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 Post subject: Re: Patterns
PostPosted: Sat Feb 16, 2013 5:19 am 
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Good optimization work Per! :roll:

These are variations on connecting parts of Anaconda patterns:

CU2 D F U2 F' R MU' R2 MU' B' L' U2 L D
3x: 3 Connected Crosses (13 stm*)

CU2 TD TF TU2 TF' TR MU' TR2 MU' TB' TL' TU2 TL TD
5x: 3 Connected Crosses (13 btm)


The two following sequences could certainly be improved:

R' ND' F2 ND F' NR' F2 NR F R
R' F' U NF2 U' F U NF2 U' R
TR' NF' TU T3B2 TU' NF TU T3B2 TU' TR
5x: 3 Connected Asymmetric Crosses (25 btm)

D F2 D' R B2 R' D F2 D' R B2 R'
R B2 L U2 NB' NU' NB NU U2 L' B2 R'
TR TD2 TF MR MF TU MR TU' TB' TL2 TD' CF'
5x: Another Variation (30 btm)


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 Post subject: Re: Patterns
PostPosted: Sun Feb 17, 2013 10:50 am 
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glazik wrote:
Good optimization work Per! :roll:

These are variations on connecting parts of Anaconda patterns:

CU2 D F U2 F' R MU' R2 MU' B' L' U2 L D
3x: 3 Connected Crosses (13 stm*)

CU2 TD TF TU2 TF' TR MU' TR2 MU' TB' TL' TU2 TL TD
5x: 3 Connected Crosses (13 btm)


The two following sequences could certainly be improved:

R' ND' F2 ND F' NR' F2 NR F R
R' F' U NF2 U' F U NF2 U' R
TR' NF' TU T3B2 TU' NF TU T3B2 TU' TR
5x: 3 Connected Asymmetric Crosses (25 btm)

D F2 D' R B2 R' D F2 D' R B2 R'
R B2 L U2 NB' NU' NB NU U2 L' B2 R'
TR TD2 TF MR MF TU MR TU' TB' TL2 TD' CF'
5x: Another Variation (30 btm)


Well done! No improvements found :|

Per

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 Post subject: Re: Patterns
PostPosted: Sun Feb 17, 2013 1:30 pm 
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I found a Python variation which would be impossible on a 3x3x3 because of the centers.
This is a first, unoptimized attempt:

4x: Fat Python (Order 3)
U2 R2 (MD2 B2 MU' B2 MU R2 MD' R2 (B2 MD')2) R'
U' F L2 F' MR ML F L2 F' U R' U' MR' ML' U'
MR F2 MR2 D2 MR
MU WR2 MD2 WF2 MU' WF2 MD2 WR2
MR' D2 MR2 F2 ML' SF WD' B
L TD (MF WR2 MF2 WR2 MF) TD' L' F'
SR2 F2 MU F2 MU' F2 MD F2 MD' L2 MU R2 TD MB2 TD' (76 btm)


Edit:
These algorithms just do the centers:

4x: Fat Python (centers only)
U2 B2 ML2 (WD2 ML)2 B2 D2 MR SD2 ML'
D2 R2 MF2 (WD2 MF)2 R2 U2 MB SD2 MF' (24 btm)

... and the edges:
4x: Fat Python (edges only)
U2 R U' WR' U R' U' WR2 U L U' WR' U L' U2 (15 btm)


Last edited by Waran on Sun Feb 17, 2013 5:40 pm, edited 1 time in total.

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 Post subject: Re: Patterns
PostPosted: Sun Feb 17, 2013 4:58 pm 
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Centers have been improved, but maybe not optimized yet :wink:

MR2 F2 U2 (WU2 MR WU2 MR') U2 F2 MR2
MF2 R2 D2 (MF WU2 MF' WU2) D2 R2 MF2

4x: Fat Python (centers only) (18 btm)


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 Post subject: Re: Patterns
PostPosted: Sun Feb 17, 2013 5:06 pm 
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... so, this reduces the amount of moves down to 33: :mrgreen:

4x: Fat Python (Order 3)
MR2 F2 D2 ML WD2 ML' U2 B2 ML2 MB2 L2 D2 MB WD2 MB' U2 R2 MF2
U2 R U' WR' U R' U' WR2 U L U' WR' U L' U2 (33 btm)


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 Post subject: Re: Patterns
PostPosted: Sun Feb 17, 2013 6:13 pm 
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By optimizing edges a gain of 4 moves is obtained:
CR2 D L2 F' WU F WR2 F' WU F R2 U'
4x: Fat Python (edges only) (11 btm)

