Search found 1940 matches

by BlinkerSpawn
February 21st, 2020, 10:35 pm
Forum: The Sandbox
Topic: Ordinals in googology
Replies: 169
Views: 5739

Re: Ordinals in googology

So instead I'll work on a way to turn trees into ordinals... This notation, given I'm interpreting it correctly, has limit e_0. Proof: From the successorship and expansion rules we get that a-b must have value a+b. The tree (a+1)-0 is equivalent to a-a-a-a-... with w a's, so the value of (a+1)-0 is...
by BlinkerSpawn
February 21st, 2020, 10:17 pm
Forum: Patterns
Topic: Soup-based syntheses
Replies: 151
Views: 37510

Re: Soup-based syntheses

Soup for a double eureka variant with twits: x = 35, y = 71, rule = B3/S23 34bo$32b2o$33b2o18$8b2o6b2o$7bo2bo4bo2bo$8b2o6b2o5$o24bo$4o18b4o$3bo 18bo$3bo18bo3$3o20b3o4$3o20b3o3$3bo18bo$3bo18bo$4o18b4o$o24bo5$8b2o6b 2o$7bo2bo4bo2bo$8b2o6b2o18$33b2o$32b2o$34bo! Note that the related xp30_252y1252z04r4...
by BlinkerSpawn
February 16th, 2020, 3:03 pm
Forum: The Sandbox
Topic: Challenges
Replies: 252
Views: 61688

Re: Challenges

New number challenge I made up: You have a number x. You square it, sort the digits in non-descending order, and remove exactly one digit. The resulting number is 123456. What is the lexicographically smallest x? 1112. "Lexicographical" doesn't mean anything because the number of digits in x is for...
by BlinkerSpawn
February 16th, 2020, 2:57 pm
Forum: The Sandbox
Topic: Accumulation [GAME]
Replies: 78
Views: 529

Re: Accumulation [GAME]

+52
Hunting: 404 Not Found
testitemqlstudop: 333
PkmnQ: 247
Moosey: 163
BlinkerSpawn: 79
Gustone: 65
Hdjensofjfnen: 46
EV2: 41
by BlinkerSpawn
February 14th, 2020, 12:20 am
Forum: The Sandbox
Topic: Accumulation [GAME]
Replies: 78
Views: 529

Re: Accumulation [GAME]

+27
Hunting: 202
Moosey: 78
testitemqlstudop: 54
BlinkerSpawn: 27
Hdjensofjfnen: 17
by BlinkerSpawn
February 10th, 2020, 9:00 pm
Forum: Patterns
Topic: Oscillator Discussion Thread
Replies: 1245
Views: 550226

Re: Oscillator Discussion Thread

This suggests a maybe tractable route, although I don't know that the grin (or equivalent) and the spark can be inserted in such close proximity: x = 13, y = 15, rule = B3/S23 2b2o5bo$10bo$2ob3o4bo$2b2o5bo$2bo8bo$5b2o3bo$5bobobo$3bobob2o$4bo$10b o$9b3o$9b3o$8b2ob2o$9b3o$9b3o! Another generation bac...
by BlinkerSpawn
February 9th, 2020, 2:45 pm
Forum: The Sandbox
Topic: Smallest still lifes with specific islands
Replies: 10
Views: 383

Re: Smallest still lifes with specific islands

Hitting the 30+'s: xs7_134og: (39) x = 11, y = 9, rule = LifeHistory 2A3.2A$A.A2.A3.2A$2.A4.C2.A$2.2A2.2C.A$2A3.C3.2A$.A.2C2.2A$A2.C4.A$2A 3.A2.A.A$4.2A3.2A! xs7_13co: (27) x = 10, y = 10, rule = LifeHistory 8.2A$7.A.A$7.A$4.2C.2A$5.C2.A$2A.A2.C$.A.2A.2C$.A2.A2.C$2.A2.A$3.2A! xs7_1bs: (26) x = 10, y...
by BlinkerSpawn
January 26th, 2020, 11:28 am
Forum: Patterns
Topic: Soup search results
Replies: 2123
Views: 1236308

Re: Soup search results

A soup I found for an xs32 in 2018, still the only soup for it and there is no listed synthesis yet, the soup might be useful: soup Reduces to a small seed fairly easily: x = 19, y = 23, rule = B3/S23 o$b2o6bo$2o6b3o2$5b2o$5bob2o$5bob2ob2o$6b2o2b2o$11bo3$16bo$14b4o$13b2o 3bo$12bo3b2o$13b4o$14bo2$10...
by BlinkerSpawn
January 8th, 2020, 7:34 pm
Forum: Patterns
Topic: Synthesising Oscillators
Replies: 1003
Views: 741133

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: 1245
Views: 550226

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: 99
Views: 6361

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: 252
Views: 61688

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: 252
Views: 61688

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: 16
Views: 1739

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: 169
Views: 5739

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: 169
Views: 5739

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: 99
Views: 6361

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: 1245
Views: 550226

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: 1245
Views: 550226

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: 252
Views: 61688

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: 1245
Views: 550226

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: 169
Views: 5739

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: 315
Views: 76693

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: 1245
Views: 550226

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: 99
Views: 6361

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...