, y = 8, rule = LifeHistory
4.2E2.E.E$A2.A.A2.2E.A.2E$AE2A2.2A3.A.E$2.D.2A.DA.A2.A$AEAE3.2A.E2A$E
2.E$7.4E$7.E2.E!
Code: Select all
x = 6, y = 8, rule = LifeHistory
.3A$A2.A$.4A$2.A$3.A$.4A$2.A2.A$2.3A!
- October 8th, 2019, 3:41 pm
- Forum: The Sandbox
- Topic: Ordinals in googology
- Replies: 186
- Views: 53877
Re: Ordinals in googology
So how does dco(a+n) compare to the hierarchies? And where is dco(gamma_0+n) in the fgh? Does it eventually exceed f_a(n) for all n < gamma_0 or something? Or is it only fgh_(something in the Veblen hierarchy)-ish? As I've stated before, I think Goodstein sequences are less powerful than dco, makin...
- October 7th, 2019, 10:33 pm
- Forum: The Sandbox
- Topic: Ordinals in googology
- Replies: 186
- Views: 53877
Re: Ordinals in googology
Isn't it also stronger than the HH? Given: dco(a+1,n) = dco(a, n+1 )+1 In that case, dco(Γ_0+n) catches up to f_Γ_0(n), since the HH catches up to the fgh at e_0, and thus dco(Γ_0+n) = dco(Γ_0,n) >= HH(Γ_0,n) = f_Γ_0(n) (for large enough n) Incorrect. Hardy and FGH are related in that if f_a(n) = H...
- October 7th, 2019, 8:12 pm
- Forum: The Sandbox
- Topic: Ordinals in googology
- Replies: 186
- Views: 53877
Re: Ordinals in googology
dco(a) is slightly stronger than the SGH:
SGH wrote: s(a+1,n) = s(a,n)+1
s(a,n) = s(a[n],n)
dco wrote: s(a+1,n) = s(a,n+1)+1
s(a,n) = s(a[n]+a[n-1]+...+a[0],n+1)
- October 4th, 2019, 10:39 pm
- Forum: The Sandbox
- Topic: Largest total computable function competition
- Replies: 170
- Views: 57519
Re: Largest total computable function competition
Yes, that's right for unidimensional arrays. But I don't get anything above 2d Let the first non-one entry after b be the "active point" P and the separator before it S. Decrease S according to the following rules, and call the result S': {k #} -> {k-1 #} {# 1,k #} -> {# b,k-1} If this separator ha...
- October 4th, 2019, 5:09 pm
- Forum: The Sandbox
- Topic: Stabilise [GAME]
- Replies: 60
- Views: 17708
Re: Stabilise [GAME]
127: x = 19, y = 11, rule = LifeHistory 11.2E$11.E.E$9.2E2.E$E.EA.EA.A2.2E.AE$2E.A.AD2.2A2.ED.E$3.E.A.2A.DA.A 2.A$3.A.A.E2.2A.E2A$4.E2.E$7.2E6.3E$15.E2.E$17.2E! Can be trivially modified to save an OFF and get you to 94: x = 19, y = 11, rule = LifeHistory 11.2E$11.E.E$9.2E2.E$E.EA.EA.A2.2E.AE$2E.A....
- October 3rd, 2019, 9:48 pm
- Forum: The Sandbox
- Topic: Stabilise [GAME]
- Replies: 60
- Views: 17708
Re: Stabilise [GAME]
I believe the minimum is 174 (5/14), you're almost there.Hdjensofjfnen wrote: ↑October 3rd, 2019, 1:49 amI am pretty sure the above is minimal.
One above minimal (177):Code: Select all
rle
- October 2nd, 2019, 5:17 pm
- Forum: The Sandbox
- Topic: Stabilise [GAME]
- Replies: 60
- Views: 17708
Re: Stabilise [GAME]
alternate x = 8, y = 9, rule = LifeHistory 2.2E.AE$.A.E.E$.A.E.E$2A2.E$2.2E$2.E2.D$3.E2.EA$4.A2.A$5.2A! The red cell is impossible 42 is the min (this pattern is actually 45, A for Awesome got 42) Incorrect, 41: x = 7, y = 7, rule = LifeHistory E.2A.EA$2E.A.A$3.A.A$3.ED2E$2.2A$2.A2.AE$3.AE.A! 39, w...
- September 30th, 2019, 4:43 pm
- Forum: The Sandbox
- Topic: Ordinals in googology
- Replies: 186
- Views: 53877
Re: Ordinals in googology
∂ |-> w∂ is the same as w^∂ |-> w^(1+∂), so f(i) is w^{i'th limit of successors} = w^(wi). The "last fixed point" does not exist because there is no greatest ordinal. There has to be something wrong with that logic, because if ∂ = w2 = w+w, then it is implied that w+w = w(w+w), or w+w = w^2+w^2. Of...
- September 27th, 2019, 9:41 am
- Forum: The Sandbox
- Topic: Ordinals in googology
- Replies: 186
- Views: 53877
Re: Ordinals in googology
...This topic is taking over BOTH the LTCFC and TFNCAQ so now it deserves its own thread. Primarily I'm concerned about large ordinals here. For example, the first fixed point of ∂ |-> w∂ is w^w. Hence we can make a function: f(i) = the i-th fixed point of ∂ |-> w∂ What would f(2) be? f(w)? Would t...