This now gives 29 btm, still improveable I think, maybe by permuting blocks of edges + centers:
4x: Fat Python (29 btm)


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 Post subject: Re: Patterns
PostPosted: Mon Feb 18, 2013 5:17 pm 
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I did some transformations to get three interchangeable parts.
Maybe this helps to further improve the algorithm:

4x: Fat Python
MR2 F2 (D2 ML SD2 MR' U2) F2 MR2
MF2 R2 (D2 MF SD2 MB' U2) R2 MF2
U L2 B' WD B SR2 F' WD' F R2 U' (29 btm)


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 Post subject: Re: Patterns
PostPosted: Tue Feb 19, 2013 4:31 pm 
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I found an alternative solution:

4X: Fat Python (29 btm).

I guess this one is easier to optimise :wink:

EDIT:

Already done:

4X: Fat Python (28 btm).

Now it is hard to optimise further - unless using a new approach :roll:

Per :solved:

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 Post subject: Re: Patterns
PostPosted: Wed Feb 20, 2013 12:25 pm 
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No sequence shorter than 28 btm could be found, even by insertion, so I further worked on updating a few Big Dots patterns:

MR2 F2 T3U2 MR' WU2 MR U2 F2 MR2
4x : (b,f,u) (9 btm)

MR2 TF2 WU2 MF2 U2 MR WU2 MR' U2 F2 MR2
4x: (l,r) (b,f,u) (11 btm)

MD2 F2 R2 MD WR2 MD' T3R2 F2 MD2
MF2 R2 D2 MF WU2 MF' T3D2 R2 MF2
4x : (f,b,l,d,r) (18 btm)

MR2 F2 T3U2 MR WU2 MR' U2 F2 MR2
MF2 R2 D2 MF WU2 MF' T3D2 R2 MF2
4x : (u,b,f)(d,r,l) (18 btm)


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 Post subject: Re: Patterns
PostPosted: Wed Feb 20, 2013 3:22 pm 
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I found a new way to do the centers:

4X: Fat Python (23 btm).

This also improves:

4X: (u,b,f)(d,r,l) (13 btm).

Beat this :lol:

Per :wink:

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 Post subject: Re: Patterns
PostPosted: Wed Feb 20, 2013 6:47 pm 
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@ Per
I have no idea how you managed to find another, even shorter solution ... but it's cool! 8-)


BTW, it's possible to transform a Fat Python into a nice Double Python.
(This pattern was posted before, but the shortest solution then was 61 moves long):

4x: Double Python
MU' R2 MU2 F2 MD' WF WD WF' MU F2 MU2 R2 TU
L2 B' WD B SR2 F' WD' F R2 U'
SR2 F2 MU F2 MU' F2 MD F2 MD' L2 MU R2 TD MB2 TD' (38 btm)


A Fat Python of order 6 is possible as well:

4x: 6 Big Dots (u,r,f,d,b,l) combined with ...
MR' F2 MR ML F2 ML'
WD' MR' F2 MR ML F2 ML' WD
WR' WD' WR WD
SR2 MF2 SR2 MB2 (22 btm)

4x: Fat Python (edges only) is equal to ...
D R' D' ML' D R D' ML
D' F2 R' MD' R SF U SF' R' MD R SF U' B F D
MB2 R' TB D MB' R MB R' D' B' R MB (36 btm)


4x: Fat Python (Order 6)
MR' F2 MR ML F2 ML'
WD' MR' F2 MR ML F2 ML' WD
WR' WD' WR WD
SR2 MF2 SR2 MB2
D R' D' ML' D R D' ML
D' F2 R' MD' R SF U SF' R' MD R SF U' B F D
MB2 R' TB D MB' R MB R' D' B' R MB (58 btm)


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 Post subject: Re: Patterns
PostPosted: Thu Feb 21, 2013 10:14 am 
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Big Dots
Per used long setup sequences (5 moves):
(u,b,f)(d,r,l) (13 btm)
NU' R2 NU2 F2 ND' (WF WU' WF' WU) ND F2 NU2 R2 NU

The same trick can be applied to the remaining 2 3-cycles: 8-)
(u,r,f)(d,b,l) (13 btm)
MR U2 MR2 F2 ML (WU WR WU' WR') ML' F2 MR2 U2 MR'
4x : (u,r,f)(d,b,l) (13 btm)

