L2L4 Documentation ("Finished") and Discussion

[StachuK1992]

As a few of you know, I decided a few days ago that I would document and learn L2L4.
It seems as though no one else was taking major initiative in working on it, and I needed a new documentation project, so 12 days later, I'm done generating the 220 algorithms and documenting them.

The previous thread was here where some discussion and a tiny bit of progress was made. I still need to sift through this for algorithms and whatnot to make my list better.

This is the general idea of L2L4:
Solve a 1x3x3 block, often called a "layer" in any typical layer-by-layer method.
Solving one edge at a time, solve the edge and corner orientations and permutations, in whatever order.

As you can imagine, this method is extremely alg-heavy, totaling for a "pure" system to be 220.
Through a bit of research, the order presented here seems to be the most fitting.

Without further ado, here are the algs:
CO, which solves FL while orienting the LL corners.
CP, which solves FR while permuting the LL corners, making sure not to disturb the orientations of said corners.
then do a y2!
EO, which solves FL while orienting the remaining edges making sure not to disturb anything other than the final 6 edges which are in the working zone
EP, which permutes the final 5 edges.

A few example solves:

F2 R L U' B2 F' D B F L2 D F' U F2 U D L' B2 L2 U R U' D' R2 U2

1) U B' L F L F' L2 F2 L' F R U' x2
2) R' D2 L2 D F D R2 U2 R'
3) R2 B R' U B U2 R2 U R B' U y
4) R2 U2 F R F' U' R2 F' U' F U' R2 U2
5) R' U R U R' U2 R U' R' U' R U2

U L' B' L U F D U2 B R' F2 R B' R B' U' D L B2 R D R2 B2 R' F2
1) (x2 F2 U2 L F R' D L F) (R D2 L' D2 R U2 R') as you can tell, Thom's better than me at FL
2) U d2 R U R' U L' F2 L2 F2 L
3) U2 R U R U D' R U R' D R2 U2 R' U R'
4) y2 U' R U R' F' U2 R' F' R F
5) U' R U R2 U R U R' U' R' U' R' U R' U' R' U2

Be warned - these algs...they need much revision. I wanted to get this idea out there, and an alg ready for ever case. If you have any additions/changes/fixes, please let me know. In fact, I still need one alg for CP.

Advantages:
After the first layer, the average TPS should be fairly fast as it's essentially just alg after alg.
Recognition is *not* a problem. Just find the edge while looking at the last layer.
Good for TeamBLD?

Disadvantages:
Movecount, perchance.
lots of algs.


I will be learning these, apart from CO, and here's why I feel that my CLS hack for L2L4 shall be sufficient:
Rather than doing a full 1x3x3, I plan to do a 1x2x3 with a 1x1x2 attached (basically FL - a corner)
Then, using a CLS alg or a WV case, or even an intuitive F2L 'alg' I can solve that final corner, CO, and the final edge.
Then just continue with the rest of the method.


I do realize that I make a lot of these threads where I just publish something and it gets bashed. Oh well; I put time into these and I know they have a decent potential.


Thanks for reading, and let me know your thoughts.
Stachu

PS - Please please please give me better algs.

 

[cincyaviation]

<3 statue. I might just learn this for some purpose yet to be determined, I'll see how it does with OH.

 

[StachuK1992]

For learning this, here's the order I guess I'd learn this in:
EP - because it's Easy to Practice
EO - because it's really hard to do intuitively (for me) on the spot and it's a good large chunk.
CP - because it's probably faster to learn than CO, and CO can be done swiftly in two steps with just 'normal' LL algorithms.
and finally CO

 

[cincyaviation]

For learning this, here's the order I guess I'd learn this in:
EP - because it's Easy to Practice
EO - because it's really hard to do intuitively (for me) on the spot and it's a good large chunk.
CP - because it's probably faster to learn than CO, and CO can be done swiftly in two steps with just 'normal' LL algorithms.
and finally CO

Honestly i would learn EP last because it's just 2 easy 3 cycles. I would probably just learn them in order, maybe do CP first though.

 

[irontwig]

inb4lrn2waterman

 

[riffz]

I might learn some of these 5-cycle edge algs in the hopes that they may pop up in a BLD solve

I would like to learn this because I'm very curious about the method's potential, but I am truly terrible at block building a first layer.

 

[StachuK1992]

Honestly i would learn EP last because it's just 2 easy 3 cycles. I would probably just learn them in order, maybe do CP first though.

Aww, you didn't get my EP joke (Easy to Practice!) But hrm, I'll probably just jump around in sets from different steps.

I would like to learn this because I'm very curious about the method's potential, but I am truly terrible at block building a first layer.

For some reason, I just can't blockbuild on while/yellow half as well as any other face. I may switch to another color as my main just for this method.

