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rubikcollector123

Post subject: Re: Patterns Posted: Tue Jul 16, 2013 8:35 pm 

Joined: Fri Nov 05, 2010 2:20 am Location: Wherever

I was surprised when I realised it could be done. (It is not even that difficult to acheive.) EDIT: it actually is quite difficult to acheive. I got lucky the first time.
I will now attempt to solve as much as possible into a true one sided mezon. Hopefully.....
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Last edited by rubikcollector123 on Sat Jul 20, 2013 3:22 am, edited 1 time in total.


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themathkid

Post subject: Re: Patterns Posted: Tue Jul 16, 2013 8:53 pm 

Joined: Sat Sep 15, 2012 7:42 am


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rubikcollector123

Post subject: Re: Patterns Posted: Sat Jul 20, 2013 3:06 am 

Joined: Fri Nov 05, 2010 2:20 am Location: Wherever

After many days of effort......
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darryl

Post subject: Re: Patterns Posted: Sat Jul 20, 2013 10:42 am 

Joined: Fri Feb 18, 2000 8:50 am Location: chicago, IL area U.S.A

Wow! Very well done. Did you document the sequence?
d


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rubikcollector123

Post subject: Re: Patterns Posted: Sat Jul 20, 2013 10:52 am 

Joined: Fri Nov 05, 2010 2:20 am Location: Wherever

I first made the shape of the pattern without messing up the mezon portion. This is not considerably challenging.
Then I solved what was left using commutators that weren't disabled by the bandaging.
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Andrea

Post subject: Re: Patterns Posted: Fri Sep 13, 2013 10:12 am 

Joined: Wed Apr 13, 2011 8:37 am Location: Germany

Snakes with Traiphum's 5x5x5 Attachment:
flatsnake.jpg [ 100.02 KiB  Viewed 4695 times ]
Attachment:
snake.jpg [ 97.27 KiB  Viewed 4695 times ]
Attachment:
cobra.jpg [ 93.4 KiB  Viewed 4695 times ]


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darryl

Post subject: Re: Patterns Posted: Fri Sep 13, 2013 12:07 pm 

Joined: Fri Feb 18, 2000 8:50 am Location: chicago, IL area U.S.A

Well done on the snake in the 2nd picture! That one is my favorite of the three, and probably one of my favorite patterns out of all the twisty puzzles now.
d


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pytlivyj_1

Post subject: Re: Patterns Posted: Mon Sep 16, 2013 12:51 pm 

Joined: Tue Mar 24, 2009 12:52 pm

1) Snake on a mirror cube:2) Snake on a void cube:The return alternation of colours of the snake is possible only due to void parity!!!


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Waran

Post subject: Re: Patterns Posted: Wed Oct 02, 2013 3:12 pm 

Joined: Sat Jan 28, 2006 6:04 am Location: Switzerland

@ Andrea and pytlivyj_1 Your snakes on the Traiphum' 5x5x5, Mirror Cube and Void Cube are awesome! So, let's do another, exotic one with lots of colors: 5x: Triple PythonNU' R2 NU2 F2 ND' NB' NF NU' ND NB NF' NU F2 NU2 R2 TU L2 B' NU' ND B SR2 F' NU ND' F R2 U' F (WR' MD WR MD' WR MF WR' MF') F' SR2 F2 NU F2 NU' F2 ND F2 ND' L2 NU R2 TD NB2 TD' B2 MF NL' L U' NL' MU' NL U NL MU L' MF' B2 ND' B NL MU NL' B2 NL B2 MU' B2 NL' B ND NF2 MR' NF' R NF MR NF' R' NF' TU TR2 MD TL2 TU' TF2 TR MD' TR' TB2 TR TU TD' TF' MD' MR2 (105 btm) Well, the solution turned out quite long. I hope someone can optimize it.


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pytlivyj_1

Post subject: Patterns Posted: Thu Oct 03, 2013 8:52 am 

Joined: Tue Mar 24, 2009 12:52 pm

"12 axs" on CHIMERA 2x2+6x6 in comparison with "12 strips" on a cube 2Ń…2Ń…2:"12 strips" on a cube 2Ń…2Ń…2: R2 U2 F2 R2  four consecutive turns around of one corner. Interesting property of this pattern: arbitrary we take a cube in hands by any party to ourselves and is solved in an initial condition by the same algorithm. If have got "not on that corner", we make algorithm twice.