These 2 short sequences can now be used to improve a few other cycles such as:
(u,r,f,d,b,l) = (u,r,f)(u,d,b,l) = (u,r,f)(d,b,l,u) = (u,r,f)(d,b,l) (d,u)
MR U2 MR2 F2 ML WU WR WU' MR' F2 MR2 U2 MR'
WR2 MF2 WR2 MF2
4x : (u,r,f,d,b,l) (17 btm)

(u,b,f,d,r,l) = (u,b,f)(u,d,r,l) = (u,b,f)(d,r,l,u) = (u,b,f)(d,r,l) (d,u)
MU' R2 MU2 F2 MD' WF WU' WF' MU F2 MU2 R2 MU
WR2 MF2 WR2 MF2
4x : (u,b,f,d,r,l) (17 btm)


Fat Python (Edges only)
The pattern has been partitioned in 2 parts.
Shorter sequences may be obtained by better partitioning, though.
Part 1
D2 R MD2 R' D2 B D' B' R MD2 R' B D B'
Part 2
R2 D2 R WF' D' WF D R' D2 R2
4x : Fat Python (Edges only) (22 btm)

Fat Python (Order 6)
Edges
R2 D2 R WF' D R MD2 R' D2 B D' B' R MD2 R' B D T3B' D R' D2 R2
Centers (u,r,f,d,b,l)
WR2 ML' U2 ML2 F2 ML' WU' WR' WU MR F2 ML2 U2 ML MF2 WR2 MF2
4x : Fat Python (Order 6) (38 btm)


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 Post subject: Re: Patterns
PostPosted: Thu Feb 21, 2013 2:26 pm 
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Hi 8-)

I improved the fat python (order 6), the edges part.

T3U- F WR- B WU- F- WR- WU- B- WR- U NF2 U2 NF2 TU2 NF2 NU2 (17 btm)

This gives:

4X: Fat Python (order 6) (34 btm).

No useful insertion points found ...

Per

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 Post subject: Re: Patterns
PostPosted: Thu Feb 21, 2013 4:27 pm 
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By partitioning the algorithm of edges in 2 parts, a gain of 2 moves is obtained:

CU' D' F WR' B WU' F' WR' WU' B' WR' U
WR2 ML' U2 ML2 F2 ML' WU' WR' WU MR F2 ML2 U2 ML MF2 WR2 MF2
MF2 U2 MF2 TU2 MF2 MU2

4x : Fat Python (Order 6) (32 btm)


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 Post subject: Re: Patterns
PostPosted: Tue Feb 26, 2013 4:17 pm 
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@ glazik and perfredlund
That was excellent optimization work! :mrgreen:


I thought about applying a Python on a 6x6x6 cube and ended up with this quite colorful pattern.
The six colors of the cube are present on each face.

6x: 6-Color-Python
VU' R2 VU2 F2 VD' WF WD WF' VU F2 VU2 R2 T3U
L2 B' WD B SR2 F' WD' F R2 U'
MU' TR2 MU2 TF2 MD' M2F M2D M2F' MU TF2 MU2 TR2 T3U
TL2 TB' M2D TB S2R2 TF' M2D' TF TR2 TU'
T3U T3R2 T3U' (49 btm or 48 btm actually)


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 Post subject: Re: Patterns
PostPosted: Sun Mar 03, 2013 7:08 am 
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A shorter solution could'nt be found for the 6-color Python, so I decided to search for new/shorter/alternate sequences of 4x Big Dots: :)

(f,b)(r,u)
(f,b)(r,l):
WD WR2 WD' WR2
(r,l,u):
MF2 L2 U2 WU2 MF' WU2 MF U2 L2 MF2
(f,b)(r,u) = (f,b)(r,l,l,u) = (f,b)(r,l) (r,l,u):
MB2 WU WF2 WU' L2 T3U2 MF' WU2 MF U2 L2 MF2
4x : (f,b)(r,u) (12 btm)


There are just 5 distinct cases for dots (or rings) 6-cycle, up to inversion + symmetry:

WD' WF WD' WF' MB2 WD2 MB2
4x : (u,b,r,d,f,l) (7 btm)

WF' WU WF MD SR2 MD' L2 B2 MD' SF2 MU F2 R2
4x : (f,u,r,l,b,d) (13 btm)

MU' R2 MU2 F2 MD' WF WU' WF' MU F2 MU2 R2 MU WR2 MF2 WR2 MF2
4x : ( u,b,f,d,r,l) (17 btm)

MR U2 MR2 F2 ML WD' WR WD MR' F2 MR2 U2 MR' WR2 MF2 WR2 MF2
4x : (u,r,f,d,b,l) (17 btm)

