Search found 1909 matches

by BlinkerSpawn
Yesterday, 5:21 pm
Forum: The Sandbox
Topic: Ordinals in googology
Replies: 46
Views: 840

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: 30
Views: 1001

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: 30
Views: 1001

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: 30
Views: 1001

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: 2550

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: 46
Views: 840

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: 2550

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: 2550

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: 46
Views: 840

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: 46
Views: 840

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: 46
Views: 840

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: 146
Views: 14341

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: 2550

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: 2550

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.
by BlinkerSpawn
October 2nd, 2019, 5:17 pm
Forum: The Sandbox
Topic: Stabilise [GAME]
Replies: 43
Views: 2550

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...
by BlinkerSpawn
September 30th, 2019, 4:43 pm
Forum: The Sandbox
Topic: Ordinals in googology
Replies: 46
Views: 840

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...
by BlinkerSpawn
September 27th, 2019, 9:41 am
Forum: The Sandbox
Topic: Ordinals in googology
Replies: 46
Views: 840

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...
by BlinkerSpawn
September 24th, 2019, 3:00 pm
Forum: Patterns
Topic: Synthesis components
Replies: 40
Views: 6831

Re: Synthesis components

chris_c wrote:
A for awesome wrote:Might be reducible to 5G.

Code: Select all

x = 19, y = 13, rule = B3/S23
2bo8bo$3b2o6bobo3bo$2b2o7b2o3bo$16b3o$10bo$8bobo$9b2o$bo$b2o$obo4b2o$
7bo$8b3o$10bo!
Now hold on just a second:

Code: Select all

x = 18, y = 13, rule = B3/S23
2bo$3b2o$2b2o2$12bobo$12b2o$13bo$bo$b2o$obo4b2o$7bo8bo$8b3o4b2o$10bo4b
obo!
by BlinkerSpawn
September 22nd, 2019, 12:57 pm
Forum: The Sandbox
Topic: Absolutely Useless Patterns Not Worthy Of Patterns Thread
Replies: 520
Views: 118238

Re: Absolutely Useless Patterns Not Worthy Of Patterns Thread

Reductions and continuations for the PD game: x = 57, y = 36, rule = LifeHistory 22.2A.2C.2A$23.C.2A.C$6.2A3.A10.C6.C16.2A$5.A.A2.A.A5.2A.C8.C.2A9.2C 2.A3.2C2.2A$5.C4.C2.A5.A.CA6.AC.A6.2A.C2.CA3.C2.C2.A$3.2C.4C.2C5.A2.C 8.C2.A6.A.CA.C4.C.AC.A$2.A2.C4.C7.2A2.C6.C2.2A5.A2.C2.C3.AC2.C.2A$3.A .A2.A.A12....
by BlinkerSpawn
September 20th, 2019, 7:46 pm
Forum: Patterns
Topic: Oscillator Discussion Thread
Replies: 982
Views: 516811

Re: Oscillator Discussion Thread

A for awesome wrote:
Bullet51 wrote:It's probably known, but I haven't found it in jslife.
(P11)

Code: Select all

rle
Attempt at a reduction:

Code: Select all

rle
One cell further:

Code: Select all

x = 15, y = 14, rule = Life
9bo$3bo2bobobo$3b4obobo$b2o4bobo$o3b2obo$b3obob2o$3bobobo$5bob2o4b2o$
5bobo3bo2bo$4bo2bobob2o$5b2ob2o$6bo3b3o$6bob2o2bo$7bobo!
by BlinkerSpawn
September 17th, 2019, 3:26 pm
Forum: Scripts
Topic: Puzzles and "Project von Neumann"
Replies: 30
Views: 9711

Re: Puzzles and "Project von Neumann"

Would auto-generated history be of any use, a la Seeds of Destruction? Here's an idea for the server-side implementation. Each puzzle will be a list of (cell list 1, cell list 2 @ t). Basically, each line means "when each of the cells in cell list 1 are toggled, there must be some generation 0 < i ≤...
by BlinkerSpawn
September 17th, 2019, 3:08 pm
Forum: Patterns
Topic: Synthesis components
Replies: 40
Views: 6831

Re: Synthesis components

Hdjensofjfnen wrote:That block can get there via a boat-bit and a conversion, right?
Of course.
by BlinkerSpawn
September 16th, 2019, 8:33 pm
Forum: The Sandbox
Topic: Thread for Non-CA Academic Questions
Replies: 286
Views: 71195

Re: Thread for Non-CA Academic Questions

What is the growth rate of this , in the fgh? Under a stronger version where a copies are made instead of two, I get this analysis: a{1,1,1}e = a(^e)a a{1,c,1}1 = a{a{a,c-1,a}a,c-1,a}a a{b,c,1}1 = a{b-1,c,a{b-1,c,1}a}a a{b,c,d}1 = a{b,c,d-1}a{b,c,d-1}a a{b,c,d}0 = a a{1,1,1}a = w (1) a{1,1,2}a = w+...
by BlinkerSpawn
September 16th, 2019, 8:01 pm
Forum: Patterns
Topic: Oscillator Discussion Thread
Replies: 982
Views: 516811

Re: Oscillator Discussion Thread

P11: rle Two reductions: x = 42, y = 18, rule = Life 36b2o$10b2o23bo2bo$6b2o3bo24b2obo$6bo2bo23b3o3bo$4bobob3o18b2obo4b2ob 2o$3bobobo4b2ob2o12b2obo2b2obobo$4bo2bo2b2obobo16bobobobo2bo$b3o3bobob obo2bo12b3ob2o3b4o$bo2b3ob2o3b4o11bo3bobo$3bo3bobo18bo2b3o4b2o$2b2o2b 3o4b2o11bobobo8bo$o2bobo8bo10bobo2b...
by BlinkerSpawn
September 16th, 2019, 7:44 pm
Forum: Patterns
Topic: Synthesis components
Replies: 40
Views: 6831

Re: Synthesis components

A component which should significantly reduce the spider: x = 38, y = 47, rule = B3/S23 10$28bo$20b2o6bobo$19bo2bo5b2o$19bo2bo$20b2o4$7bo$8b2o15b2obo$7b2o8b3o 4bo2b2o$23bobo3b2o$24bob2o3bo$26bob3o$26bobo$20b3o2b2o$26bobo$26bob3o$ 10b3o11bob2o3bo$12bo10bobo3b2o$4b2o5bo5b3o4bo2b2o$5b2o18b2obo$4bo4$20b...