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pytlivyj_1

Post subject: Patterns Posted: Thu Oct 03, 2013 9:01 am 

Joined: Tue Mar 24, 2009 12:52 pm

"Snake" on CHIMERA 2x2+6x6:This snake has return alternation of colours too!


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Waran

Post subject: Re: Patterns Posted: Thu Oct 03, 2013 3:15 pm 

Joined: Sat Jan 28, 2006 6:04 am Location: Switzerland

The patterns on the Chimera 2x2+6x6 are impressing! Since I don't have such smashing cubes, I am using a humble 5x5 for another snake. It's a sort of a single path Python that meanders close to the boundaries of the cube: 5x: Python on the edge(MR2 ND L2 ND')2 TB2 ND TB2 ND' TB2 NU TB2 NU' TR2 NU TR2 TU' B2 TU TD NB TU' TD' B2 TU TD NB' TD' ND' B' ND' NR ND NR' ND NB' ND' TB ND D' MR2 D NR NB D' MR2 D NB' NR' (52 btm)


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Elias Acrich

Post subject: Re: Patterns Posted: Thu Oct 03, 2013 4:55 pm 

Joined: Wed May 22, 2013 3:47 am

Made with a dino dodecahedron!
Attachments: 
20131003_234728.jpg [ 2.29 MiB  Viewed 4452 times ]

_________________ Before I was eliasthecollector93... It took too long to log in


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glazik

Post subject: Re: Patterns Posted: Sat Oct 05, 2013 11:49 am 

Joined: Wed Oct 12, 2011 12:54 pm

Hi Walter, A few patterns have been improved and I guess shorter solutions could still be found from better partitioning 5x: Triple PythonU2 R U' F L2 F' NL NR' F L2 F' U R' U' NR NL' U' NU' L2 NU2 B2 (NU' NB NF' ND' NU NB' NF ND) B2 NU2 L2 NU SR2 F2 NU F2 NU' F2 ND F2 ND' L2 NU R2 TD NB2 TD' B2 MF NL' L U' NL' MU' NL U NL MU L' MF' B2 ND' B NL MU NL' B2 NL B2 MU' B2 NL' B ND NF2 MR' NF' R NF MR NF' R' NF' TU TR2 TF2 MU TF MR' TF TL2 TF' MR TF TD' CF2 CU2 5x: Triple Python (95 btm)5x: Edge PythonTB2 ND TB2 ND2 F2 ND MF2 ND' F2 ND T3B2 NU TB2 NU' TR2 NU TR2 NU' NB NR U' MF2 U NR' NB' TR' NU NR NU' NB NU' NB' NU R U' MF2 B2 TU TD NB TU' TD' B2 TU TD NB' TD' 5x: Edge Python (47 btm)5x: PythonTB2 NU' TB2 NU2 F2 NU' MF2 NU F2 NU' T3B2 ND' TB2 ND TR2 ND' TR2 TD TR MF TR' NB2 TR MF' TR' TD' 5x: Python (26 btm)An upper bound of 57 moves (OBTM: Outer Block Turn Metric) has been published recently for God's number of a 4x4x4 cube. The upper bound in BTM should however be lower than that, because there are more basic moves in sets in BTM than in OBTM. By tweaking the 'Winding Hexagon' algorithm, it has been possible to lower the move count from 61 down to 56 BTM, just below the new OBTM bound: 4x: Winding HexagonEdges: MD2 R' B U' MR2 TU B' U' B MU' MR2 B' U F U2 F' R MD2 R' F U2 F' R TB2 SR' B R SF L' MB2 L SF' R' B' SR B2 Centers: B MU MF' MB' MU F MU' MB MF MU F' MU MR MU' R' MU MR' MU' R MU2 B' 4x: Winding Hexagon (56 btm)


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leRAFs

Post subject: Re: Patterns Posted: Mon Oct 07, 2013 5:51 pm 

Joined: Thu Aug 30, 2012 3:33 pm Location: France


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AndyChilly

Post subject: Re: Patterns Posted: Mon Oct 07, 2013 5:57 pm 

Joined: Fri Jun 21, 2013 3:39 am Location: Rye, East Sussex

That hexaminx pattern looks awesome.
_________________ How to sum up my solving skills..."I try, I try, I fail. I try, I try, PREVAIL!"