(d,u,b,f,l,r)
(d,u):
WR2 MF2 WR2 MF2
(d,b,f,l,r):
WU MF' U2 MB MF U2 MF' WU' MF U2 MF' MB' U2 MF
(d,u,b,f,l,r) = (d,u)(d,b,f,l,r):
WU WR2 MF2 WR2 MF U2 MB MF U2 MF' WU' MF U2 MF' MB' U2 MF
4x : (d,u,b,f,l,r) (17 btm)

@Walter: (u,f,r,d,l,b) (24 btm) can be readily obtained from (u,r,f,d,b,l) (17 btm) by symmetry:
MF' U2 MF2 R2 MB' WU' WF' WU MF R2 MF2 U2 MF WF2 MR2 WF2 MR2
4x : (u,f,r,d,l,b) (17 btm)


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 Post subject: Re: Patterns
PostPosted: Sun Mar 03, 2013 11:29 am 
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@ glazik
Yes, you're absolutely right! Thanks for the hint! All (u,r,f,d,b,l) algorithms in the pattern database are now tranformed into (u,f,r,d,l,b).


These are three new Big Dots:

4x: 4 Big Dots (u,r) (f,d)
WD WR2 MF R2 MB' MF' R2 MB WR2 WD' MB' R2 MB MF R2 MF' (16 btm)

4x: 4 Big Dots (u,f) (r,u)
WD' WF2 MR' F2 ML MR F2 ML' WF2 WD ML F2 ML' MR' F2 MR (16 btm)

4x: 5 Big Dots (u,b) (r,f,l)
MD2 R2 B2 MU SF2 MD' F2 R2 MD2
ML WF R2 WF' MR' ML' WF R2 WF' MR (19 btm)


Big Dots that are still missing are:

4x: 4 Big Dots (u,r,f,d)
4x: 4 Big Dots (u,f,r,d)
4x: 4 Big Dots (u,r,d,f)
4x: 6 Big Dots (u,b) (r,d) (f,l)
4x: 6 Big Dots (u,d) (r,f,b,l)
4x: 6 Big Dots (l,b) (u,r,d,f)
4x: 6 Big Dots (l,b) (u,d,r,f)


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 Post subject: Re: Patterns
PostPosted: Mon Mar 04, 2013 5:27 am 
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@Walter: the 4x subdir has been replaced with the 6x one at your website, maybe you could check it, thanks in advance.


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 Post subject: Re: Patterns
PostPosted: Mon Mar 04, 2013 12:59 pm 
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@ glazik
This should be fixed now.
BTW, thanks to the many contributions here, the page is growing rapidly.
It currently features more than 2700 patterns. :D


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 Post subject: Re: Patterns
PostPosted: Mon Mar 04, 2013 1:07 pm 
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Waran wrote:
@ glazik
This should be fixed now.
BTW, thanks to the many contributions here, the page is growing rapidly.
It currently features more than 2700 patterns. :D


At the rate it is growning, we may end up with every pattern possible :)

-d


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 Post subject: Re: Patterns
PostPosted: Tue Mar 05, 2013 4:34 pm 
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Here is a solution for two of the missing Big Dots patterns:

4x: 4 Big Dots (u,r,f,d)
(WF2 MR2)2
MR' D2 ML MR D2 ML'
WF MR' D2 ML MR D2 ML' WF' (18 btm or 17 btm actually)


(u,f,r,d) is a reflected version of (u,r,f,d):

4x: 4 Big Dots (u,f,r,d)
(WR2 MF2)2
MF D2 MB' MF' D2 MB
WR' MF D2 MB' MF' D2 MB WR (18 btm or 17 btm actually)


Last edited by Waran on Tue Mar 05, 2013 4:53 pm, edited 1 time in total.

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 Post subject: Re: Patterns
PostPosted: Tue Mar 05, 2013 4:51 pm 
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All patterns of the list are now done (may need to be optimized though): :D

(u,f,r,d)
(d,u)
MB2 WR2 MB2 WR2
(d,f,r)
WR2 MB U2 MB' MF' U2 MF WR' MB U2 MB' MF' U2 MF WR'
(u,f,r,d) = (d,u,f,r) = (d,u)(d,f,r)
MB2 WR2 MB' U2 MB' MF' U2 MF WR' MB U2 MB' MF' U2 MF WR'
4x : (u,f,r,d) (16 btm)

(u,r,f,d) is obtained from (u,f,r,d) by point reflection:
4x : (u,r,f,d) (16 btm)


