Thread: "2x2x2x1: Gyro rotations, and seeking the equivalent 4D"

From: Marc Ringuette <ringuette@solarmirror.com>
Date: Mon, 3 Sep 2018 11:35:39 -0700
Subject: Re: [MC4D] 2x2x2x1: Gyro rotations, and seeking the equivalent 4D



CORRECTION -- I mixed up some axes, so the best part of my last message
ended up quite scrambled.   I got all confused because the corner axes
of the regular and mini puzzle are named differently (R-L versus I-O).  
Here's a better version of the comparison.


For the 2x2x2x2:    the short exchange of the U-D and corner (R-L) axes
is Iy Oy', while the pure rotation, FOro, is Iy Oy' Rx2 Bz2 Uy2 Rx2.  
The short half-exchange is Iy.
For the 2x2x2x1:    the short exchange of the U-D and corner (I-O) axes
is M y M, while the pure rotation, FRro, is  M y M R2 F2 R2 z2.  The
short half-exchange is M U M.


Note that I'm using a tweaked version of Luna's gyro for the 2x2x2x1,
FRro, where I put the y rotation in between the restacks. This version
draws out the parallels between the 2x2x2x1 FRro and my favorite gyro
for the 2x2x2x2, ROIL FOro.  The connection is deep enough that there
are even three versions of each rotation:  the short one on the physical
puzzle, the longer one with cleanup moves to correspond to a one-click
MC4D rotation, and the short half-exchange, that re-aligns only half of
the puzzle corners.


Whatever the details, the parallel between these is still sweeeet.


--Marc


On 9/3/2018 10:22 AM, Marc Ringuette ringuette@solarmirror.com
[4D_Cubing] wrote:
> Here's a different gyro for the 2x2x2x1, FUro, that corresponds
> (CORRECTION, NOT REALLY) to the mini version of my favorite gyro, the
> ROIL version of the FUro (CORRECTION, FOro) gyro.  The connection is
> deep enough that there are even three versions of each rotation:  the
> short one on the physical puzzle, the longer one with cleanup moves to
> correspond to a one-click MC4D rotation, and the short half-exchange,
> that re-aligns only half of the puzzle corners.
>
>
> For the 2x2x2x2:    the short exchange of the L-R and I-O (CORRECTION,
> U-D and L-R) axes is Iy Oy', while the pure rotation, FUro
> (CORRECTION, FOro), is Iy Oy' Rx2 BO2 UO2 Rx2.   The short
> half-exchange is Iy.
> For the 2x2x2x1:    the short exchange of the L-R and I-O axes is E X
> E, while the pure rotation, FUro, is  E X E F2 U2 F2 Y2.  The short
> half-exchange is E R E.




From: Marc Ringuette <ringuette@solarmirror.com>
Date: Mon, 3 Sep 2018 13:27:40 -0700
Subject: Re: [MC4D] 2x2x2x1: Gyro rotations, and seeking the equivalent 4D



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Hi, Luna, thanks for the help in trying to spec out how to squeeze the
2x2x2x1 into the virtual 2^4 by bandaging and recoloring.

Yes, I like your two sequences as candidates for the physical 2x2x2x1
RFro gyro and its equivalent macro in the virtual version.

For bandaging on the virtual puzzle, I was thinking to allow the turns
RO, LO, FO, BO, UO, DO, and the RFro gyro macro sequence, and treat pink
and purple as the same color.

I like how it looks when I zoom the "Eye W Scale" knob to flatten the
I/O dimension, to reflect that the I and O stickers of the RLIOFB faces
remain identically colored.  We have to imagine the pieces of the In
face poking out through the corners.

I need to try making some moves and then doing a gyro.

Yes!  This seems to be working, the two puzzles track each other! Pic
and initial simplistic macro file attached.

I even made a bonus macro for the M S sequence, although I haven't
settled on how to handle the junctions-out states.  I don't think it'll
be particularly difficult, though.

Cheers
Marc

On 9/3/2018 11:13 AM, Luna Harran scarecrowfish@gmail.com [4D_Cubing] wrote:
> Are these equivalent positions?
>
> (M S R2 F2 R2 Y' Z2 on physical puzzle)
> (FRro' UF2 IF2 UF2 on virtual puzzle)
>



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Hi, Luna, thanks for the help in trying to spec out how to squeeze
the 2x2x2x1 into the virtual 2^4 by bandaging and recoloring.



Yes, I like your two sequences as candidates for the physical
2x2x2x1 RFro gyro and its equivalent macro in the virtual version.



For bandaging on the virtual puzzle, I was thinking to allow the
turns RO, LO, FO, BO, UO, DO, and the RFro gyro macro sequence, and
treat pink and purple as the same color.



I like how it looks when I zoom the "Eye W Scale" knob to flatten
the I/O dimension, to reflect that the I and O stickers of the
RLIOFB faces remain identically colored.  We have to imagine the
pieces of the In face poking out through the corners.



