Challenges

[Moosey]

Beg pardon?

Code: Select all

x = 29, y = 43, rule = B2c3aei4ajnr5acn/S2-ci3-ck4in5jkq6c7c
10b2o$10b2o3$15b2o$15b2o5$2o$2o19b2o$23bo$22bo$5b2o11b3o$5b2o11bo2bo$
18bobo$19b2o19$26b2o$28bo$27bo$23b3o$23bo2bo$23bobo$24b2o!

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x = 32, y = 36, rule = B2c3aei4ajnr5acn/S2-ci3-ck4in5jkq6c7c
2o$2o3$5b2o$5b2o6$11b2o$13bo$12bo$8b3o$8bo2bo$8bobo$9b2o12$29b2o$31bo$
30bo$26b3o$26bo2bo$26bobo$27b2o!

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x = 20, y = 33, rule = B2c3aei4ajnr5acn/S2-ci3-ck4in5jkq6c7c
6b2o$6b2o3$11b2o$11b2o6$17b2o$19bo$18bo$14b3o$14bo2bo$14bobo$15b2o10$b
3o$o2bo$2obo$2bo3bo$4bobo$5bo!

[testitemqlstudop]

That's because the repeat time for the horrendously slow B is several dozen ticks; coupled with the massive spark the replicator produces you can't use it to fast edgy shoot into a stream.

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x = 121, y = 43, rule = B2c3aei4ajnr5acn/S2-ci3-ck4in5jkq6c7c
2o$2o81b2o$83b2o2$5b2o$5b2o81b2o$88b2o6$94b2o$96bo$95bo$91b3o$91bo2bo$
91bobo$92b2o3$2b3o$bo2bo$b2obo$3bo3bo$5bobo$6bo9$35b2o$37bo80b2o$36bo
83bo$32b3o84bo$32bo2bo79b3o$32bobo80bo2bo$33b2o80bobo$116b2o!

SEE?

[Moosey]

SEE?

I already did SEE that it was a high-repeat time "reflector". I was just pointing out additionally that the stream running through the output can collide with the input before the input even hits the reflector, i.e. it's not a very good inserter.
Also we're beginning to get to the point where we may start slinging insults at each other so maybe we should just stop.

[Moosey]

Here's a challenge: make a computer in WWEJ3 which extends its RAM when it is running low on it (i.e has effectively infinite memory)

[fluffykitty]

Does a register machine with infinitely extensible registers count?

[Moosey]

Does a register machine with infinitely extensible registers count?

Sure, anything which adds new memory when running low.

[testitemqlstudop]

What about a machine the consistently makes new memory no matter what?

[Moosey]

What about a machine the consistently makes new memory no matter what?

Doesn't matter.

[testitemqlstudop]

If that's so, you can attach a UC to an existing computer that consistently builds new units of RAM.

[Moosey]

What's your best solution for LSSCG(3)?

[fluffykitty]

http://conwaylife.com/forums/viewtopic. ... 175#p77366

[PkmnQ]

Prove or disprove the existence of a function such that f((3a+2)+(3b+2)) = f((3a+2)*(3b+2)) and f(3n+2) is not equal to f(3n+5).

[Moosey]

Define fundamental sequences for as far as you can! Presumably the farthest you could get is w_1ck,unless you can define
1. An infinite series of ordinals smaller than w_1ck which provably approach w_1ck and not a smaller value
2. Fundamental sequences with lengths that are far larger than w (Buchholz's definition does this, but probably doesn't do it in a nearly satisfactory way; also, {1,2,3,4,5,6,7,8...} (length = w_1ck) still doesn't really define w_1ck)
3. Something else that I didn't think of

Speaking of Buchholz's definition, is "Buchholz's" pronounced with a "ziz" (as in the word "frizzes") sound at the end or a "sz" (as in the word "holes") sound at the end?

[EvinZL]

CHALLENGE: give me the ability to find a rule that actually sparks mild interest.

this is a joke, don't take it seriously please. but if you CAN, please do.

You find interesting patterns you would like to make work in some variant and figure out a rule that lets it work.
EDIT: or you could tweak rules like B2-ac3i/S023 or B3-rn5/S0245, the ones i've focused on.

[testitemqlstudop]

Define the largest countable ordinal you can.
Disclaimer: fluffykitty is probably really good at this, though I imagine a lot of you are.

First fixed point of a |-> a^^^^... a times....^^^^a

[Moosey]

Define the largest countable ordinal you can.
Disclaimer: fluffykitty is probably really good at this, though I imagine a lot of you are.

First fixed point of a |-> a^^^^... a times....^^^^a

Most say that's gamma_0
For some reason saibian says w^^^w = gamma_0

[testitemqlstudop]

For some reason saibian says w^^^w = gamma_0

ridiculous

a-th fixed point of a |-> a^^^^... a times....^^^^a

[PkmnQ]

Define the largest countable ordinal you can.
Disclaimer: fluffykitty is probably really good at this, though I imagine a lot of you are.

Alright, first imagine w_w_w_w...
Then make every w into w^w^w^w^w...
Then turn every w into w_w_w_w...
And you get the idea.
When drawn, it would look like a triangle with a bunch of gibberish in the middle.

[Moosey]

Define the largest countable ordinal you can.
Disclaimer: fluffykitty is probably really good at this, though I imagine a lot of you are.

