## Search found 1932 matches

- January 8th, 2020, 7:34 pm
- Forum: Patterns
- Topic: Synthesising Oscillators
- Replies:
**992** - Views:
**735605**

### Re: Synthesising Oscillators

Syntheses involving a catalyst Saves a glider: x = 40, y = 32, rule = B3/S23 34bo4bo$32b2o3b2o$33b2o3b2o3$20b2o$17b2o2bo$18b3o$16bo$9bo6b3o$7bobo9b o$8b2o8bobo$18bo2bo$19bobo$20bo3$8b2o$7bobo$9bo$36b2o$3b2o30b2o$2bobo 10bo21bo$4bo10b2o3bo$14bobo2b2o10b2o$19bobo9bobo$31bo$23b2o$22b2o$b2o 21bo$obo$2b...

- January 7th, 2020, 6:20 pm
- Forum: Patterns
- Topic: Oscillator Discussion Thread
- Replies:
**1188** - Views:
**541724**

### Re: Oscillator Discussion Thread

A small p12, also with a 1-2-3-4 in it. I think 12 is the lowest known number of rotor cells in a true-period p12. x = 20, y = 15, rule = B3/S23 12b2o$4bo2bo2bo2bo2bo$2b3o2b4obo3b3o$bo3b2o4bo7bo$bo2bo3b2o4b4obo$2obo 2b2ob2o2bo4bo$2bob2obo3bo2b4o$2bo2bo2b3ob2o$3bobobo2bo4bo$2b2obob2obob 4o$5bo2bobo$...

- December 12th, 2019, 4:34 pm
- Forum: Patterns
- Topic: 19-bit still life syntheses
- Replies:
**92** - Views:
**5172**

### Re: 19-bit still life syntheses

That higher-clearance insertion has now helped solve xs19_03p68oz39c32 and about eight relatives. I've been trying to make a component sequence to do this other transformation, as well. So far, no luck, but it's getting closer: x = 128, y = 13, rule = B3/S23 85bo2bo$89bo$84b6o$85bobo$4bo5b2o32bo39b...

- December 5th, 2019, 4:00 pm
- Forum: The Sandbox
- Topic: Challenges
- Replies:
**240** - Views:
**60713**

### Re: Challenges

I interpreted the rules as allowing two expressions, each of which could use at most one of each symbol, is that not the case?

- December 5th, 2019, 3:39 pm
- Forum: The Sandbox
- Topic: Challenges
- Replies:
**240** - Views:
**60713**

### Re: Challenges

A difficult number-puzzle: go from 16 to 25 in two moves, using only the number two, the operations +, *, ^, /, and -, (only one operator per use) and adding together all digits once (per use). Not all of these must (or in this case can) be used. Either subtract two or multiply by two, then raise t...

- December 5th, 2019, 3:31 pm
- Forum: The Sandbox
- Topic: Guess the sequence [GAME]
- Replies:
**15** - Views:
**1597**

### Re: Guess the sequence [GAME]

a(n) = digits of 9n in ascending ordertestitemqlstudop wrote: ↑July 31st, 2019, 11:18 pmDo as the title.

#0:Code: Select all

`9 18 27 36 45 45 36 27 18 9 99 18 117 126 135 144 135 126 117 18 189 189 27 126 225 234 234 225 126`

- November 29th, 2019, 5:10 pm
- Forum: The Sandbox
- Topic: Ordinals in googology
- Replies:
**166** - Views:
**4934**

### Re: Ordinals in googology

Can anyone explain me ordinals significantly bigger than the BHO? In many commonly used ordinal notations, W_1 acts as a fixed point of psi_0. We can then define psi_1 which creates expressions with W_1, and define W_2 as a fixed point of psi_1. Many strong notations, such as Pi and Pair Sequence S...

- November 28th, 2019, 5:53 pm
- Forum: The Sandbox
- Topic: Ordinals in googology
- Replies:
**166** - Views:
**4934**

### Re: Ordinals in googology

Can anyone explain me ordinals significantly bigger than the BHO? In many commonly used ordinal notations, W_1 acts as a fixed point of psi_0. We can then define psi_1 which creates expressions with W_1, and define W_2 as a fixed point of psi_1. Many strong notations, such as Pi and Pair Sequence S...