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rubikcollector123

Post subject: Re: Patterns Posted: Mon Oct 07, 2013 6:12 pm 

Joined: Fri Nov 05, 2010 2:20 am Location: Wherever

leRAFs wrote: There is my first hexaminx pattern! And for your second, try flipping every edge! I don't have a hexaminx, but it must look cool.
_________________ A budding puzzle designer!
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leRAFs

Post subject: Re: Patterns Posted: Mon Oct 07, 2013 6:23 pm 

Joined: Thu Aug 30, 2012 3:33 pm Location: France

Thanks Andychilly! I'm quite proud of it rubikcollector123 wrote: And for your second, try flipping every edge! I don't have a hexaminx, but it must look cool. That's exactly what I've planned to do


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martywolfman

Post subject: Re: Patterns Posted: Thu Oct 10, 2013 6:17 am 

Joined: Tue Sep 11, 2012 1:51 pm Location: Bedford, England


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Waran

Post subject: Re: Patterns Posted: Mon Oct 14, 2013 2:57 pm 

Joined: Sat Jan 28, 2006 6:04 am Location: Switzerland

@ glazik Fantastic optimization work! glazik wrote: An upper bound of 57 moves (OBTM: Outer Block Turn Metric) has been published recently for God's number of a 4x4x4 cube. This recent reduction of the upper bound from 82 to 57 moves is indeed a major breakthrough! ... and it kind of encourages to keep the algorithms below that new mark. I checked the 4x4 patterns on my site and was surprised that they are already below 57 moves, except for two: For the first pattern I just found a new approach and managed to cancel out 18 moves. The algorithm has been reduced form 83 to 65 moves: 4x: Layered AnacondasMU' F' MU2 D2 ML B' TL D2 SF2 U2 MR TU2 SR2 SF2 MD2 SR2 D2 L' B ML' D2 MU2 F MU L2 B MR' B' L2 B MR B' U2 B2 R' TL' WD ML' MF2 ML2 MF2 WD' L R B2 U2 ML MF R MF' ML' MF R' MF' MR' TB' L MB MR MB' MR' L' B MR MB (65 btm) I also found a new solution for the second one, but with 71 moves the algorithm is still quite long. Both patterns look almost identical. The difference is that in the pattern above the two Anacondas meander on different layers, while in this later version they are closely intertwined: 4x: Woven AnacondasMU' F' MU2 D2 ML B' TL D2 SF2 U2 MR TU2 SR2 SF2 MD2 SR2 D2 L' B ML' MU2 D2 F WF2 MU B2 MU' WF2 MU B2 (MR' WD2 MR D2)2 MF' WR2 TF MR' F' L2 F MR TF' WR2 MF L2 F' MR MB' MR' F MR MB MR' SD MF MD' MF' U MF TD MB' D' MF' D MB D2 (71 btm)


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AndyChilly

Post subject: Re: Patterns Posted: Tue Oct 15, 2013 3:02 am 

Joined: Fri Jun 21, 2013 3:39 am Location: Rye, East Sussex

I dont know if anyone else has attempted a chequer board pattern on the Hexaminx but I shall ask two important questions both need answering Question 1: is it not possible? (I can't seem to get around this parity issue.) Question 2: Am I an idiot? Attachment:
photo 1.JPG [ 437.65 KiB  Viewed 4187 times ]
Attachment:
photo 2.JPG [ 574.94 KiB  Viewed 4187 times ]
Attachment:
photo 3.JPG [ 460.17 KiB  Viewed 4187 times ]
_________________ How to sum up my solving skills..."I try, I try, I fail. I try, I try, PREVAIL!"


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pytlivyj_1

Post subject: Patterns Posted: Tue Oct 15, 2013 1:46 pm 

Joined: Tue Mar 24, 2009 12:52 pm

At attempt to rearrange edges in return alternation of colours always there is a parity of two elements. Check up this case on a usual Megaminx.


