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 Post subject: Re: Patterns
PostPosted: Thu Jan 24, 2013 1:51 pm 
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I slightly improved your recently posted pattern as well: :wink:

4x: Fat Checkered Rings
F2 L2 U SR2 U' F' SD' L' B2 L SD
B' (WD' (ML MD ML') (MR' MU' MR))
L2 B2 (SR U' MR2 U SR' U' MR2 U) B2 L2 SF' (32 btm)


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 Post subject: Re: Patterns
PostPosted: Thu Jan 24, 2013 2:25 pm 
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I just found new ways to create Checkerboard Cubes on a 5x5x5: :D

5x: Checkerboard Cube (Order 3)
WF (U' NL2 NR2 U D NL2 NR2 D' SR' D NL2 NR2 D' U' NL2 NR2 U SR)
ND NU' MF' WD' MD2 NB NF' MD' (27 btm)

5x: Checkerboard Cube (Order 6)
WF (U' NL2 NR2 U D NL2 NR2 D' SR' D NL2 NR2 D' U' NL2 NR2 U SR)
ND NU' MF' WD NL2 NR2 NB' NF MD' (28 btm)


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 Post subject: Re: Patterns
PostPosted: Thu Jan 24, 2013 3:58 pm 
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Since I am at it, here are some more:

5x: 2 Checkerboards
U2 (WR2 WD NB2 NF2 WD' MR2) U2 (8 btm)

5x: 4 Checkerboards (Order 2)
F2 NR2 SF2 TR2 NF2 SR2 NF2 L2 B2
NU2 ND2 (11 btm)

I am stuck with this one. Is there a way to do it more efficiently?

5x: 4 Checkerboards (Order 2)
NF2 NB2 D' NF2 NB2 D U NF2 NB2 U' NF2 NB2
ND SR D2 SR' NU' ND' SR D2 SR2 U2 SR NU' ND' SR' U2 SR NU2 ND
MF' WR' MF WR' MD' WR MD WD' MR' WD WR WF' MR WF (44 btm)


Last edited by Waran on Fri Jan 25, 2013 6:30 pm, edited 1 time in total.

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 Post subject: Re: Patterns
PostPosted: Fri Jan 25, 2013 6:06 am 
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Some of those checkerboard patterns have already been posted.

Here is a new one:

5X: Multicheckered Cube (Order 3) (25 btm).

And another variation:

5X: Multicheckered Cube v2 (Order3) (26 btm).

Both composed of 2 easy parts :wink:

Per

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 Post subject: Re: Patterns
PostPosted: Fri Jan 25, 2013 7:10 am 
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A rather huge improvement:

5X: 4 Checkerboards (Order 2) (28 btm).

Pretty optimal now :P

Per

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Last edited by perfredlund on Sat Jan 26, 2013 3:57 am, edited 1 time in total.

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 Post subject: Re: Patterns
PostPosted: Fri Jan 25, 2013 5:20 pm 
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@ Per
Awesome! Excellent work! 8-)

I started working on a very similar one (which wasn't posted before).
... this is what I've got so far:

5x: 4 Checkerboards (Order 4)
F' L B D2 (L SD2 SR ND SR' SD2 SR ND' R') D2 B' SR B U2 (L NU SR SD2 SR' NU' SR SU2 R') U2 B' R' F
R2 F2 R' NF R F2 R' NF' R'
B2 SR2 SF2 ND F2 ND' B2 SR2 B2 L2 ND F2 ND' F2 L2
NR' MD2 NR MD' NR VD MR2 ND2 MF2 ND' MR2 ND2 MF2 NR' MD NR' MD NR (73 btm)


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 Post subject: Re: Patterns
PostPosted: Sat Jan 26, 2013 4:14 am 
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You could have easily appended my solution and derived:

5X: 4 Checkerboards (Order 4) (34 btm).

Per :D

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 Post subject: Re: Patterns
PostPosted: Sat Jan 26, 2013 4:37 am 
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Yet another improvement:

5X: 4 Checkerboards (Order 4) (26 btm).