 

[oll+phase+sync]

inb4lrn2waterman

I don't fully understand, but this are my thoughts to believe in the higher potential of L2L4
- watermann requires CLL recognition wich was harder to learn (at least for me)
- also the edge steps in watermann require some "piece searching" in the back of the cube,
- you use many .. turn R as apropiet ... unturn R ... stuff , witch may not be super speed friendly

EDIT The old thread is a bit overcrouded but I try to repeat some of the highlights of L2L4

Most algs belong in the CP category (over 100) but if just know the cases where the edge is in U layer its just 27 + 27(with missoriented edge) the other cases have a probability of less than 2%
Your chances to get an placed edge (for free) are over 20%
reachen EO with on additional edge placed (E or U layer) gives you the option to 3-cycle (two 3cycles) to the end.

Learn EP first, cause from the 16 cases, 4 are EPLLs, 1 is a conjugated H-Perms, 2 are conjugated Z-Perms , 3 are conjugated Us, only 6 are new 5-cycles.
It may come handy if you get an solved LS corner fro free + COLL + EP5

 

[Cyrus C.]

Awesome. A solve using this will look so funny.

 

[cincyaviation]

Awesome. A solve using this will look so funny.

Imagine if feliks or rowe learned this. 1st layer... gogogo DONE!

 

[StachuK1992]

Imagine if feliks or rowe learned this. 1st layer... gogogo DONE!

My plan:

Do LBL solves for a while being 'color neutral.'
Every time I used red cross, "WOAHH LL SKIP."

Red crosses -> LL skips. Fact.

 

[Zubon]

I love reading about new methods and I think you've done a great job!

However in the time it takes me to solve one layer, I could just use F2L and insert the edges at the same time. For me, there is not much difference in time between solving the first layer and first two layers using CFOP.

If I understand your method correctly?

CFOP - Cross + CE pairs + 2 algs
L2L4 - Cross + corners + 4 algs

If some people could make the first layer using block building or another method, L2L4 would not require a cross, but I am not good enough to do that....

So this method is useful for people that would rather do 2 more algs than insert CE pairs instead of corners.

 

[Diniz]

If some people could make the first layer using block building or another method, L2L4 would not require a cross, but I am not good enough to do that....

So this method is useful for people that would rather do 2 more algs than insert CE pairs instead of corners.

Thats the idea Zubon, blockbuild the first layer, so it would be First layer + 4 algs

And CFOP is more like: Cross- CE Pair -CE Pair -CE Pair -CE Pair- 2 algs =p

 

[oll+phase+sync]

I love reading about new methods and I think you've done a great job!

However in the time it takes me to solve one layer, I could just use F2L and insert the edges at the same time.

I belive Mark Waterman mentioned to solve First Layer with Corners First strategy in 16 moves. If corners or the cross are very simple I would go that way, but most of the time I use basic blockbuilding.

That way I often just need 13 moves or less. I also feel that it's easiest (to finish 1st layer) if you started with a 1x2x3, but that might just be because I cannot plan ahead full first layer befor starting.

... so in contrast to stachu I prefer to skip an edge in first layer.

But just dealing with on color should make this kind of blockbuilding much easier than for example Petrus

Personally I also feel that doing L2L4 color neutral is much easier than F2L or waterman color neutral.

 

[FatBoyXPC]

Zubon: If you were to build a layer "F2L style," don't forget that it is easily done without any cube rotations. Obviously though, as stated, using a block building method would be far more efficient for building a layer.

Stachu: I really appreciate all the work done with this, this is actually something I've been wanting to toy with, but I'm far too lazy (and busy) to put in the time that you have for this!

 

[irontwig]

I don't fully understand, but this are my thoughts to believe in the higher potential of L2L4
- watermann requires CLL recognition wich was harder to learn (at least for me)
- also the edge steps in watermann require some "piece searching" in the back of the cube,
- you use many .. turn R as apropiet ... unturn R ... stuff , witch may not be super speed friendly

But then again it's more efficient (low 40stm, even sub-40 with good FL, which rivals full ZB), requires half the number of algs and is proven to be fast. Has anybody thought of doing CLL on R rather than U for Waterman thus saving one or two rotations?

 

[somerandomkidmike]

But then again it's more efficient (low 40stm, even sub-40 with good FL, which rivals full ZB), requires half the number of algs and is proven to be fast. Has anybody thought of doing CLL on R rather than U for Waterman thus saving one or two rotations?

I've tried with some cases. The sune on the right is easy. There are some cases that are very difficult.

 

[StachuK1992]

A quick idea I'm having, that is making me wary because it's not 'pure.'

regular first 3 steps. This will lead us to be having 6 edges remaining (FL, FR, U-layer) and everything else solved.

