Semi-freestyle 3-cycle for edges

[Lucas Garron]

This is the general idea about turbo as I understood it:

1) Get 3 edges at 3 fixed positions (orientation doesn't matter so setups are short)
2) Cycle 3 edges using 1 of 8 different algorithms.

This way you solve 2 edges completely (orientation + permutation) at a time

I don't know anything about TuRBo corners

No idea what that means. But yesterday night I stumbled across an idea for 3-cycling edges using nearly normal memo. The main idea is that a quarter turn on L or R will "flip" the orientation of an edge, allowing you to cycle a flipped piece in to a flipped position (which gets solved with setup moves). There may be up to one edge left flipped per cycle and some parities.

So as long as no edges in a cycle are flipped, the normal 3-cycle rules apply: <U, F, D, B, L2, R2> setups are free. Every time a piece in the cycle is encountered that is flipped, each piece remaning must be flipped before being cycled (using R, R', L, L', M, M', E, E', S, or S'). When another flipped piece is encountered, the rest should not be flipped, and so on...
It's not quite freestyle, but feels like it. Cycling is still restricted and memo is like in normal 3-cycle, except that for good performane, EP and EO should be combined or interleaved (wchich might reduce looking time?). It's only that L, R, etc. are used for setups to deal with parity during cycling.

(CODE just makes text monospaced)
Here's an edges-only scramble generated using Cube Explorer:
L2 D' U B2 D F L' B F2 L' U' F' R B L B2 F2 

The cycles are (ignoring orientation):
UF -> BR -> UL -> UB -> DF -> DL -> UR -> BL ;  FL -> DR -> DB -> FR

Orientation (F = Flipped; O = Oriented Correctly/Not Flipped)
O     O     F     O     F     O     F     F  ;  F     F     F     F

Whether to be flipped before being cycled:
O     O     O     F     F     O     O     F  ;   O     F     O     F
(The last piece of the cycle will return to the beginning oriented in both cycles.)

Here's how I would solve it using this idea (let's hope my cycling algs aren't confusing...):
{Setup BL - O} B.
{Cycle} B2U'B'U'BUBUBU'B.
{Undo BL Setup - O} B'.
{UB Setup - F} B'R'.
{DF Setup - F} D'L'.
{Cycle}U'F'U'F'U'FUFUF.
{Undo DF Setup - F} LD.
{Undo UB Setup - F} RB.
{No setup}.
{Cycle} LUL'U'L'U'L'ULU.
{Setup DR - F} R
FDFD2F'D'F'D'F2D
{Undo Setup DR - F} R'
{Parity Setup} RU'FL
{Parity} M2'U'M2'U2'M2'U'M2'
{Undo Parity Setup} L'F'UR'
See an [url=http://archive.garron.us/solves/2007/BLD_edge_idea_1.htm]animation[/url]

Each piece is flipped during setup according to the parity of preceeding flipped pieces in the cycle. Flipping or non-flipping continues until after a flipped piece. That way, the previous pie ce will be placed corrrectly into that one, and the piece taken out flipped inserted flipped, and un-set-up correctly.
If there were more edges, the orientation and corresponding flip during setup will be as follows:
OOOOOFOOOOOFOOOFOOOOFOFOOOOFFOOOFOFFOFFOOFFFOFFFFOFFFOFFOFFOFFFOFFOFFFOFFOFF
OOOOOFFFFFFOOOOFFFFFOOFFFFFOFFFFOOFOOFOOOFOFFOFOFFOFOOFOOFOOFOFFOFFOFOOFOOFO
That should help. Note that the last "F" on top will cause the last cycle piece to return to the first cycle piece's position flipped, because the next letter in the bottom would be "F."

I didn't really go into parities: They occur whenever there are an odd number of flipped pieces are in a cycle or a piece is placed but misoriented. Those than be flipped by any algs or methods...
Parities are also not too special. They work like normal, escept the two edges alone have to be switch. The only thing is that orientation could get confusing in a parity.

I don't plan to try this for corners. My CO is nice (and it will be easy to get CP down), and 3 orientations could gt confusing...

Does anyone else get this? Does it seem like a good idea. Feel free to comment, improve, ask for elucidation or ask for an example solve of and edge case.
I'm planning to improve on my current technique, try M2, and experiment with this, and see which works best.

Edit 1: Fixed some annoying Notepad line-splitting...
Edit 2: Comment: I just realized that "freestyle" in the tile is kinda inappropriate... Freestyle would worry about cycling with commutators, not interpreting a restricted system to work more generally...

 

[Lucas Garron]

Erik just posted TuRBo, I see...

So TuRBo deals with orientation in the alg by using standard positions, while this uses standard 3-cycle orientation-preserving algs with setups to deal with orientation...

I like mine more

 

[pjk]

Hey Lucas,
Yeah, I had that same thought after seeing Matyas solve over and over again. Setups will fix orientation, and you 3 cycle them. The only different in memo would be to remember which setup you did and how it affected the orientation. I definitely want to give it a shot sometime.

 

[Lucas Garron]

The only different in memo would be to remember which setup you did and how it affected the orientation.

Actually, you memo the orientation and then figure out the setup (probably while blindfolded). But it doesn't involve keeping track of how setup affects orientation, except during R/L/M/E/S quarter turns... You just add a constraint to steups, but they end up like normal, only a bit longer...

 

[LarsN]

I have been toying with this idea as well, but I found it too difficult to keep track of the flipping. But after seing you setting it up like this, I'll give it a try again.
Nice exampel...

 

[hait2]

seems similar to my extension to the 3cycle method i was talking about a while back where i eliminated EO

i just used basic 3cycle though, bring the edges to the U layer as usual and do the normal alg. except i bring them to the U layer in such a way that fixes their orientation

it's pretty simple to look at it like this:
there's 4 cases (c=correct, w=wrong)

0 - CC
1 - WC
2 - WW
3 - CW

the number indicates what piece you have to 'screw up' (use a R/R' L/L' or a slice) when you bring to the U layer. the 2 letters indicate the orientation of the first 2 pieces in the cycle

so if u have a cycle that starts off with 2 unoriented edges (WW)
then when bringing the edges to the U layer, you would screw up the 2nd edge in the cycle (since 2 - WW)

it's pretty simple, i've been using it a while, no progress as of yet though.

there's minor complications (like odd oriented edges in a cycle) which are easily seen during memo and i fix them right away (so not *really* eliminating EO, but pretty close)

i also have something similar for corners but i'm still working out the kinks (you'd need 8 algs, but currently i really don't like 3 of them)
it's like 3-cycle 2.0

 

[Erik]

Erik just posted TuRBo, I see...

So TuRBo deals with orientation in the alg by using standard positions, while this uses standard 3-cycle orientation-preserving algs with setups to deal with orientation...

I like mine more

wrong, I don't care about orientation when thinking up the setup moves I just check the orientation after the setup moves and apply one of the 8 algorithms to solve 2 pieces.