This should be hard to beat :mrgreen:

Per

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 Post subject: Re: Patterns
PostPosted: Sat Jan 26, 2013 6:12 am 
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perfredlund wrote:
This should be hard to beat :mrgreen:

Well, not really. :wink:

5x: 4 Checkerboards (Order 4)
U ND' NL2 NR2 TD2 NB2 NF2 U' NU NB2 NF2 TD2 NL2 NR
MD2 NR MD' NR MD NR' MD NR' MD NR (24 btm)


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 Post subject: Re: Patterns
PostPosted: Sat Jan 26, 2013 6:13 am 
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Of course the middle layer can be left out:

5X: Top and Bottom Checkered Cube (Order 4) (14 btm).

Also quite nice :wink:

Per

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 Post subject: Re: Patterns
PostPosted: Sun Jan 27, 2013 3:26 am 
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Haha, I spoke too soon. Well done Walter :)

However, taste this:

5X: 4 Checkerboard Faces (Order 4) (23 btm).

Per :wink:

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 Post subject: Re: Patterns
PostPosted: Sun Jan 27, 2013 5:43 am 
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Allright! How about this?:

5x: 4 Checkerboard Faces (Order 4)
WF MD WF MD' WF' MR WF'
WR2 MR TD2 NB2 NF2 U' NU NB2 NF2 T3D2 NL2 MD2 NR2 U ND' (22 btm)

If we continue like that, we may find the optimal solution one day. :wink:


Edit:
I just found an alternative solution with the same lenght:

5x: 4 Checkerboard Faces (Order 4)
WF MD WF MD' WR2 WF MR WF MR
TD2 NB2 NF2 U' NU NB2 NF2 T3D2 NL2 MD2 NR2 U ND' (22 btm)


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 Post subject: Re: Patterns
PostPosted: Sun Jan 27, 2013 11:34 am 
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Woah!! Nice backwards optimisation ! :|

I found minor improvement:

5X: 4 Checkerboard Faces (Order 2) (27 btm).

I'm sure this is easy to beat, but starting to get lazy already :roll:

Per

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 Post subject: Re: Patterns
PostPosted: Sun Jan 27, 2013 6:07 pm 
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This is a new pattern of spirals who are running over 3 faces.
The 3 sprials on the upper, right and front face have the same shape.
When twisted around the center, they fit perfectly together:

5x: Interlaced Spirals
F' R2 D' SR F R L F D F SD' L' U'
U R' (NF2 R F R' VF2 R F' R' MF2) R U'
D' L (NB2 L' B' L VB2 L' B L MB2) L' D
D2 F2 R' L' (ND WF MU' ND' WF' MU) R L F2 D2
U2 F' B' L2 (NL ND' NL' ND) L2 B F U2 (65 btm or 61 btm actually)


... I couldn't resist to further optimize this one:

5x: 4 Checkerboard Faces (Order 2)
TU' NL2 NR2 TU2 NB2 NF2 TU'
NB2 NF2 NL2 TR2 ND2 NU2
L2 ND2 SR2 NU' ND' MF WR MF' SR MF WR' MF' SR' (26 btm)


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 Post subject: Re: Patterns
PostPosted: Mon Jan 28, 2013 7:04 am 
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I could also not resist to optimise:

5X: Interlaced Spirals (52 btm).

I guess the part where i do the centers could be optimised further ... :wink:

Per

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 Post subject: Re: Patterns
PostPosted: Mon Jan 28, 2013 8:37 am 
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As i thought, here goes a minor improvement. Gaining 2 turns by better centers:

5X: Interlaced Spirals (50 btm).

Per :lol:

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 Post subject: Re: Patterns
PostPosted: Mon Jan 28, 2013 5:46 pm 
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I replaced part one to gain two more moves:

5x: Interlaced Spirals
SF L2 B2 (U' NR2 U SR U' NL2 NR2 U SR' U' NL2 U) B2 L2 SF'
U2 F2 L' SF2 U2 SF' SD' B2 D B WR' B L2 B' WR
B' U2 L2 (WD' VL WD VL' VU NL VU' NL') L2 U2 B F (48 btm)


Edit:
I just found another solution:

5x: Interlaced Spirals
R' U2 B' SD- R U D R B R SF D'
B' L2 B2 (U' NR2 U SR U' VR2 U SR' U' MR2 U) B2 L2 F2
U2 L2 (WD' VL WD VL' VU NL VU' NL') L2 U2 B F (43 btm)


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 Post subject: Re: Patterns
PostPosted: Wed Jan 30, 2013 4:27 am 
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I decided to utilise the center rotations of

R- U2 B- SD- R U D R B R SF D- F-

and i improved the pattern:

5X: Interlaced Spirals (41 btm).