(u,r,d,f)
(u,r,d,f) = (u,r,d)(u,f) = (d,u,r)(u,f) = (d,u) (d,r)(u,f)
(d,u)
MR2 WF2 MR2 WF2
(d,r)(u,f)
WU WF2 MR' F2 ML MR F2 ML' WF2 WU' ML F2 ML' MR' F2 MR
(u,r,d,f)
WU MR2 WF2 MR F2 ML MR F2 ML' WF2 WU' ML F2 ML' MR' F2 MR
4x : (u,r,d,f) (17 btm)


(u,b)(r,d)(f,l)
(u,b,r,d,f,l)
WU WF WU WF' MB2 WU2 MB2
(u,f,r)
MR' F2 MR ML F2 ML' WU MR' F2 MR ML F2 ML' WU'
(u,b)(r,d)(f,l) = (u,b,r,d,f,l) (u,f,r)
WU ML' D2 ML MR D2 MR' WF ML' D2 ML MR D2 MR' WU WF' MB2 WU2 MB2
4x : (u,b)(r,d)(f,l) (19 btm)


(u,d)(l,r,f,b)
(u,d)(l,r,f,b) = (u,d)(l,r)(l,f,b) = (u,d)(l,r)(l,f,b) = (u,d)(l,r)(f,b,l) = (u,d)(l,r)(f,b) (f,l)
(u,d)(l,r)(f,b)
MU2 WF2 MU2 WR WF2 WR'
(f,l)
MU' WR U2 WR' MD MU WR U2 WR' MD'
(u,d)(l,r,f,b)
MU WF2 MU2 WR WF2 U2 WR' MD MU WR U2 WR' MD'
4x : (u,d)(l,r,f,b) (13 btm)


(l,b)(u,d,r,f)
(r,u)(l,d)(b,f)
MF WU' WR2 WU WF' WR2 MB'
(b,l)
MD' WR D2 WR' MU MD WR D2 WR' MU'
(r,u)(l,d,b,f) = (r,u)(l,d)(l,b,f) = (r,u)(l,d)(b,f,l) = (r,u)(l,d)(b,f) (b,l)
MF WU' WR2 WU WF' WR2 MB' MD' WR D2 WR' MU MD WR D2 WR' MU'
Apply symmetry:
(l,b)(u,d,r,f)
MD WB' WL2 WB WD' WL2 MU' MF' WL F2 WL' MB MF WL F2 WL' MB'
4x : (l,b)(u,d,r,f) (17 btm)


(l,b)(u,r,d,f)
WF MD' F2 MD MU F2 MU' WL MD' F2 MD MU F2 MU' WF' WL'
4x : (l,b)(u,r,d,f) (16 btm)

EDIT: some sequences have been improved since by better insertion...


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 Post subject: Re: Patterns
PostPosted: Wed Mar 06, 2013 12:01 pm 
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Waran wrote:
Here is a solution for two of the missing Big Dots patterns:

4x: 4 Big Dots (u,r,f,d)
(WF2 MR2)2
MR' D2 ML MR D2 ML'
WF MR' D2 ML MR D2 ML' WF' (18 btm or 17 btm actually)


(u,f,r,d) is a reflected version of (u,r,f,d):

4x: 4 Big Dots (u,f,r,d)
(WR2 MF2)2
MF D2 MB' MF' D2 MB
WR' MF D2 MB' MF' D2 MB WR (18 btm or 17 btm actually)


In fact these 2 are symmetrically invariant! (basically identical) :wink:

Per

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 Post subject: Re: Patterns
PostPosted: Wed Mar 06, 2013 12:46 pm 
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Alternative solution:

4X: Big Dots (u,b)(r,d)(f,l) (19 btm)

EDIT:

Slightly improved:

4X: Big Dots (u,b)(r,d)(f,l) (18 btm)

Per :solved:

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Last edited by perfredlund on Wed Mar 06, 2013 1:41 pm, edited 2 times in total.