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glazik

Post subject: Re: Patterns Posted: Fri Oct 18, 2013 3:13 am 

Joined: Wed Oct 12, 2011 12:54 pm

@ Walter, The two patterns have been slightly improved: MU' F' MU2 D2 ML B' TL D2 SF2 U2 MR TU2 SR2 SF2 MD2 SR2 D2 L' B ML' D2 MU2 F MU L2 F2 TD2 MB MD2 MF' MR' WF MR D2 F2 B MR' B' L2 B MR B' MR' TB' L MB MR MB' L' U' MR' MD MR U MR' MD' B MR MB 4x: Layered Anacondas (59 btm)MU' F' MU2 D2 ML B' TL D2 SF2 U2 MR TU2 SR2 SF2 MD2 SR2 D2 L' B ML' MU2 D2 F WF2 MU B2 MU' WF2 MD R2 WU MR WU' R2 WU MR' B2 MF' WR2 TF MR' F' L2 F MR TF' WR2 MF L2 SU' MF MD' MF' U MF TD MB' D' MD MB' MD' F MD MB MD' TF' D MB D2 4x: Woven Anacondas (69 btm)A few building blocks: 2 Lines (f,d) (8 btm)MR' WD2 MR D2 MR' WD2 MR D2 WU' R2 WU MR WU' R2 WU MR' WU L2 WU' MR WU L2 WU' MR' WU TL2 WU' MR WU TL2 WU' MR' ML' WF2 ML F2 ML' WF2 ML F2 4 Lines (f,d)(u,l) (14 btm)ML' WF2 MR F2 MR' WF2 MR SF2 WR' MF WR B2 WR' MF' 6 Lines (f,d)(u,l)(r,b) (20 btm)ML' WF2 MR F2 MR' WF2 MR SF2 D2 WR' MD WR D2 WR' MD' MF WR B2 WR' MF' The patterns above are about solutions not far from the upper bound of God's number of a 4x4x4 cube. We may also be interested in finding solutions near the lower bound, which is currently set to 29 btm. In this thread, it has been hypothesized that combining double edge flips with small diagonals may give solutions of more than 29 moves, as shown in the following *unoptimized* pattern: R2 D WR2 D2 WR' D R D' MR F2 MR' D2 MR D2 ML2 F2 ML' F2 ML F2 D2 MR2 D' R MR' MU' TR MD MF TR' MU TR MU' MF' WU R' 4x: 3 Double Edge Flips + 3 Small Diagonals (35 btm)


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benpuzzles

Post subject: Re: Patterns Posted: Fri Oct 18, 2013 7:56 am 

Joined: Fri Dec 28, 2012 1:50 pm Location: Near Las Vegas, NV

andychilly wrote: I dont know if anyone else has attempted a checker board pattern on the Hexaminx but I shall ask two important questions both need answering
Question 1: is it not possible? (I can't seem to get around this parity issue.) It isn't and I just realized why: There are 30 edge pieces on a Megaminx, and so if you are swapping edge pairs, you will have to end up swapping 15 pairs (an odd number) which is impossible (you can only swap an even number of pairs).
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AndyChilly

Post subject: Re: Patterns Posted: Fri Oct 18, 2013 8:10 am 

Joined: Fri Jun 21, 2013 3:39 am Location: Rye, East Sussex

benpuzzles wrote: It isn't and I just realized why: There are 30 edge pieces on a Megaminx, and so if you are swapping edge pairs, you will have to end up swapping 15 pairs (an odd number) which is impossible (you can only swap an even number of pairs). Aw thats a shame, would have been satisfying to finish that. I will not resort to pulling out peices and repositioning them. I would love it if Oliver could make some earth stickers for the hexaminx. Maybe Ill ask him on pay day.
_________________ How to sum up my solving skills..."I try, I try, I fail. I try, I try, PREVAIL!"


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mocenigo

Post subject: Re: Patterns Posted: Fri Oct 18, 2013 9:50 am 

Joined: Wed Apr 06, 2011 4:27 pm Location: Munich, Germany


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TheCubingKyle

Post subject: Re: Patterns Posted: Sun Oct 20, 2013 2:15 pm 

Joined: Sun Jul 14, 2013 11:10 pm


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Waran

Post subject: Re: Patterns Posted: Tue Oct 22, 2013 6:14 pm 

Joined: Sat Jan 28, 2006 6:04 am Location: Switzerland

@ mocenigo Nice algorithm! Algorithms with a sevenfold repetition can't be found often indeed! @ glazik Great algorithms! Allright, let's have a look at algorithms close to the current lower bound of 29 moves btm. This first one has exactly 29 moves, while the others require a little bit more. However, they look quite simple and I am sure that optimal solutions would be all below 29 moves: 4x: 2 RingsF2 L2 D F' TB2 R2 MB2 TR2 MB2 MR2 U' R B2 R' WD R WF2 R' D MR' TD' TR TF2 TL' TU TL' TU' TL2 TF2 (29 btm) 4x: Double AnacondaL2 D2 MR2 F2 ML2 D2 TF2 MR2 MF2 D2 F2 L2 WD2 B' (MU' L2 MU L' MB' L2 MB L) MB' (ML' TD TL2 TU' ML TU TL2 TD') TB (32 btm) 4x: 4 Small Edge TrianglesMR' U' MR MF D' MF' MR' U MR MF D MF2 R' MF MU L' MU' MF' R MF MU L MU2 F' MU MR B' MR' MU' F MU MR B MR' (34 btm) 4x: 4 Peaks, 6 DiagonalsTR D' MF2 SD MB2 U F U' MB2 U SB D' MF2 D B' U F' MD2 F SU' B' MU2 B D' B' MU2 SF' MD2 F TF2 TU' TR2 TU2 TR' TU2 TR2 TF2 TR' (38 btm)