Good brain exercise :oops:
Many previous posted patterns could have been improved in the same way :wink:

Per

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 Post subject: Re: Patterns
PostPosted: Thu Jan 31, 2013 4:15 pm 
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@ Per
Wow, that's a very clever solution! Great job!

I explored different approaches but didn't found shorter algorithms so far.


Check out this rather chaotic version! :mrgreen:

5x: Interlaced Spirals (Chaotic Version)
R' U2 B' SD' R U D R B R SF D'
B' L2 B2 (U' NR2 U SR U' VR2 U SR' U' MR2 U) B2 L2 F2
U2 L2 (WD' NR' MU' MR' NU' NL ND VR VU NL' VU') L2 U2 B F (46 btm)


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 Post subject: Re: Patterns
PostPosted: Thu Jan 31, 2013 4:38 pm 
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Here is a new and very colorful pattern:

5x: 8 Small Winding Rings
ND' NR' NF'
(L2 U2 F2 NF NB NR NL NU ND F2 U2 L2
F2 U2 L2 NU' ND' NR' NL' NF' NB' L2 U2 F2)
NF NR ND
F' B2
(NR2 D' (TR' NB NR NB' R) D NR2
NL2 U' (TL' NB NL NB' L) U NL2
NU2 R' (TU' NB NU NB' U) R NU2
ND2 L' (TD' NB ND NB' D) L ND2)
B2 F (70 btm)


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 Post subject: Re: Patterns
PostPosted: Fri Feb 01, 2013 3:54 am 
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That is fabulous Walter. One sixth of the pattern can be done like so:

1. NB NF NR NF- (setup)
2. [NF NB TD2 NF- NB-,U] bar commutator)
3. NF NR- NF- NB- (undo setup)

This becomes:

5X: Partial winding rings. (18 btm).

This would be 108 turns for your pattern. I can immediately see how at least 12 turn could be saved.Still a far way to improve your 70 turns :( Nice challenge :wink:

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Last edited by perfredlund on Fri Feb 01, 2013 5:01 am, edited 1 time in total.

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 Post subject: Re: Patterns
PostPosted: Fri Feb 01, 2013 5:01 am 
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Using a symmetric version of part 1 i gained 1 turn:

5X: 8 Small Winding Rings (69 btm).

Per :wink:

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 Post subject: Re: Patterns
PostPosted: Sat Feb 02, 2013 8:43 am 
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First attempt at a new pattern:

5X; 8 Linked Loops (79 btm).

Per

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 Post subject: Re: Patterns
PostPosted: Sat Feb 02, 2013 4:50 pm 
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@ Per

Your idea of the Partial Winding Rings is fantastic.
Instead of doing the edges and centers seperately, this algorithm does it at once.
Nevertheless the current solution will end up longer, the concept is great.


BTW, the origin of this was a 3x3x3 pattern I like a lot:

3x 2 Winding Rings
D R B2 F SD R F' R' B SD2 F' L U' (13 btm)


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 Post subject: Re: Patterns
PostPosted: Sun Feb 03, 2013 5:26 am 
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Here is the full Winding Rings pattern using my sequence:

5X: 8 Winding Rings (108 btm).

In reality 16 turns cancel out and it becomes 92 turns.... :mrgreen:

EDIT:

Here it is written out in a better way:

1. NBNF(NRNBTD2NF-NB-UNFNBTD2NF-NB-U-NFNR-CF)4NF-NB-
2. CR-NBNF(NRNBTD2NF-NB-UNFNBTD2NF-NB-U-NFNR-CU2)2NF-NB-CR

5X: 8 Winding Rings (92 btm).

Per :solved:

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 Post subject: Re: Patterns
PostPosted: Sun Feb 03, 2013 3:48 pm 
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Hi,

These two patterns have been slightly improved:

5x: 4 Checkerboard Faces (Order 2) (25 btm)

5x: 8 Small Winding Rings (68 btm)


These two are unoptimized:

2 Winding Rings (3x cube)
D F R2 L MU L B' L' F MU2 F' L U'
Scale to 5x cube:
(D F R2 L M3U L B' L' F M3U2 F' L U')'
(TD TF TR2 TL MU TL TB' TL' TF MU2 TF' TL TU')
Correct side effect on centers:
MU' NL D NU' MR NU D' NL' D R' NU' MR' NU R D' MU
5x: 2 'Ring in a Ring' (40 btm)

5x: 6 4-Blade Rings (Order 2) (33 btm)


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 Post subject: Re: Patterns
PostPosted: Sun Feb 03, 2013 4:57 pm 
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I solved the centers part of the 8 Small Winding Rings pattern.

