Search found 1050 matches

by toroidalet
January 9th, 2020, 8:21 pm
Forum: The Sandbox
Topic: Largest total uncomputable function competition
Replies: 35
Views: 2130

Re: Largest total uncomputable function competition

Assuming your function is defined, its strength would still be less than ω_1 (we can remove the CK because all admissible ordinals of countable order are countable) because you can view it as the diagonalization across f_ω_α(n)^CK, where α(n) is the minimum order of the busy beaver equivalent for n ...
by toroidalet
January 8th, 2020, 2:55 pm
Forum: Patterns
Topic: Oscillator Discussion Thread
Replies: 1188
Views: 541028

Re: Oscillator Discussion Thread

Hardly:

Code: Select all

x = 20, y = 15, rule = B3/S23
b2o5b2o$b2o5b2o3$bo7bo$3o5b3o7bo$o9bo7bo$b3o3b3o7bobo$18bo$4bobo11bo$
18bo$18bo$17bobo$b2o5b2o8bo$b2o5b2o8bo!
by toroidalet
January 8th, 2020, 2:48 pm
Forum: The Sandbox
Topic: Stabilise [GAME]
Replies: 52
Views: 3624

Re: Stabilise [GAME]

That would actually be 59. Here's 54: x = 13, y = 10, rule = LifeHistory 3.C.CA$.3C.CDC.2C$A3.C2.A.2C$.A2.C.2A$2.A.C2.A$.2A.C2.C.A$5.3C.3A$12. A$5.2A.2C.A$5.2A.2C.2A! EDIT: 53: x = 13, y = 12, rule = LifeHistory 4.A$3.A.A$3.C.C$.3C.2CD.2C$A3.C4.2C$.A2.C$2.A.CA$.2A.C2.C.A$5.3C.3A$ 12.A$5.2A.2C.A$5.2A...
by toroidalet
January 7th, 2020, 1:54 am
Forum: General Discussion
Topic: Create your own terminology
Replies: 102
Views: 39550

Re: Create your own terminology

So this puffer is clean? (run in Golly for at least 100 thousand generations to see the puffer-ness) x = 47, y = 24, rule = B2i3/S23-ce5ry6i 3o$o2bo$b3o19$43b3o$43bo2bo$44b3o! Also, with this example, it's sort of hard to tell where the engine is . Similarly, what would be the engine of a caterpilla...
by toroidalet
January 5th, 2020, 9:11 pm
Forum: Other Cellular Automata
Topic: Gems (B3457/S4568)
Replies: 8
Views: 1306

Re: Gems (B3457/S4568)

13-cell explosive growth:

Code: Select all

x = 2, y = 11, rule = B3457/S4568
bo$2o$2o$bo$bo$bo$bo$bo$bo$bo$bo!
EDIT: explosive growth in a 20-cell (2*10) bounding box. I believe both of these are close to minimal.

Code: Select all

x = 10, y = 2, rule = B3457/S4568
5ob4o$10o!
by toroidalet
December 31st, 2019, 5:47 pm
Forum: General Discussion
Topic: Thread for basic questions
Replies: 1712
Views: 460193

Re: Thread for basic questions

Here's an example of a nonperiodic way to fulfill the parity condition (imagine the block rows extend infinitely) x = 68, y = 71, rule = B1357/S1357 34b2o$34b2o2$34b2o$34b2o2$34b2o$34b2o2$34b2o$34b2o2$34b2o$34b2o2$34b2o $34b2o2$34b2o$34b2o2$34b2o$34b2o2$34b2o$34b2o2$34b2o$34b2o2$34b2o$34b 2o2$34b2o$...
by toroidalet
December 30th, 2019, 3:31 pm
Forum: The Sandbox
Topic: Rule Golf
Replies: 4
Views: 1622

Re: Rule Golf

(This isn't exactly related to the topic of this thread but I wasn't sure where else to put this) How many table lines (counting variables) are needed for a Life ruletable? Here's a 21-line table using rotate4reflect symmetry (I can provide details on how it works if needed): @RULE GolfLife @TABLE n...
by toroidalet
December 28th, 2019, 1:19 am
Forum: Website Discussion
Topic: Pattern viewer for forum threads
Replies: 1409
Views: 317931

