## Search found 1920 matches

- 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...

- Yesterday, 10:37 pm
- Forum: The Sandbox
- Topic: Ordinals in googology
- Replies:
**125** - Views:
**2203**

- November 12th, 2019, 12:12 am
- Forum: The Sandbox
- Topic: Thread for Non-CA Academic Questions
- Replies:
**301** - Views:
**72579**

- 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...

- 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...

- 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

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:
**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 ...

- 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
!
```

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

### 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:
**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...

- 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 ...

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

### 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:
**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...

- 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...

- 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...

- 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...

- 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)(...

- October 8th, 2019, 9:43 pm
- Forum: The Sandbox
- Topic: Stabilise [GAME]
- Replies:
**43** - Views:
**2786**

### 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:
**43** - Views:
**2786**

### 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:
**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...

- 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...

- 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)

- 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...

- 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....

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

### 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`