Here is what i have so far (by inverting my solution):

5X: 8 Center Rings (44 btm).

Looking at the side permutations it can be seen that we dont really have 8 disjoint cycles of the centres, only visually it appears like that ... :wink: I will pursue this later :)

Per

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Last edited by perfredlund on Mon Feb 04, 2013 3:33 am, edited 1 time in total.

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 Post subject: Re: Patterns
PostPosted: Sun Feb 03, 2013 6:54 pm 
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In this version the centers in the upper and lower half are rotated in different directions:

5x: 8 Small Winding Rings (Version 2)
ND2 B F R2 (NR' ND' NR ND) SR2 (NL' ND' NL ND) L2 F' B' L R B2 (NB' ND' NB ND) SF2 (NF' ND' NF ND) F2 R' L' ND'
NF NR
(B2 U2 R2 NL' NR' NB' NF' NU' ND' R2 U2 B2
R2 U2 B2 NU ND NB NF NL NR B2 U2 R2)
NR' NF' ND' (61 btm)


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 Post subject: Re: Patterns
PostPosted: Mon Feb 04, 2013 9:41 am 
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Version 2 has been slightly improved:
5x: 8 Small Winding Rings (Version 2) (58 btm)


By including +centers, more variations can be obtained.
Notice that shorter solutions may be found by combining xcenters and +centers in the same alg, needs more work though ;-)

5x: Rings (Variation 1) (64 btm)

5x: Rings (Variation 2) (94 btm)

5x: Rings (Variation 3) (52 btm)

5x: Rings (Variation 4) (81 btm)


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 Post subject: Re: Patterns
PostPosted: Tue Feb 05, 2013 4:09 am 
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Here is a minor improvement:

5X: Rings (Variation 2) (92 btm).

Note striking similarity with my Winding Rings contribution. Only TD2 is replaced with T3D2 at 4 places ... :wink:

EDIT:

Further improvement:

5X: Rings (Variation 2) (84 btm).

Parts:
1. NL- (NF2 NB- D2 NF NB T3U NF- NB- D2 NF NB T3U- NF CR)4 NL
2. CF (NL- NF2 NB- D2 NF NB T3U NF- NB- D2 NF NB T3U- NF NL CU2)2 CF-

And also:

4X: 8 Small Winding Rings (84.btm).

Per :solved:

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Last edited by perfredlund on Tue Feb 05, 2013 7:12 am, edited 1 time in total.

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 Post subject: Re: Patterns
PostPosted: Tue Feb 05, 2013 5:41 am 
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Slightly longer but very compact notation:

5X: Rings (Variation 1) (68 btm).

Per :wink:

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 Post subject: Re: Patterns
PostPosted: Tue Feb 05, 2013 9:01 am 
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New contribution:

5X: 8 Small Whirled Rings (116 btm).

Only a first attempt. Inspired by recently posted patterns. This can surely be improved :)

Per

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 Post subject: Re: Patterns
PostPosted: Tue Feb 05, 2013 11:07 am 
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The algorithm can be improved by adding edges to center rings (still quite long):
Edges (39 btm):
D U
L2 F' (NR2 SF R SF' NR2 SF R' NR2 SF' R SF NR2 SF' R') F L2
R2 F' (NL2 SF L SF' NL2 SF L' NL2 SF' L SF NL2 SF' L') F R2
U' D'
5x: 8 Small Whirled Rings (101 btm)

Another variation:
5x: 6 Whirled Checkerboards (63 btm)

This last one may have been done before:
5x: 8 Corner-Rings (77 btm)


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 Post subject: Re: Patterns
PostPosted: Tue Feb 05, 2013 3:03 pm 
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A rather huge improvement;

5X: 8 Corner-Rings (50 btm).

