Search found 1932 matches

by BlinkerSpawn
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...
by BlinkerSpawn
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$5bo2bobo$...
by BlinkerSpawn
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...
by BlinkerSpawn
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?
by BlinkerSpawn
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...
by BlinkerSpawn
December 5th, 2019, 3:31 pm
Forum: The Sandbox
Topic: Guess the sequence [GAME]
Replies: 15
Views: 1597

Re: Guess the sequence [GAME]

testitemqlstudop wrote:
July 31st, 2019, 11:18 pm
Do 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
a(n) = digits of 9n in ascending order
by BlinkerSpawn
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...
by BlinkerSpawn
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...
by BlinkerSpawn
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 =...
by BlinkerSpawn
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...
by BlinkerSpawn
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!
by BlinkerSpawn
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...
by BlinkerSpawn
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...
by BlinkerSpawn
November 14th, 2019, 10:37 pm
Forum: The Sandbox
Topic: Ordinals in googology
Replies: 166
Views: 4934

Re: Ordinals in googology

PkmnQ wrote:
November 14th, 2019, 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: 309
Views: 75549

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: 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...
by BlinkerSpawn
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...
by BlinkerSpawn
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

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: 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 ...
by BlinkerSpawn
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
!
by BlinkerSpawn
October 31st, 2019, 9:49 pm
Forum: The Sandbox
Topic: Ordinals in googology
Replies: 166
Views: 4934

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: 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...
by BlinkerSpawn
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 ...
by BlinkerSpawn
October 23rd, 2019, 5:21 pm
Forum: The Sandbox
Topic: Ordinals in googology
Replies: 166
Views: 4934

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: 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...