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On 7/28/2018 3:06 AM, 'Eduard Baumann' ed.baumann@bluewin.ch [4D_Cubing]
wrote:
>
> Question to Marc: what is R[U] exactly in the names of the macro's?
>
Hi, Ed!�� I explain this in my videos, but I should write it down too.��
Here it is.
In my ROIL Zero macros,
� R [ U ]� ==�� on the R cube, make a U move (leaving a side-effect on
the buffer)
�������������� ==�� Rz2 Ix' Rz2
and similarly for the other R [ DLRFB ] using the same buffer, namely,
the four In+Left pieces.�� This is similar to the historical RKT solving
style for MC4D.
If you perform any sequence of R []� such that the sum of the clockwise
quarter-twists adds up to 0 mod 4, then the buffer will emerge
unchanged.� For instance,
�� Sune on R� ==� R [ R U R' U R U2 R' ] == a rearrangement of the U
face of the R cube leaving no side-effects elsewhere.
These macros allow MC4D to follow along with a physical 2x2x2x2 solution
that is done in my convenient ROIL Zero style, that allows the solver to
perform 3D algorithms on any of the R, L, I, or O subcubes of the
physical puzzle, performing a sequence of (individually
parity-violating) 4-cycles, AS LONG AS the sum of the turns adds up to 0
mod 4 when the puzzle halves are reattached.
Nobody but me has used the ROIL Zero style yet, except for "Can Chris
Solve", who did something almost identical in his followup video where
he reconciles his use of 3D algorithms with the requirements of
permutation parity on the MC4D 2^4 puzzle.�� I've cued it up here:
��� https://youtu.be/S6SYi49VZgU?t=2m50s
A few other solvers have simply ignored permutation parity, as I did a
year ago until it was brought to my attention.� Ignoring parity --
freely using 4-cycle twists without counting parity at all -- is even
more convenient, and internally consistent, but solves a slightly
different puzzle than our gold standard of MC4D.��� Doing so leads to a
situation where the physical puzzle can spend a long time in an odd
permutation parity state that cannot be duplicated by MC4D at all.��
Maybe this is fine for you!�� I, and Chris, decided to split the
difference.�� We retained our really convenient shorthand for performing
3D algorithms on the physical puzzle, while doing enough housekeeping to
ensure that the physical puzzle and MC4D are always in compatible states
when the subcubes are reattached at the end of each algorithm.� By
providing these macros, I'm making our approach as kosher as possible,
by providing an explicit way to translate any carefully executed ROIL
Zero solution into a canonical one.
Cheers
Marc
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Thanks a lot!
Ed
----- Original Message -----=20
From: Marc Ringuette ringuette@solarmirror.com [4D_Cubing]=20
To: 4D_Cubing@yahoogroups.com=20
Sent: Saturday, July 28, 2018 7:15 PM
Subject: ROIL Zero explanation, was Re: [MC4D] correction and question
=20=20=20=20
On 7/28/2018 3:06 AM, 'Eduard Baumann' ed.baumann@bluewin.ch [4D_Cubing] =
wrote:
Question to Marc: what is R[U] exactly in the names of the macro's?
Hi, Ed! I explain this in my videos, but I should write it down too. =
Here it is.
In my ROIL Zero macros,=20
R [ U ] =3D=3D on the R cube, make a U move (leaving a side-effect o=
n the buffer)
=3D=3D Rz2 Ix' Rz2
and similarly for the other R [ DLRFB ] using the same buffer, namely, th=
e four In+Left pieces. This is similar to the historical RKT solving styl=
e for MC4D.
If you perform any sequence of R [] such that the sum of the clockwise q=
uarter-twists adds up to 0 mod 4, then the buffer will emerge unchanged. F=
or instance,
Sune on R =3D=3D R [ R U R' U R U2 R' ] =3D=3D a rearrangement of th=
e U face of the R cube leaving no side-effects elsewhere.
These macros allow MC4D to follow along with a physical 2x2x2x2 solution =
that is done in my convenient ROIL Zero style, that allows the solver to pe=
rform 3D algorithms on any of the R, L, I, or O subcubes of the physical pu=
zzle, performing a sequence of (individually parity-violating) 4-cycles, AS=
LONG AS the sum of the turns adds up to 0 mod 4 when the puzzle halves are=
reattached.=20=20=20
Nobody but me has used the ROIL Zero style yet, except for "Can Chris Sol=
ve", who did something almost identical in his followup video where he reco=
nciles his use of 3D algorithms with the requirements of permutation parity=
on the MC4D 2^4 puzzle. I've cued it up here:
https://youtu.be/S6SYi49VZgU?t=3D2m50s
A few other solvers have simply ignored permutation parity, as I did a ye=
ar ago until it was brought to my attention. Ignoring parity -- freely usi=
ng 4-cycle twists without counting parity at all -- is even more convenient=
, and internally consistent, but solves a slightly different puzzle than ou=
r gold standard of MC4D. Doing so leads to a situation where the physica=
l puzzle can spend a long time in an odd permutation parity state that cann=
ot be duplicated by MC4D at all. Maybe this is fine for you! I, and Chr=
is, decided to split the difference. We retained our really convenient sh=
orthand for performing 3D algorithms on the physical puzzle, while doing en=
ough housekeeping to ensure that the physical puzzle and MC4D are always in=
compatible states when the subcubes are reattached at the end of each algo=
rithm. By providing these macros, I'm making our approach as kosher as pos=
sible, by providing an explicit way to translate any carefully executed ROI=
L Zero solution into a canonical one.
Cheers
Marc
=20=20
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On 7/28/2018 3:06 AM, 'Eduard Baumann' ated=20
href=3D"mailto:ed.baumann@bluewin.ch">ed.baumann@bluewin.ch [4D_Cubin=
g]=20
wrote:
>
Question to Marc: what is R[U] exactly in the names of the=20
macro's?