FL+FR
ELL.

Thoughts? ELL can be done extremely fast, and recognition for both parts seems feasible. Also, you can use ELL for other methods, unlike pure L2L4 that can only be very seldom used.

Concerning waterman, I have never actually looked into it much besides when I initially started cubing - I'll be sure to do that at some point today.

Zubon, fat: always a pleasure developing.

I'm going to explore the possible FL+FR idea now, but I thought it would be important to get 'pure' L2L4 out and running first.

-statue

Edit -
FL+FR, ELL idea:
36 cases + 29 cases = 65

compared to pure:
56 cases + 29 cases = 72 algs

Advantages:
ELL is fast, and can be totally <M,U>
ELL is already documented and researched pretty well.
Less # of cases

Disadvantages:
I feel bad for not using a 'pure' system.
EP6 is totally <R,U> and is nice.

I'll have to check move-count after I find some decent stuff for these 36.

 

[StachuK1992]

Here are some FL+FR algs.
A lot of them are just ELL hacks.

An alternative for the EO and EP steps in L2L4:

-Solve FL and FR after completing the y2 or d2.		36 cases
-ELL.							29 cases

ELL has already been documented well

Number of cases for FL + FR

FL good		4
	FR good		continue
	FR bad		R2 U2 R2 U' F R D R2 D' F' R'
	UF good		R2 U' R U R U R U' R' U' R
			x M' U' M U2 M' U' M x' 
	UF bad		y' R U R U R U' R' U' R' U' 
	
FL bad		4
	FR good		y' {FL good FR bad}
	FR bad		F R2 U2 R' L F2 L' U R' L F' L' F'
	UF good		x U (r U R' U') M (U R U' R') x'
	UF bad		F2 U R U F U2 F' R' F'

FR good		4
	FL good		F2 U2 F2 U2 F2
	FL bad		U M U' R' U' M' U R
	UF good		x M' U M U2 M' U M x'
	UF bad		x M2 U' M' U2 M U' M2 x'
	
FR bad		4
	FL good		x R2 U' M U R2 U M' U' x'
	FL bad		U F U' F' R F R' U' R U F' R'
	UF good		U F M U' M U F' U' 
	UF bad		x U' (L' U' L U) M' (U' L' U l) U x'
	
UF good		10
	FL good		x M' U' M U2 M' U' M x'
	FL bad		x U' (l' U' L U) M (U' L' U L) U x' 
	FR good		L U L U L2 U' L' U' L' U2
	FR bad		F R' F2 R2 U' R' L F L2 U2 L F'
			U R2 U2 R2 U' R F' R' F2 R U F U' R'
			R U R' F' U2 R' F' R F' U2 F2 U2 F2
	UL good		U' L' F' U2 F L U R U2 R'
	UL bad		U2 R U2 R' U' L' F' U2 F L
	UB good		F U2 R U' R' L F L' U2 F'
	UB bad		F' L F2 L2 U' L2 F2 L2 U' L F
			F R U2 R' U' L U F2 U' L' F' U
	UR good		U' R F U F' R' U' L' U' L U2
	UR bad		F L U L F2 L' U' L' F'
	
UF bad		10
	FL good		x M2 U M' U2 M U M2 x'
	FL bad		x U (R U R' U') M' (U R U' r') u' x'
	FR good		(U L' U M') (U' L U M)
	FR bad		F2 R2 F R U' F' R2 F R U F' R' F
	UL good		R' D' F' D R U R U R' U'
	UL bad		U' L' U L U R F U' F' R'
	UB good		F' U2 R' F' R F U2 R U R'
			F' U2 R' F' R L' U L U2 F
	UB bad		L2 F' U2 L2 U2 L2 U2 L2 F L2 
	UR good		F U R U R' L F' L' U' F' 
	UR bad		U2 F R2 F2 R2 U' R2 F2 R2 U' F'

This idea = ~11+11=22 moves.
Original, pure idea = 12+12=24 moves.

This idea = mainly <R,U,F> then <M,U>
Original = mainly <R,U,F> then <R,U>

 

[oll+phase+sync]

But then again it's more efficient (low 40stm, even sub-40 with good FL, which rivals full ZB), requires half the number of algs and is proven to be fast. Has anybody thought of doing CLL on R rather than U for Waterman thus saving one or two rotations?

I think Kirjava did - but how to do CLL recognition on R when my hand covers the R Layer? I also end up in the high 40stm / low 50 stm though I believe the my penalty for not knowing all Watermann EO cases should be only 4 moves and for not knowing watermann optimal CLL mayby 1 move penalty.

Also the fact that watermann is rarly used, makes me believe that a more mainstream compatibel system, could become more used even if it requires faster turning.