I need to try making some moves and then doing a gyro.



Yes!  This seems to be working, the two puzzles track each other!  
Pic and initial simplistic macro file attached. 



I even made a bonus macro for the M S sequence, although I haven't
settled on how to handle the junctions-out states.  I don't think
it'll be particularly difficult, though.



Cheers

Marc



On 9/3/2018 11:13 AM, Luna Harran scarecrowfish@gmail.com
[4D_Cubing] wrote:

cite="mid:CAK-NJMAhYCY60LxirC=zJA38JxRO2qbtdiaBDi=8m5LS9+Ku=A@mail.gmail.com">


Are these equivalent positions?




(M S R2 F2 R2 Y' Z2 on physical puzzle) 

(FRro' UF2 IF2 UF2 on virtual puzzle)















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From: Marc Ringuette <ringuette@solarmirror.com>
Date: Tue, 4 Sep 2018 12:00:55 -0700
Subject: Re: [MC4D] 2x2x2x1: Gyro rotations, and seeking the equivalent 4D



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Hi gang!

I had a lively day yesterday exploring the nature of the 2x2x2x1 mini
puzzle, also known as the twisty stacky 2^3.   Thanks to Luna
particularly for a bunch of help with it!   Thanks also to Andy, Dylan,
and Joel.


"Cuboid, not so much."   After studying it for a couple of days, our
consensus is that this mini puzzle should probably NOT be called a
"2x2x2x1 cuboid".  That would be more misleading than helpful.  The 4D
version of it has the dimensions of the 2x2x2x1 cuboid, but the stacking
moves and/or the Gyro move, that provide access to the full 12
orientation states of the 4D pieces, do not seem to correspond to 4D
rotations that would apply naturally to generalized cuboid puzzles.  In
fact, I've stopped calling the Gyro for the puzzle "the FR rotation" or
even a rotation at all.   It moves and reorients pieces, and it holds
the F-B and R-L axes fixed, but unless we discover that the Gyro has a
natural geometric interpretation as a 4D rotation, I'll quit calling it
a rotation altogether.

As Luna says about the mini puzzle, "I think it's just a subset of the
2^4. A puzzle that's obvious with our physical puzzle, but ultimately
random. It's still interesting though."


I've made a reasonably nice emulation of the mini puzzle inside the MC4D
2^4 hypercube puzzle using a big pile of macros.   Hopefully that'll
help us clarify further what the mini-puzzle is in relation to the full
puzzle and to other subsets of it.  Here's a 10 minute side-by-side video.

  32   Side by side demo for 2x2x2x1 mini puzzle    10m14s
https://youtu.be/e0aUuN0L1Dc

I've attached my MC4D macros file to this mail.   Anybody with MC4D can
play with the virtual mini-puzzle.   I've scrambled and solved the
puzzle using the macro buttons, and it's not too horrible to use.    The
handles for the macros are my usual ones, with the mnemonic "IFUR FUR"
(find the IFUR sticker, and click its F U R subfaces).   Just go into
macro creation mode using those handles, then click freely on the
buttons.   Sliding the "Eye W Scale" knob to the right will make the I-O
axis skinnier as in my video.

All later macro buttons can be composed from sequences of the first 7
(the twists and the Gyro).  Non-obvious algorithms used:
   Gyro(phys) = M S R2 F2 R2 y' z2    (from Luna)
   Gyro(virt macro using 2^4 moves) = RFro UF2 IF2 UF2   (from Luna)
   M U M' (virt macro using prev macros) = x Gyro L2 F2 L x' Gyro B2 L2
x   (from Marc)
   Monoflip RUF by x2 =  y' S R S' R U2 R' U' R U' R' U2 S R' S y R U
R' U R U2 R' U2  (from Marc, applies to both real & virt 2x2x2x1)


Probably we'll end up considering the 2x2x2x1 mini puzzle to be a fun
oddity:  a somewhat arbitrarily defined subset puzzle that's quick and
easy to try if you already have Melinda's 2x2x2x2.


Cheers
Marc


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From: Marc Ringuette <ringuette@solarmirror.com>
Date: Tue, 4 Sep 2018 12:40:39 -0700
Subject: Re: [MC4D] 2x2x2x1: Gyro rotations, and seeking the equivalent 4D



Here's the result of yesterday's efforts (and a few hours this morning
making the video and writing the summary), as sent to the mailing list. 
You probably shouldn't watch the whole video - it's pretty obscure.  
Skim the message below, and sample a minute of the video, that's my
suggestion.

   https://youtu.be/e0aUuN0L1Dc


M.