And yes i think this was done before :wink:

Per

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 Post subject: Re: Patterns
PostPosted: Tue Feb 05, 2013 4:40 pm 
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I found an alternative, slightly shorter solution for the 8 Corner-Rings:

5x: 8 Corner-Rings
D' L2 D2 R (D' R2)2 WF2 R D WR2 WF2 (U' R)2
(TR' TU)2 MF2 MR2 TD' TR' MF2 (TR2 TD)2 TR' TD2 TL2 TD
F' R F (TB U2 TB' NU' TB U2 TB' NU) F' R' F (48 btm or 47 btm actually)


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 Post subject: Re: Patterns
PostPosted: Wed Feb 06, 2013 4:58 am 
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Further optimisation:

5X: 8 Corner-Rings (44 btm).

1. D- L2 D2 R (D- R2)2 WF2 R D WR2 WF2 (U- R)2
2. R- D R (TL B2 TL- NB- TL B2 TL- NB) R- D- R
3. (TR- TU)2 MF2 MR2 TD- TR- MF2 (TR2 TD)2 TR- TD2 TL2 TD

I reordered Walter's 3 parts (and used some symmetry) to obtain cancellation :wink:

Per

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 Post subject: Re: Patterns
PostPosted: Thu Feb 07, 2013 12:30 pm 
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Algorithm improved again by optimizing edges: :wink:
Edges (30 btm):
D U F2
SU2 (L B NU2 B' NU2 SR B ND2 B' ND2 R') SU2 (L' ND2 B ND2 B' SR' NU2 B NU2 B' R)
F2 U' D'
5x: 8 Small Whirled Rings (92 btm)


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 Post subject: Re: Patterns
PostPosted: Thu Feb 07, 2013 2:36 pm 
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perfredlund wrote:
I solved the centers part of the 8 Small Winding Rings pattern.

Here is what i have so far (by inverting my solution):

5X: 8 Center Rings (44 btm).

Looking at the side permutations it can be seen that we dont really have 8 disjoint cycles of the centres, only visually it appears like that ... :wink: I will pursue this later :)

Per

I managed to further improve Per's algorithm: :mrgreen:

The permutation of the centers is different compared to Per's solution.
Now we have a 14-cycle, a 4-cycle and a 2-cycle.
Before, the solution was composed of a 20-cycle and a 4-cycle.

5x: 8 Center Rings
B (NU2 R' NU' ND NR2 NU ND' R NU' NR2 NU') B'
L D (NB' NF NU NB NF' NU') D' L'
L D (NF2 NL2)2 D' L'
L (ND' NU NF2 NU' ND NF2) L'
NU ND' NL NR' NU' ND NL' NR (47 btm or 40 btm actually)


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 Post subject: Re: Patterns
PostPosted: Thu Feb 07, 2013 4:16 pm 
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By optimizing the algorithm of center 8 3-cycles (instead of (2c)(4c)(4c)(14c)), a 2-move gain is further obtained:
ND U2
MR2 NR2 B' (TR' NU NR NU' R) B NR2 MR2
NL2 F' (TL' NU NL NU' L) F NL2
NB2 L' (TB' NU NB NU' B) L NB2
MF2 NF2 R' (TF' NU NF NU' F) R NF2 MF2
U2 ND'
5x: 8 Center Rings (38 btm)

Same gain for the '8 Small Winding Rings' pattern: 8-)
5x: 8 Small Winding Rings (66 btm)


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 Post subject: Re: Patterns
PostPosted: Fri Feb 08, 2013 5:45 am 
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Well done Glazik, that inspired me:

5X: 8 Small Speckled Rings (66 btm).

Per :wink:

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Last edited by perfredlund on Sat Feb 09, 2013 2:37 pm, edited 4 times in total.

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 Post subject: Re: Patterns
PostPosted: Fri Feb 08, 2013 6:23 am 
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Yet another contribution:

5X: 8 Small Y-Twists (47 btm).