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 Post subject: Re: Patterns
PostPosted: Wed Mar 06, 2013 1:07 pm 
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A very slight improvement (by insertion):

(u,b)(r,f,l)
(u,b)(r,f,l) = (l,r,f)(u,b) = (l,r)(l,f)(u,b) = (l,r) (l,f)(u,b)
(l,r)
WF2 MU2 WF2 MU2
(l,f)(u,b)
WF' WR2 MU L2 MD' MU' L2 MD WR2 WF MD' L2 MD MU L2 MU'
(u,b)(r,f,l)
WF' WR2 MU L2 MD' MU' L2 MD MR2 WF2 ML2 WF' MD' L2 MD MU L2 MU'
4x : (u,b)(r,f,l) (18 btm)


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 Post subject: Re: Patterns
PostPosted: Fri Mar 08, 2013 7:19 pm 
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This pattern shows a pair of Anacondas wrapping around all six faces.
If you rotate the cube to follow the snakes, you may see that they are woven together.
Due to it's color scheme it's quite challenging to build this pattern:

5x: Woven Anacondas
B U R' ND2 R U' B' U B R' ND2 R B' U' F L D' NR2 D L' F' L F D' NR2 D F' SR D B' NU2 B D' R' D R B' NU2 B R' D'
TB' R' NB MR' NB' R TB NU' B' MR B NU NL MF NF' R' MF2 NU MF2 NU' R NF MF' NL' F' NR F NR' MF2 MU' NR F' NR' F MU MF2
NF2 NU B' NU' NF2 NB NU B NU' NB' ND' R' ND NL' ND' R ND NU' NF2 NL F NL' F' NF2 NU F NL F' NR2 B NL' B' NR2 B NL NU' NL' D NL NU ND NL' D' NL B' NR' B ND' B' NR (127 btm or 126 btm actually)


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 Post subject: Re: Patterns
PostPosted: Fri Mar 08, 2013 7:43 pm 
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darryl wrote:
Waran wrote:
BTW, thanks to the many contributions here, the page is growing rapidly.
It currently features more than 2700 patterns. :D
At the rate it is growning, we may end up with every pattern possible :)

Only 43,252,003,274,489,853,300 to go. :wink:

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 Post subject: Re: Patterns
PostPosted: Sat Mar 09, 2013 3:19 am 
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KelvinS wrote:
darryl wrote:
Waran wrote:
BTW, thanks to the many contributions here, the page is growing rapidly.
It currently features more than 2700 patterns. :D
At the rate it is growning, we may end up with every pattern possible :)

Only 43,252,003,274,489,853,300 to go. :wink:


i do not agree that every permutation constitutes a pattern. A pattern should be visually striking or show some other striking property :?:

Per

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 Post subject: Re: Patterns
PostPosted: Sat Mar 09, 2013 11:35 am 
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So even if one found the least striking pattern, that in itself would make it an interesting pattern.

-d


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 Post subject: Re: Patterns
PostPosted: Sun Mar 10, 2013 2:26 am 
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darryl wrote:
So even if one found the least striking pattern, that in itself would make it an interesting pattern.

-d


No, absolutely not! Is the least attractive girl still attractive ?? :P

Per

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 Post subject: Re: Patterns
PostPosted: Sun Mar 10, 2013 5:37 am 
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My approach for the Woven Anacondas is based on this simple edge algorithm:

5x: Woven Anaconda (edges only)
(B U R' ND2 R U' B' U B R' ND2 R B' U' CR' CF')3 (42 btm)

If it is possible to move a few centers along with it, the final solution would be much shorter.


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 Post subject: Re: Patterns
PostPosted: Sun Mar 10, 2013 1:56 pm 
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I impoved the centers part of the woven anacondas:

5X: Woven Anacondas (centers only) (46 btm).

The final improved pattern:

5X: Woven Anacondas (87 btm).

I bet this can be still further improved :wink: Glazik? :mrgreen:

EDIT:

One turn gained for the edges part:

5X: Woven Anacondas (86 btm).

Per :solved:

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 Post subject: Re: Patterns
PostPosted: Mon Mar 11, 2013 2:45 am 
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Hi,
Here is what I have so far. :)

1- Partition the edge sequence in two and use a long setup sequence to give a shorter alg (shorter can still be obtained I think):

Shortest edge 6 2-cycles found (11 btm):
NL D2 SF2 U2 NR TU2 SR2 SF2 ND2 SR2 D2

New edges (32 btm)
(NU' F' NU2 D2 NL B' L) (NL D2 SF2 U2 NR TU2 SR2 SF2 ND2 SR2 D2) (L' B NL' D2 NU2 F NU)
L2 B NR' B' L2 B NR B'



2- Partion again the whole sequence to cancel more moves:

New partition (74 btm)
NU' F' NU2 D2 NL B' L NL D2 SF2 U2 NR TU2 SR2 SF2 ND2 SR2 D2 L' B NL' D2 NU2 F NU
NU' WF2 NU B2 NU' WF2 NU B2
NF' WR2 NF L2 NF' WR2 NF L2
L2 B NR' B' L2 B NR B'
NR' WU2 NR D2 NR' WU2 NR D2
F' NR VB' NR' F NR VB NR'
R' NU VL' NU' R NU VL NU'
U' NF VD' NF' U NF VD NF'