Re: Pattern viewer for forum threads

Although the anti-aliasing is gone, the annoying slowness that occurs at zoom levels with more than 1 pixel/cell is still there. I made a video showing rendering bugs, you can find it at https://www.youtube.com/watch?v=mpltWadncZg (the forums don't let you upload videos). It also includes a centerin...
by toroidalet
December 26th, 2019, 2:07 am
Forum: The Sandbox
Topic: Rule Table Thread
Replies: 21
Views: 4691

Re: Rule Table Thread

I thought about adding transition rules so that mismatched tiles die out, but since the tiling is anisotropic there would be a vast amount of 4¹² rules. Never underestimate the power of variables: @RULE Wangtiledeath @TABLE n_states:12 neighborhood:vonNeumann symmetries:none var reddown={0,1,4,6,11...
by toroidalet
December 24th, 2019, 10:13 pm
Forum: Website Discussion
Topic: Pattern viewer for forum threads
Replies: 1409
Views: 317931

Re: Pattern viewer for forum threads

I tried experimenting, and I'm not sure that it's actually the grid edge that's causing the first problem. Instead, when pixels below a certain height are visible, it stops rendering live (or visited) cells altogether. (interestingly, in the holiday theme the snow will fall as though there are no ce...
by toroidalet
December 23rd, 2019, 7:56 pm
Forum: Website Discussion
Topic: Pattern viewer for forum threads
Replies: 1409
Views: 317931

Re: Pattern viewer for forum threads

For me (I use Safari 9.1.3) the viewer will fail to render patterns whenever the edge or gridlines are in view.
by toroidalet
December 23rd, 2019, 7:47 pm
Forum: The Sandbox
Topic: Guess the sequence [GAME]
Replies: 14
Views: 1554

Re: Guess the sequence [GAME]

1,2,5,9,8,6,1,11,21,51,... a(n)=the 180° rotation of the nth number which is still a number when read upside down (i.e composed only of 0,1,2,5,6,8,9) The problem with this thread is that you get a lot of sequences like 6,6,3,3,8,3,5,5, and no one's going to guess that it's "every other digit of 6√...
by toroidalet
December 17th, 2019, 2:21 pm
Forum: Other Cellular Automata
Topic: Rules with the most amount of spaceships
Replies: 4
Views: 274

Re: Rules with the most amount of spaceships

Life has ℵ_0 speeds (for instance, caterloopillars), which is the maximum cardinality possible (since all speeds are triples of natural numbers). I'm also pretty sure that HighLife has that number of replicator ship speeds, too. There are also a great deal of non-totalistic rules with an infinite se...
by toroidalet
December 14th, 2019, 12:28 pm
Forum: Bugs & Errors
Topic: Golly not responding
Replies: 7
Views: 440

Re: Golly not responding

@JP21, please don't post completely unrelated questions outside of "anything goes" sandbox. It adds useless clutter and not much else. @EV2, the best current solution is to save your patterns frequently. Also, I don't think that switching to QuickLife will really help, since (at least for me) when G...
by toroidalet
December 12th, 2019, 12:47 am
Forum: The Sandbox
Topic: [Nonsense Writing]GoL Breaking News
Replies: 10
Views: 1689

Re: [Nonsense Writing]GoL Breaking News

Correction: he bravely runs away. A further inaccuracy: not shown was the minstrel, although this hardly matters since said minstrel was later eaten: x = 203, y = 173, rule = B3/S23 103b2o$103bobo$105bo4b2o$101b4ob2o2bo2bo$101bo2bobobobob2o$104bobobobo $105b2obobo$109bo$144b2o$95b2o47bobo$96bo7b2o40...
by toroidalet
November 24th, 2019, 3:27 pm
Forum: Other Cellular Automata
Topic: Miscellaneous Discoveries in Other Cellular Automata
Replies: 1513
Views: 304869

Re: Miscellaneous Discoveries in Other Cellular Automata

16c/728 spaceship: ship smaller: x = 286, y = 404, rule = B3-ckry4z5c7c/S2-cn3-aky4it5j 37b3o$37bo$38bo31$5b3ob3o$5bobobobo$5bobobobo$7bobo$7bobo$5bobobobo$5b 3ob3o$6bo3bo$201b2o$200bobo$202bo6$o15bo$o15bo$o15bo5$3bo9bo$3bo9bo$3b o9bo25$128b3o$128bo$129bo35$274b3ob3o$273bo2bobo2bo$273bo2bobo2bo$273...
by toroidalet
November 24th, 2019, 2:47 pm
Forum: The Sandbox
Topic: A Code-Golf challenge
Replies: 5
Views: 1407

