Search found 1920 matches

by BlinkerSpawn
Yesterday, 11:02 pm
Forum: Patterns
Topic: Oscillator Discussion Thread
Replies: 1044
Views: 521556

Re: Oscillator Discussion Thread

EDIT 2: Nothing special, just a couple new (as of 2014, at least) billiard tables (and one p5 non-billiard table): x = 114, y = 61, rule = B3/S23 6bo7bo43bobo45bobobo2$4bobo5bobo41bo49bo2$6bo7bo41bobobo45bobo2$6bo7bo 41bo5bo47bo2$4bobobo3bobobo41bobo45bobo14$13b2o$8b2o3bo45b2o$8bo5bo45b o51bo$10bo2...
by BlinkerSpawn
Yesterday, 10:37 pm
Forum: The Sandbox
Topic: Ordinals in googology
Replies: 125
Views: 2203

Re: Ordinals in googology

PkmnQ wrote:
Yesterday, 7:51 pm
What is w_1ck?
CK, fur Church-Kleene, the first non-recursive ordinal.
by BlinkerSpawn
November 12th, 2019, 12:12 am
Forum: The Sandbox
Topic: Thread for Non-CA Academic Questions
Replies: 301
Views: 72579

Re: Thread for Non-CA Academic Questions

Moosey wrote:
November 11th, 2019, 6:15 pm
How much more powerful is ah_n(a(@@a)a) compared to f_a(n)?
I'll need a clarification of the rules before I can answer, which I've already asked you for.
At least, I hope that was you from the Googology Discord that I messaged about this.
by BlinkerSpawn
November 10th, 2019, 11:55 am
Forum: Patterns
Topic: Oscillator Discussion Thread
Replies: 1044
Views: 521556

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...
by BlinkerSpawn
November 9th, 2019, 9:34 pm
Forum: Patterns
Topic: 19-bit still life syntheses
Replies: 48
Views: 1889

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...
by BlinkerSpawn
November 4th, 2019, 6:29 pm
Forum: The Sandbox
Topic: Thread for Non-CA Academic Questions
Replies: 301
Views: 72579

Re: Thread for Non-CA Academic Questions

gameoflifemaniac wrote:
November 4th, 2019, 11:24 am
Is there any lower bound on how quickly the Busy Beaver function grows?
Any computable function suffices.
by BlinkerSpawn
November 4th, 2019, 6:28 pm
Forum: The Sandbox
Topic: Ordinals in googology
Replies: 125
Views: 2203

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 ...
by BlinkerSpawn
November 1st, 2019, 4:49 pm
Forum: Patterns
Topic: Spaceship Eaters
Replies: 57
Views: 10966

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
!
by BlinkerSpawn
October 31st, 2019, 9:49 pm
Forum: The Sandbox
Topic: Ordinals in googology
Replies: 125
Views: 2203

Re: Ordinals in googology

toroidalet wrote:
October 31st, 2019, 8:32 pm
This is sort of a stupid question, but why isn't ε_1=ε_0^ω?
Epsilon numbers are the fixed points of w^, so e_a = w^(e_a) for any a.

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.
by BlinkerSpawn
October 28th, 2019, 4:43 pm
Forum: Patterns
Topic: Small Spaceship Syntheses
Replies: 322
Views: 309451

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...
by BlinkerSpawn
October 24th, 2019, 9:48 pm
Forum: The Sandbox
Topic: Thread for Non-CA Academic Questions
Replies: 301
Views: 72579

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 ...
by BlinkerSpawn
October 23rd, 2019, 5:21 pm
Forum: The Sandbox
Topic: Ordinals in googology
Replies: 125
Views: 2203

Re: Ordinals in googology

testitemqlstudop wrote:
October 13th, 2019, 11:39 pm
Is the diagonalization omega, epsilon, delta, gamma, etc. literally just w^^...n times...^w?
By most definitions, w ^{n} w is phi(n-1,0).
Gamma_0 is then w ^{w ^{w^{ ... } w} w} w, in keeping with the "standard" result f_(w+1) = s_(G0)
by BlinkerSpawn
October 19th, 2019, 8:39 pm
Forum: Patterns
Topic: 19-bit still life syntheses
Replies: 48
Views: 1889

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...
by BlinkerSpawn
October 18th, 2019, 4:40 pm
Forum: Patterns
Topic: 19-bit still life syntheses
Replies: 48
Views: 1889

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...
by BlinkerSpawn
October 15th, 2019, 3:04 pm
Forum: Patterns
Topic: 19-bit still life syntheses
Replies: 48
Views: 1889

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...
by BlinkerSpawn
October 9th, 2019, 5:11 pm
Forum: The Sandbox
Topic: Stabilise [GAME]
Replies: 43
Views: 2786

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...
by BlinkerSpawn
October 8th, 2019, 9:45 pm
Forum: The Sandbox
Topic: Ordinals in googology
Replies: 125
Views: 2203

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)(...
by BlinkerSpawn
October 8th, 2019, 9:43 pm
Forum: The Sandbox
Topic: Stabilise [GAME]
Replies: 43
Views: 2786

Re: Stabilise [GAME]

A for awesome wrote:
October 8th, 2019, 5:32 pm
103:

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!
I'd be surprised if this wasn't minimal.
I would certainly be inclined to agree, since I specifically designed it to be impossible with two OFFs, well done!
Next puzzle is yours.
by BlinkerSpawn
October 8th, 2019, 3:52 pm
Forum: The Sandbox
Topic: Stabilise [GAME]
Replies: 43
Views: 2786

Re: Stabilise [GAME]

85, as promised:

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!
New puzzle:

Code: Select all

x = 6, y = 8, rule = LifeHistory
.3A$A2.A$.4A$2.A$3.A$.4A$2.A2.A$2.3A!
by BlinkerSpawn
October 8th, 2019, 3:41 pm
Forum: The Sandbox
Topic: Ordinals in googology
Replies: 125
Views: 2203

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...
by BlinkerSpawn
October 7th, 2019, 10:33 pm
Forum: The Sandbox
Topic: Ordinals in googology
Replies: 125
Views: 2203

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...
by BlinkerSpawn
October 7th, 2019, 8:12 pm
Forum: The Sandbox
Topic: Ordinals in googology
Replies: 125
Views: 2203

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)
by BlinkerSpawn
October 4th, 2019, 10:39 pm
Forum: The Sandbox
Topic: Largest total computable function competition
Replies: 151
Views: 14932

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...
by BlinkerSpawn
October 4th, 2019, 5:09 pm
Forum: The Sandbox
Topic: Stabilise [GAME]
Replies: 43
Views: 2786

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....
by BlinkerSpawn
October 3rd, 2019, 9:48 pm
Forum: The Sandbox
Topic: Stabilise [GAME]
Replies: 43
Views: 2786

Re: Stabilise [GAME]

Hdjensofjfnen wrote:
October 3rd, 2019, 1:49 am
toroidalet wrote:
October 2nd, 2019, 11:49 pm
176

Code: Select all

rle
I am pretty sure the above is minimal.
One above minimal (177):

Code: Select all

rle
I believe the minimum is 174 (5/14), you're almost there.