5x: Woven Anacondas (74 btm)


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 Post subject: Re: Patterns
PostPosted: Mon Mar 11, 2013 10:17 am 
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@ perfredlund and glazik
Fantastic job! A total of 52 moves have been canceled out! 8-)

I scaled and enhanced glazik's algorithm to create this tangled 7x7x7 version: :mrgreen:

7x: 3 Woven Anacondas
MF' L2 D' MF NU MF' NU' D L2 NU MF NU'
F2 MR NB MR' F2 MR NB' MR'
R' ND R MU R' ND' R MU'
NU' F' NU2 D2 NL B' TL D2 SF2 U2 NR TU2 SR2 SF2 ND2 SR2 D2 L' B NL' D2 NU2 F
VF2 VB2 NU B2 NU' VF2 VB2 NU B2
NF' VR2 VL2 NF L2 NF' VR2 VL2 NF
B NR' B' L2 B NR B'
(NR' VD2 VU2 NR D2)2
F' NR VB' N3F NR' F NR VB N3F' TR'
NU VL' N3R NU' R NU VL N3R' TU'
NF VD' N3U NF' U NF VD N3U' NF'
T3R T3D2 T3F MR S3F' T3L MD' T3L' T3B' T3D2 T3R' (113 btm)


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 Post subject: Re: Patterns
PostPosted: Tue Mar 12, 2013 5:25 am 
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@Walter: the length of your sequence is 125 btm, actually.

8 moves gained on +centers (20 btm):
MU2 L MU NL' MU' L' MU NL MU2 NF' NL MU F MU' F' NL' TF MU F' MU2

Same parttition:
MU2 L MU NL' MU' L' MU NL MU2 NF' NL MU F MU' F' NL' TF MU F' MU2
NU' F' NU2 D2 NL B' TL D2 SF2 U2 NR TU2 SR2 SF2 ND2 SR2 D2 L' B NL' D2 NU2 F NU
NU' VF2 VB2 NU B2 NU' VF2 VB2 NU B2
NF' VR2 VL2 NF L2 NF' VR2 VL2 NF L2
L2 B NR' B' L2 B NR B'
NR' VD2 VU2 NR D2 NR' VD2 VU2 NR D2
F' NR VB' N3F NR' F NR VB N3F' NR'
R' NU VL' N3R NU' R NU VL N3R' NU'
U' NF VD' N3U NF' U NF VD N3U' NF'
T3R T3D2 T3F MR S3F' T3L MD' T3L' T3B' T3D2 T3R'

7x: 3 Woven Anacondas (117 btm)


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 Post subject: Re: Patterns
PostPosted: Wed Mar 13, 2013 2:50 pm 
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Further improvement:

7X: 3 Woven Anacondas (106 btm).

Still, better can be found by using insertions :wink:

Per

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 Post subject: Re: Patterns
PostPosted: Fri Mar 15, 2013 3:07 pm 
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New improvement, by rearranging the steps:

7X: 3 Woven Anacondas (102 btm).

Soon we are sub 100 for this nice pattern :wink:

Per

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 Post subject: Re: Patterns
PostPosted: Fri Mar 15, 2013 4:51 pm 
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Here we are: :D

1- Insert L2 B NR' B' L2 B NR B' into (NF' VL2 VR2 NF L2)2:
NF' VL2 VR2 TF NR' F' L2 F NR TF' VL2 VR2 NF L2

2- Replace T3U T3B2 T3R MU MR T3F MU T3F' T3L' T3D2 T3B' with:
T3F' T3D2 T3L' T3B' MU T3B MR MU T3R T3F2 T3U

7x: 3 Woven Anacondas (99 btm)


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 Post subject: Re: Patterns
PostPosted: Sun Mar 17, 2013 12:17 pm 
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This also improves the much simpler version on the 5x5x5: :D

5x: Woven Anacondas
NU' F' NU2 D2 NL B' TL D2 SF2 U2 NR TU2 SR2 SF2 ND2 SR2 D2 L' B NL' NU2 D2 F
WF2 NU B2 NU' WF2 NU B2
(NR' WD2 NR D2)2
NF' WR2 TF NR' F' L2 F NR TF' WR2 NF L2
F' NR VB' NR' F NR VB TR'
NU VL' NU' R NU VL TU'
NF VD' NF' U NF VD NF' (72 btm)


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 Post subject: Re: Patterns
PostPosted: Mon Mar 18, 2013 8:03 am 
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Further improvement:

7X: 3 Woven Anacondas (96 btm).