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glazik

Post subject: Re: Patterns Posted: Wed Oct 23, 2013 8:52 am 

Joined: Wed Oct 12, 2011 12:54 pm


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Andrea

Post subject: Re: Patterns Posted: Fri Oct 25, 2013 3:28 am 

Joined: Wed Apr 13, 2011 8:37 am Location: Germany

Hi leRAFs,
very interesting, your hexaminx pattern. A turned cube in a cube ?


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Waran

Post subject: Re: Patterns Posted: Fri Nov 01, 2013 3:36 pm 

Joined: Sat Jan 28, 2006 6:04 am Location: Switzerland

Here are a couple of more improved 4x4 patterns. A total of 23 moves have been gained: 4x: 2 TrianglesSF' U2 F2 (L' MU2 L SU' L' MU2 L SU) F2 U2 F2 R2 D2 (MD' MR' MD MR) D2 R2 B' F' (24 btm) 2 moves 4x: 1 Outlined PeakTR' (U MB2 U' TF' U MB2 U' TF) MR (WF MD' F2 MD WF' MD' F2 MD) R (19 btm) 1 move 4x: 2 Rings (3x3x3)F2 R2 U' F' U R' U2 R U' F' MF2 R2 MF2 TR2 MF2 MR2 TR' TD' TR TF2 TL' TU TL' TU' TL2 TF2 (26 btm) 6 moves 4x: 2 (Cube in a)3 CubeR' F L' U' F R2 F2 R' F' R F2 B L' B' U2 L2 MF TR' TF TD TB2 TR2 TU' TF' TD TB' (26 btm) 1 move 4x: 2 Chessboard Cubes (3x3x3)U2 F2 R' T3D' F L' F2 L T3B' R' MR2 U2 MR2 TU2 MR2 MU2 SF L2 B2 (U' MR2 U SR U' MR2 U SR') B2 L2 ((MR' MU MR) (ML MD' ML') WD) SF' (37 btm) 13 moves


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Waran

Post subject: Re: Patterns Posted: Sat Nov 02, 2013 12:00 pm 

Joined: Sat Jan 28, 2006 6:04 am Location: Switzerland

This colorful pattern reminds a little bit on Oskar van Deventer's Gear Cubes: 5x: Gear CubeD B2 D2 F' (D F2)2 WR2 F' D' WF2 WR2 U F' SD' F' (TB' L2 TB NL TB' L2 TB NL') F D NF TU' TF TU' MR2 MF2 TD TF MR2 (TF2 TD')2 TF TD2 TB2 TD' F D R D2 B U B L B2 D MR2 MD2 MF2 D' B2 L' B' U' B' D2 R' D' F' MR2 MD2 MF2 (70 btm)


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glazik

Post subject: Re: Patterns Posted: Sat Nov 02, 2013 3:45 pm 

Joined: Wed Oct 12, 2011 12:54 pm

@ Walter, A few sequences have been improved...again F2 R2 U' F' U R' U2 R U' F' MF2 R2 MF2 TR2 MF2 MR2 TR2 TB2 TU' TB' TU TB' TR2 TF TD' TF' 4x: 2 Rings (3x3x3) (25 btm) 1 moveEdges (22 btm) WR' B2 L2 U WU2 R U2 MB2 MF' U2 R' WU2 L D2 MB MF2 D2 L' U' L2 B2 WR Dots (f,d,r,b,u,l) (17 btm) MR' TB' L MB MR MB' L' U' MR' MD MR U MR' MD' B MR MB Lines (f,l,u,b,r,d) (12 btm) F2 L2 TD2 MB MD2 MF' MR' WF MR D2 L2 F2 4x: Layered Anacondas (50 btm) 15 movesEdges WR U2 R2 B WF2 L B2 MU2 MD' B2 L' WF2 R F2 MU MD2 F2 R' B' R2 U2 WR' Lines + Dots WR U2 MR' U2 B2 D2 MR' MD WR D2 WR' MD' MF WR B2 WR' MF' WF MD MB' MD' F MD TB MU' B' MD' TB MU' MB' TD MB MU MB' U' L2 CU CF' 4x: Woven Anacondas (53 btm) 16 movesAll present 4x sequences should now be below the published 57 obtm upper bound, although the actual btm bound may well be about 5354 btm. Two new 5x mixed patterns: 5x: Mixed Patterns 1 (11 btm)5x: Mixed Patterns 2 (13 btm)...plus a few sieves: 5x: 6 Sieves (u,b,r,d,f,l) (13 btm) 4 moves5x: 6 Sieves (u,d,r,l) (14 btm)5x: 6 Sieves (d,u)(l,f,r,b) (10 btm)