- November 25th, 2019, 4:29 pm
- Forum: Patterns
- Topic: 19-bit still life syntheses
- Replies:
**92** - Views:
**5172**

### Re: 19-bit still life syntheses

A slightly more expensive method from the other side: x = 23, y = 24, rule = B3/S23 15bo$14bo$14b3o2$13bo$14bo$12b3o2$19bo$17b2o$18b2o$4bo$5b2o$4b2o3$19b 2o$15b2o2bo$14bo2bobo2bo$15bobo2b3o$6b2o8bob2o$2o5b2o8bo2bo$b2o3bo11bo bo$o18bo! One fewer glider and much more clearance: x = 23, y = 20, rule =...

- November 22nd, 2019, 5:14 pm
- Forum: Patterns
- Topic: Oscillator Discussion Thread
- Replies:
**1188** - Views:
**541724**

### Re: Oscillator Discussion Thread

Indeed, four cells off the P49: That version was supposed to have a smaller footprint; if it's population you want reduced, you'll want this version: x = 18, y = 16, rule = B3/S23 8b2o$8bo$10bob2o$2b2o5b2obo$bo2bob2o4bo$o2b2obob4ob2o$b2o5bo2bobobo$3b 4o2bo2b2obo$3bobo4bo2bob2o$4bo5b4o2bo$b3o6bo3b3o...

- November 21st, 2019, 10:46 am
- Forum: Patterns
- Topic: Oscillator Discussion Thread
- Replies:
**1188** - Views:
**541724**

### Re: Oscillator Discussion Thread

More clearance in the back at the cost of some top clearance:

Code: Select all

```
x = 18, y = 15, rule = B3/S23
8b2o$6b3obobo$5bo4b2obo$5bob2o4bo$2o2b2obob4ob2o$o2bo5bo2bobobo$b2ob4o
2bo2b2obo$2bobobo4bo2bob2o$2bo2bo5b4o2bo$3b2o6bo3b3o$11b4o2bo$14bob2o$
11b2obobo$11b2obobo$15bo!
```

- November 15th, 2019, 10:37 pm
- Forum: The Sandbox
- Topic: Challenges
- Replies:
**240** - Views:
**60713**

### Re: Challenges

Find a gun with the smallest bouding diamond width perpendicular to the glider stream Simkin's p120 is gonna be pretty hard to beat at only 29hd: x = 52, y = 24, rule = LifeHistory D20.2A5.D$.D6.4B2.B.3B.BABA5.D$2.D5.4B.8BA9B$3.D3.2A5B2A16B$4.D2.2A5B 2A16BD$5.D2.B.22B.D$6.D3.B2A21BD$7.D3.2A7B2.13BD...

- November 14th, 2019, 11:02 pm
- Forum: Patterns
- Topic: Oscillator Discussion Thread
- Replies:
**1188** - Views:
**541724**

### 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...

- November 14th, 2019, 10:37 pm
- Forum: The Sandbox
- Topic: Ordinals in googology
- Replies:
**166** - Views:
**4934**

- November 12th, 2019, 12:12 am
- Forum: The Sandbox
- Topic: Thread for Non-CA Academic Questions
- Replies:
**309** - Views:
**75549**

- November 10th, 2019, 11:55 am
- Forum: Patterns
- Topic: Oscillator Discussion Thread
- Replies:
**1188** - Views:
**541724**

### 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:
**92** - Views:
**5172**

### 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:
**309** - Views:
**75549**

### 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:
**166** - Views:
**4934**

### 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:
**73** - Views:
**12462**

### 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:
**166** - Views:
**4934**

### 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:
**336** - Views:
**316695**

### 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:
**309** - Views:
**75549**

### 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:
**166** - Views:
**4934**

### 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:
**92** - Views:
**5172**

### 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...