Yay!!

Per :solved:

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 Post subject: Re: Patterns
PostPosted: Fri Mar 22, 2013 3:34 am 
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Tiny improvement:

5X: Woven Anacondas (71 btm).

Per :solved:

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 Post subject: Re: Patterns
PostPosted: Sun Mar 24, 2013 11:09 am 
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It's a classical labyrinth with forks and dead ends and you might get lost easily. :wink:

7x: Labyrinth
L' (NF' D2 NF U' NF' D2 NF U)
R L2 U' D' B2 (WD' NL N3D NR' N3U' N3R' N3D' MR' V3D N3L NU' WR) B2 D U L'
(NB U2 NB' D NB U2 NB' D') R'
MF' D2 B2 (SD' L' MD2 L SD L' MD2 L) B2 D2 MF
B2 D2 R2 (NB N3R NB' N3R') R2 D2 B2 (63 btm)


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 Post subject: Re: Patterns
PostPosted: Tue Mar 26, 2013 5:29 am 
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Nice "Easter Labyrinth" Walter :wink:

Some attempts gave no improvement. So i made a new pattern:

7X: Woven Anacondas (Order 3) (47 btm).

Naive first attempt at setting it up :|

Per :)

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 Post subject: Re: Patterns
PostPosted: Tue Mar 26, 2013 12:42 pm 
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perfredlund wrote:
Nice "Easter Labyrinth" Walter :wink:

I bed such a labyrinths would look great on easter eggs as well. :lol:


My approach for your Woven Anacondas pattern is a little bit different:

7x: Layered Anacondas (Order 3)
D L NR' NU' L2 NU NR L' NB' L2 NB D'
U' R' NL ND R2 ND' R NL' NF R2 NF' U
U (F ND' F2 ND F' NR' F2 NR) U'
B' (L' NF L2 NF' L ND L2 ND') B (44 btm or 43 btm actually)


In your version above one Anaconda is layed upon the other.
If you really want to call it woven, then I would do it this way:

7x: Woven Anacondas (Order 3)
D (L NU' L2 NU L' NB' L2 NB) D'
D' NF B' NU B2 NU' NF' B NL B2 NL' D
U (F ND' F2 ND F' NR' F2 NR) U'
U' R' NL ND R2 ND' R NL' NF R2 NF' U (44 btm or 42 btm actually)


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 Post subject: Re: Patterns
PostPosted: Wed Mar 27, 2013 7:14 am 
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Slight improvement:

7X: Layered Anacondas (Order 3) (39 btm).

Per :mrgreen:

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 Post subject: Re: Patterns
PostPosted: Thu Mar 28, 2013 5:35 am 
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Tiny improvement again:

7X: Woven Anacondas (Order 3) (41 btm).

I do not see room for further enhancement :|

Per :)

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 Post subject: Re: Patterns
PostPosted: Thu Mar 28, 2013 2:15 pm 
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Alternative solution:

7X: Woven Anacondas (Order 3) (41 btm).

1. U NR- F2 NR F ND- F2 ND F- U-
2. D NB- L2 NB L NU- L2 NU L- D-
3. D- NL B2 NL- (F- V4B) NL B2 NL- (F V4B-) D
4. U- NF R2 NF- (L- V4R) NF R2 NF- (L V4R-) U

Shuffling the 4 parts helped nothing :mrgreen:

Per

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 Post subject: Re: Patterns
PostPosted: Thu Mar 28, 2013 3:20 pm 
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Old pattern revisited:

6X: Peaks and Cubes (53 btm).

Improved the old qqwref pattern by 9 turns :mrgreen:

Per :solved:

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 Post subject: Re: Patterns
PostPosted: Fri Mar 29, 2013 4:33 pm 
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Another small improvement:

6X: Peaks and Cubes (49 btm).

Better edge cycles and some turns fused :wink:

Per :P

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 Post subject: Re: Patterns
PostPosted: Sat Mar 30, 2013 11:50 am 
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I further optimized it. It now requires only 43 moves: :mrgreen:

6x: Peaks and Cubes
SR2 (VF VB VR' VL' VF' VB' VR VL) (NR' NL' NF NB NR NL NF' NB') SR2
ML' R (U2 B' D SF' MD2 SF D' SF' MD2 F SD2 F' U SF MU2 SF' U' SF MU2 B D2) R' ML (43 btm)


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