I'm sure the latter part could be improved. This was only my first attempt :)

Per

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 Post subject: Re: Patterns
PostPosted: Mon Feb 11, 2013 1:53 pm 
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The algorithm has been improved by optimizing corner blocks and x-centers:
Corner Blocks:
CR2 TL2 TU MR2 MF2 TU2 TD' TL2 TB MR2 MU2 TB2 TF'
Centers:
F B R2
D2 NL NU' NL NU NL2 NR' ND' NR ND D2
U2 NL ND' NL ND NL2 NR' NU' NR NU U2
R2 B' F'
5x: 8 Small Y-Twists (38 btm)


Two interesting variations obtained by scaling: :wink:
Same process applied to a 6x cube:
Corner Blocks:
CR2 T3R2 T3U' T3D' T3R2 T3B' T3F'
Centers:
same as before
Variation 6x (32 btm)

Same process applied again to a 7x cube:
Corner Blocks:
CR2 T3L2 T3U MR2 MF2 T3U2 T3D' T3L2 T3B MR2 MU2 T3B2 T3F'
Centers:
same as before
Variation 7x (38 btm)


And finally, a shorter version of the 8 4-color rings pattern: :D
5x: 8 Center Rings (62 btm)


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 Post subject: Re: Patterns
PostPosted: Mon Feb 11, 2013 4:50 pm 
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Nice work Glazik :mrgreen:

Here is one that can easily be improved further, it's late already ... :o

7X: 16 Pairwise Nested Rings (78 btm).

Per

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 Post subject: Re: Patterns
PostPosted: Mon Feb 11, 2013 5:18 pm 
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Is there a more efficient way to do an Asymmetric Anaconda?
Maybe the centers in part 3 can be moved along with part 1 or 2?

5x: Asymmetric Anaconda
R' (F' NR' F2 NR F ND' F2 ND) R
TR' NF R T3B R' NF' R T3B' NR
NR' (NU B2 NU' NF' NU B2 NU' NF) NR (29 btm or 26 btm actually)


Combined with a Symmetric Anaconda the pattern looks like this:

5x: Asymmetric Double Anaconda (Solution 1)
R' (F' NR' F2 NR F ND' F2 ND) R2
(NB TU2 NB' TU NR TU2 NR' TU')
NR TD2 (TB TL MD TL' S2F MR' TF') TD2 TR'
NF' NU NF D' NF' NU' NF D (37 btm)

5x: Asymmetric Double Anaconda (Solution 2)
R' (F' NR' F2 NR F ND' F2 ND)
NR' NF R T3B R' NF' R T3B'
(NU B2 NU' NF' NU B2 NU' NF) NR
TR TD2 (TB TL MD TL' S2F MR' TF') TD2 TR' (37 btm)


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 Post subject: Re: Patterns
PostPosted: Tue Feb 12, 2013 5:33 am 
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The 2 algorithms have been slightly improved by insertion (first try):

1- 1 move gained by insertion of Part 3 into Part 2:
5x: Asymmetric Anaconda (25 btm)

2- 3 moves gained by inserting (TB2 TU' MR' S2U TL' MF' TL TD TB2) at *:
R' F' NR' F2 NR F ND' F2 ND NR' * NU B2 NU' NF' NU B2 NU' NF2 R T3B R' NF' R T3B' NR
5x: Asymmetric Double Anaconda (34 btm)


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 Post subject: Re: Patterns
PostPosted: Tue Feb 12, 2013 3:44 pm 
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Improvements:

5X: Asymmetric Anaconda (19 btm).

5X: Asymmetric Double Anaconda (29 btm).

No insertion - only better partitioning :wink:

Per :solved:

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 Post subject: Re: Patterns
PostPosted: Wed Feb 13, 2013 5:15 am 
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@ glazik and perfredlund

Yees! That was exactly what I was looking for! 8-)


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 Post subject: Re: Patterns
PostPosted: Wed Feb 13, 2013 5:44 am 
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Continuing with 'snake loops': :wink:

5x: 2 Rings (2x2x2) (22 btm)

5x: 2 Rings (2x2x2) + Symmetric Anaconda (31 btm)


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 Post subject: Re: Patterns
PostPosted: Fri Feb 15, 2013 4:18 pm 
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Nice Glazik!

I tried to improve the 2 Rings pattern - no luck so far :?

Teenie weenie improvement:

5X: Asymmetric Double Anaconda (28 btm).

Per :wink:

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Last edited by perfredlund on Sat Feb 16, 2013 3:22 am, edited 1 time in total.

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 Post subject: Re: Patterns
PostPosted: Fri Feb 15, 2013 5:18 pm 
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Yet another minor improvement:

5X: 2 Rings (2x2x2) + Symmetric Anaconda (30 btm).
Last part could have been properly inserted ...

Per :solved:

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