Re: A Code-Golf challenge

Shorter solution in b****fuck for the original challenge:

Code: Select all

+++++++[->++++++<],[<.>-] or
++++++[->+++++++<],[<.>-]
by toroidalet
November 23rd, 2019, 2:25 am
Forum: The Sandbox
Topic: Google Translate
Replies: 16
Views: 492

Re: Google Translate

Google Translate can more or less parse Russian text as almost any Slavic or Soviet language. Here is text from a Russian website being variously interpreted in Russian , Bulgarian , Croatian , Bosnian , Serbian , Slovenian , Macedonian , Ukrainian , Belarusian , Armenian , Georgian , Kazakh , Azerb...
by toroidalet
November 20th, 2019, 9:43 pm
Forum: The Sandbox
Topic: Largest total uncomputable function competition
Replies: 35
Views: 2130

Re: Largest total uncomputable function competition

I'm fairly confident you can't define a fundamental sequence for ω_1^CK in a finite number of bits, since otherwise you could use the representation to compute the sequence and thus the Busy Beaver function. Also, getting a function with growth rate ω_1 is problematic, since ω_1 has no fundamental s...
by toroidalet
November 9th, 2019, 4:17 pm
Forum: Other Cellular Automata
Topic: Rule request thread
Replies: 517
Views: 180911

Re: Rule request thread

Off-topic, but here's a repeat time 51 electron-G converter: x = 25, y = 30, rule = WW_LIFE 12.D$12.D$12.D$12.D.D$12.D$12.D$12.D$12.D$12.D$12.D$10.D.D$12.D$6.D4. D$6.D4.D3$11.2A5.2D$2.2D6.A2.A4D.2DBCD$.D9.2A5.2D.B2.D$.D19.D2.D$.D 17.2D3.D$2.D3.D4.D6.D5.D$3.D2.D4.D7.3D2.D$4.D9.2D6.D.D$5.9D.7D2.D$14. ...
by toroidalet
November 7th, 2019, 1:12 am
Forum: The Sandbox
Topic: Largest total uncomputable function competition
Replies: 35
Views: 2130

Re: Largest total uncomputable function competition

If for you, universes mean what I think they mean (each universe is a copy of the "dimension ascend" structure with the power to oracle any lower universe), then it would only be ω_(ω^(ω+1))^CK (in the future, I'll ignore the ω_^CK bit for convenience). Of course, you can add dimensions of universes...
by toroidalet
November 3rd, 2019, 4:25 pm
Forum: The Sandbox
Topic: Largest total uncomputable function competition
Replies: 35
Views: 2130

Re: Largest total uncomputable function competition

I'm pretty sure that "tape ascend" is ω_ω^CK (but much faster than the diagonal busy beaver), since it can access an arbitrary but finite (otherwise it would never halt) oracle level, making it the limit of all the oracle Turing machine functions. Similarly, "plane ascend" is ω_(ω^2)^CK,"space ascen...
by toroidalet
November 3rd, 2019, 3:43 pm
Forum: The Sandbox
Topic: Ordinals in googology
Replies: 166
Views: 4856

Re: Ordinals in googology

Is the well ordering of w_1 provable? Isn't well-orderedness part of the definition of an ordinal? If I'm missing something, then see this proof (set X to be the set of natural numbers to get the conclusion that ω_1 exists and is well-ordered) Thanks now I understand everything. But what about w-1?...
by toroidalet
October 31st, 2019, 8:32 pm
Forum: The Sandbox
Topic: Ordinals in googology
Replies: 166
Views: 4856

Re: Ordinals in googology

This is sort of a stupid question, but why isn't ε_1=ε_0^ω?
by toroidalet
October 31st, 2019, 8:28 pm
Forum: The Sandbox
Topic: RLE copy/paste thread - PHPBB12345
Replies: 90
Views: 28513

Re: RLE copy/paste thread - PHPBB12345

x = 256, y = 256, rule = B1357/S02468:T256,256 b2ob2ob2ob2ob2obob2ob2ob2ob2ob2ob3o3b3o3b3ob2ob2ob2ob2ob2ob2ob2ob2ob2o b2ob3o3b3o3b3o5b3o3b3o3b3ob2ob2ob2ob2ob3ob2ob2ob2ob2ob3o3b3o3b3o5b3o3b 3o3b3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3o3b3o3b3ob2ob2ob2ob2ob2obob2ob2o b2ob2ob2o$bo3bobo3bobo5bobo3bobo3bo5bo5...