On 9/4/2018 12:00 PM, Marc Ringuette wrote:
> Hi gang!
>
> I had a lively day yesterday exploring the nature of the 2x2x2x1 mini
> puzzle, also known as the twisty stacky 2^3.   Thanks to Luna
> particularly for a bunch of help with it!   Thanks also to Andy,
> Dylan, and Joel.
>
>
> "Cuboid, not so much."   After studying it for a couple of days, our
> consensus is that this mini puzzle should probably NOT be called a
> "2x2x2x1 cuboid".  That would be more misleading than helpful.  The 4D
> version of it has the dimensions of the 2x2x2x1 cuboid, but the
> stacking moves and/or the Gyro move, that provide access to the full
> 12 orientation states of the 4D pieces, do not seem to correspond to
> 4D rotations that would apply naturally to generalized cuboid
> puzzles.  In fact, I've stopped calling the Gyro for the puzzle "the
> FR rotation" or even a rotation at all. It moves and reorients pieces,
> and it holds the F-B and R-L axes fixed, but unless we discover that
> the Gyro has a natural geometric interpretation as a 4D rotation, I'll
> quit calling it a rotation altogether.
>
> As Luna says about the mini puzzle, "I think it's just a subset of the
> 2^4. A puzzle that's obvious with our physical puzzle, but ultimately
> random. It's still interesting though."
>
>
> I've made a reasonably nice emulation of the mini puzzle inside the
> MC4D 2^4 hypercube puzzle using a big pile of macros. Hopefully
> that'll help us clarify further what the mini-puzzle is in relation to
> the full puzzle and to other subsets of it.  Here's a 10 minute
> side-by-side video.
>
>   32   Side by side demo for 2x2x2x1 mini puzzle    10m14s
> https://youtu.be/e0aUuN0L1Dc
>
> I've attached my MC4D macros file to this mail.   Anybody with MC4D
> can play with the virtual mini-puzzle.   I've scrambled and solved the
> puzzle using the macro buttons, and it's not too horrible to use.   
> The handles for the macros are my usual ones, with the mnemonic "IFUR
> FUR" (find the IFUR sticker, and click its F U R subfaces).   Just go
> into macro creation mode using those handles, then click freely on the
> buttons.   Sliding the "Eye W Scale" knob to the right will make the
> I-O axis skinnier as in my video.
>
> All later macro buttons can be composed from sequences of the first 7
> (the twists and the Gyro).  Non-obvious algorithms used:
>    Gyro(phys) = M S R2 F2 R2 y' z2    (from Luna)
>    Gyro(virt macro using 2^4 moves) = RFro UF2 IF2 UF2   (from Luna)
>    M U M' (virt macro using prev macros) = x Gyro L2 F2 L x' Gyro B2
> L2 x   (from Marc)
>    Monoflip RUF by x2 =  y' S R S' R U2 R' U' R U' R' U2 S R' S y R U
> R' U R U2 R' U2  (from Marc, applies to both real & virt 2x2x2x1)
>
>
> Probably we'll end up considering the 2x2x2x1 mini puzzle to be a fun
> oddity:  a somewhat arbitrarily defined subset puzzle that's quick and
> easy to try if you already have Melinda's 2x2x2x2.
>
>
> Cheers
> Marc
>




From: Marc Ringuette <ringuette@solarmirror.com>
Date: Tue, 4 Sep 2018 12:44:31 -0700
Subject: Re: [MC4D] 2x2x2x1: Gyro rotations, and seeking the equivalent 4D



Oops!  That 2nd copy was intended for my mother, who I had chatted with
yesterday in the middle of my puzzle project and was curious to see the
result.  You MC4Ders are supposed to watch and read the whole thing.  ;)

Heh.
Marc

On 9/4/2018 12:40 PM, Marc Ringuette wrote:
> Here's the result of yesterday's efforts (and a few hours this morning
> making the video and writing the summary), as sent to the mailing
> list.  You probably shouldn't watch the whole video - it's pretty
> obscure.   Skim the message below, and sample a minute of the video,
> that's my suggestion.
>
>    https://youtu.be/e0aUuN0L1Dc
>
>
> M.




From: Marc Ringuette <ringuette@solarmirror.com>
Date: Tue, 4 Sep 2018 19:12:27 -0700
Subject: Re: [MC4D] 2x2x2x1: Gyro rotations, and seeking the equivalent 4D



Hello Marc,

FYI, I discussed your mini puzzle to Don Hatch last night and he was unders=
tandably skeptical. He did however think that the general class of 4D cuboi=
ds should be easy for him to implement, so I expect he will knock that out =
soon. It's again unfortunate that our code bases had accidentally diverged,=
and we talked about resolving that but it could be quite a while before re=
sults show up in MC4D at least. Anyway, I forwarded your video from this mo=
rning to him. He watched it and replied simply "Ah ok, I believe it."

Your use of nested macros is an extremely clever and useful trick.

