# Message #4075

From: Marc Ringuette <ringuette@solarmirror.com>

Subject: ROIL Zero explanation, was Re: [MC4D] correction and question

Date: Sat, 28 Jul 2018 10:15:40 -0700

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