Alright, first imagine w_w_w_w...
Then make every w into w^w^w^w^w...
Then turn every w into w_w_w_w...
And you get the idea.
When drawn, it would look like a triangle with a bunch of gibberish in the middle.

that's uncountable
Possiby about an inaccessible cardinal

[Moosey]

Challenge: make a bf program that queries for an x and then gets a roughly m^^x for some m as a result in one of the data slots (I.e. tetrational growth if you increment x)
Preferably, respond with an RLE in the bf rule. Not just the program but something that actually starts computing, for, say, x=3

If you need help starting a program, here's how you set up:

Code: Select all

x = 80, y = 4, rule = bf
qJ5.2qU.2qU2.3qU.qU3.2qU3.qU3.2qU6.2qU.3qU2.qU2.2qU2.3qU2.2qU5.qU.qU.
3qU.2qU2.3qU$2.pR3.2qU.2qU2.qU.qU.qU.qU.2qU2.qU.qU.2qU7.qU3.qU2.qU.qU
.2qU3.qU3.qU6.3qU.2qU2.2qU2.2qU$6.qU2.qU.qU.3qU.3qU.qU.qU.qU.qU.qU7.
2qU3.qU2.qU.qU.qU.qU2.qU2.2qU6.qU.qU.3qU.qU.qU.3qU$2.I.qX!

Though you also need an input tape:

Code: Select all

x = 15, y = 4, rule = bf
12.qJ$14.pR$3rSrM$14.I!

[Moosey]

Challenge: come up with an OCF
Example, extremely close to madore's psi:

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C_0(a) = {0,1,w,W}
C_(n+1)(a) = C_(n)(a) U C_(n+1)(a-1) U {b+c,bc,b^c,psi(d), b,c,d ∈ C_n(a), d < a} U {b+c,bc,b^c,psi(d), b,c,d ∈ C_(n+1)(a-1), d < a}, a not a lim ord; 
C_(n+1)(a) = C_(n)(a) U {b+c,bc,b^c,psi(d), b,c,d ∈ C_n(a), d < a}; a a lim ord
C(a) = U (n<w) (C_n(a))
psi(a) = b|(b<W & b ∉ C(a) & ∄c|(c<b & c ∉ C(a)))

It's quite likely that my modification of madore's psi did positively nothing to it.

I shall call it: the First Totally Pointless Venture By Moosey Into Making A Totally Pointless Ordinal Collapsing Function, or the FTPVBMIMATPOC Function

[fluffykitty]

https://googology.wikia.org/wiki/User_b ... on_to_OCFs

[Moosey]

Alright, this makes the STPVBMIMATPOC Function:

Code: Select all

C_0(a) = {0,1,w,W} U {a}
C_(n+1)(a) = C_n(a) U {b+c, bc, b^c, b^^e, psi(d) |b,c,d∈C_n(a), d<a,e =< w}
C(a) = U (n<w)(C_n(a))
psi(a) = b|(b<W & b ∉ C(a) & ∄c|(c<b & c ∉ C(a)))

Also extremely similar to madore's if not the same
psi(0) > e_0

[Moosey]

Challenge: make a bf program that queries for an x and then gets a roughly m^^x for some m as a result in one of the data slots (I.e. tetrational growth if you increment x)
Preferably, respond with an RLE in the bf rule. Not just the program but something that actually starts computing, for, say, x=3

If you need help starting a program, here's how you set up:

Code: Select all

x = 80, y = 4, rule = bf
qJ5.2qU.2qU2.3qU.qU3.2qU3.qU3.2qU6.2qU.3qU2.qU2.2qU2.3qU2.2qU5.qU.qU.
3qU.2qU2.3qU$2.pR3.2qU.2qU2.qU.qU.qU.qU.2qU2.qU.qU.2qU7.qU3.qU2.qU.qU
.2qU3.qU3.qU6.3qU.2qU2.2qU2.2qU$6.qU2.qU.qU.3qU.3qU.qU.qU.qU.qU.qU7.
2qU3.qU2.qU.qU.qU.qU2.qU2.2qU6.qU.qU.3qU.qU.qU.3qU$2.I.qX!

Though you also need an input tape:

Code: Select all

x = 15, y = 4, rule = bf
12.qJ$14.pR$3rSrM$14.I!

Complete:
(Check that this is the right code):
,[>>++[[[>]+[<]>-]>[>]<<[->[-<++>]<<]]>[<+>-]<<<-]

Tetrational growth with respect to input in BF:

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x = 60, y = 6, rule = bf
9.qR$7.qJ$9.pR$3rSrM$9.I$10.HD2F2A3DFCADECFBCFDFC2EDBFDBE2AFC2E2CFDEA
FBC3EBC!

And I think this is pentational:

Code: Select all

x = 81, y = 6, rule = bf
9.qR$7.qJ$9.pR$3rSrM$9.I$10.HD2F2AD2F2A3DFCADECFBCFDFC2EDBFDBE2AFC2E
2CFDEAFBC3EBC2FD2EA2FBC4EBC!

Suggesting something Knuth-y-- you can keep extending it:

Code: Select all

#C Hexational
x = 101, y = 5, rule = bf
6.qJ$8.pR$2rSrM$8.I$9.HD2F2AD2F2AD2F2A3DFCADECFBCFDFC2EDBFDBE2AFC2E2C
FDEAFBC3EBC2FD2EA2FBC4EBC2FD2EA2FBC4EBC!

(Obviously even with small input that gets really large really fast)

Challenge: make one that grows at about f_w(n)

[Moosey]

Easy challenge: write a URL for a google search, where the google search is a URL for the post you respond to this with.