-Melinda

On 9/4/2018 12:40 PM, Marc Ringuette ringuette@solarmirror.com [4D_Cubing] =
wrote:
> Here's the result of yesterday's efforts (and a few hours this morning
> making the video and writing the summary), as sent to the mailing list.
> You probably shouldn't watch the whole video - it's pretty obscure.
> Skim the message below, and sample a minute of the video, that's my
> suggestion.
>
> =C2=A0=C2=A0 https://youtu.be/e0aUuN0L1Dc
>
>
> M.
>
>
> On 9/4/2018 12:00 PM, Marc Ringuette wrote:
>> Hi gang!
>>
>> I had a lively day yesterday exploring the nature of the 2x2x2x1 mini
>> puzzle, also known as the twisty stacky 2^3.=C2=A0=C2=A0 Thanks to Luna
>> particularly for a bunch of help with it!=C2=A0=C2=A0 Thanks also to And=
y,
>> Dylan, and Joel.
>>
>>
>> "Cuboid, not so much."=C2=A0=C2=A0 After studying it for a couple of day=
s, our
>> consensus is that this mini puzzle should probably NOT be called a
>> "2x2x2x1 cuboid".=C2=A0 That would be more misleading than helpful.=C2=
=A0 The 4D
>> version of it has the dimensions of the 2x2x2x1 cuboid, but the
>> stacking moves and/or the Gyro move, that provide access to the full
>> 12 orientation states of the 4D pieces, do not seem to correspond to
>> 4D rotations that would apply naturally to generalized cuboid
>> puzzles.=C2=A0 In fact, I've stopped calling the Gyro for the puzzle "th=
e
>> FR rotation" or even a rotation at all. It moves and reorients pieces,
>> and it holds the F-B and R-L axes fixed, but unless we discover that
>> the Gyro has a natural geometric interpretation as a 4D rotation, I'll
>> quit calling it a rotation altogether.
>>
>> As Luna says about the mini puzzle, "I think it's just a subset of the
>> 2^4. A puzzle that's obvious with our physical puzzle, but ultimately
>> random. It's still interesting though."
>>
>>
>> I've made a reasonably nice emulation of the mini puzzle inside the
>> MC4D 2^4 hypercube puzzle using a big pile of macros. Hopefully
>> that'll help us clarify further what the mini-puzzle is in relation to
>> the full puzzle and to other subsets of it.=C2=A0 Here's a 10 minute
>> side-by-side video.
>>
>> =C2=A0 32=C2=A0=C2=A0 Side by side demo for 2x2x2x1 mini puzzle=C2=A0=
=C2=A0=C2=A0 10m14s
>> https://youtu.be/e0aUuN0L1Dc
>>
>> I've attached my MC4D macros file to this mail.=C2=A0=C2=A0 Anybody with=
MC4D
>> can play with the virtual mini-puzzle.=C2=A0=C2=A0 I've scrambled and so=
lved the
>> puzzle using the macro buttons, and it's not too horrible to use.
>> The handles for the macros are my usual ones, with the mnemonic "IFUR
>> FUR" (find the IFUR sticker, and click its F U R subfaces).=C2=A0=C2=A0 =
Just go
>> into macro creation mode using those handles, then click freely on the
>> buttons.=C2=A0=C2=A0 Sliding the "Eye W Scale" knob to the right will ma=
ke the
>> I-O axis skinnier as in my video.
>>
>> All later macro buttons can be composed from sequences of the first 7
>> (the twists and the Gyro).=C2=A0 Non-obvious algorithms used:
>> =C2=A0=C2=A0 Gyro(phys) =3D M S R2 F2 R2 y' z2=C2=A0=C2=A0=C2=A0 (from =
Luna)
>> =C2=A0=C2=A0 Gyro(virt macro using 2^4 moves) =3D RFro UF2 IF2 UF2=C2=
=A0=C2=A0 (from Luna)
>> =C2=A0=C2=A0 M U M' (virt macro using prev macros) =3D x Gyro L2 F2 L x=
' Gyro B2
>> L2 x=C2=A0=C2=A0 (from Marc)
>> =C2=A0=C2=A0 Monoflip RUF by x2 =3D=C2=A0 y' S R S' R U2 R' U' R U' R' =
U2 S R' S y R U
>> R' U R U2 R' U2=C2=A0 (from Marc, applies to both real & virt 2x2x2x1)
>>
>>
>> Probably we'll end up considering the 2x2x2x1 mini puzzle to be a fun
>> oddity:=C2=A0 a somewhat arbitrarily defined subset puzzle that's quick =
and
>> easy to try if you already have Melinda's 2x2x2x2.
>>
>>
>> Cheers
>> Marc
>>
>
>
> ------------------------------------
> Posted by: Marc Ringuette
> ------------------------------------
>
>
> ------------------------------------
>
> Yahoo Groups Links
>
>
>
>





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