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Waran

Post subject: Re: Patterns Posted: Sun Nov 03, 2013 9:49 am 

Joined: Sat Jan 28, 2006 6:04 am Location: Switzerland

glazik wrote: All present 4x sequences should now be below the published 57 obtm upper bound, although the actual btm bound may well be about 5354 btm. Even better! By improving another algorithm, all 4x sequences are now below 55 moves: 4x: Winding HexagonMD2 R' B U' MR2 TU B' U' B MU' MR2 B' U F U2 F' R MD2 R' F U2 F' R TB2 SR' B R SF L' MB2 L SF' R' B' SR B MD MB MD' B MD MB' MD' MB2 MR2 WF MR' F' MR WF' MR' F MR' MB2 (54 btm) 2 moves The next one with the same lenght is this Whirl pattern: 4x: 2 WhirlsMR' U' MR MF D' MF' MR' U MR MF D MF2 R' MF MU L' MU' MF' R MF MU L MU2 F' MU MR B' MR' MU' F MU MR B MR' D2 R' L' (F2 MB' WD MB WD' F2) SR' (F B MR' MD' MR MD F' B') R2 D2 (54 btm) I just checked the 5x sequences. The longest algorithm there requires up to 95 moves. As far as I know an upper bound for the 5x5x5 hasn't been found yet. But even without that mark it is obvious that some of them might be far from optimal. 5x: 4 Outlined HeartsF' L B D2 (L SD2 SR ND SR' SD2 SR ND' R') D2 B' L' F' MR' F2 U' (SF MR SF' R L SF MR' SF' R' L') U F2 MR (NU' F2)4 NU' NL2 F ND F' NL2 F ND' SF ND' NL2 B' SL' ND' NL2 ND NL2 SL B ND NL2 B MF2 TU' (NU2 MF D2 MF ND2 NU2 MF' TD2 MF') TU MF2 (76 btm) 5x: 2 Rings (4x4x4)TU2 NF TU TB2 TU' NF' TU TB2 TR TB' TR' NF2 TR TB TR' NF2 TU TL2 ND' TF2 TR2 ND' TR2 ND TR2 NU' TR2 NU TF2 TL2 B2 R2 (VB NL VB' WR' VU NL' VU' WR) R2 B2 TU' R' NU MR NU2 MR' NU R TU TB' NF VU2 NF' D' NF VU2 NF' D TB (61 btm)


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glazik

Post subject: Re: Patterns Posted: Sat Nov 09, 2013 4:11 pm 

Joined: Wed Oct 12, 2011 12:54 pm

All 4x sequences should now be 53 moves long or less : B' MD MB MD' B MD MB' MD' MB2 MR2 WF MR' F' MR WF' MR' F MR' MB2 MB2 D2 SR D' R' SU' L MD2 L' SU R D SR' TD2 R U' F2 U R' MB2 R U' F2 U F D' MR2 MF' D F' D' TF MR2 F' D R' 4x: Winding Hexagon (53 btm) 1 moveMR B' MR' MU' F' MU MR B MR' MU' F MU MU L' MU' MF' R' MF MU L MU' MF' R MF MF D' MF' MR' U' MR MF D MF' MR' U MR D2 R2 F2 SR MB' WD MB WD' SR' SF' MR' MD' MR MD B' F' R2 D2 4x: 2 Whirls (52 btm) 2 moves5x sequences have again been shortened F' L B D2 L SU2 SR ND SR' SU2 SR ND' R' D2 B' L' F F2 MR' F2 U' SF MR SF' R L SF MR' SF' R' L' U F2 MR F2 F2 NU' F2 NU' F2 NU' F2 NU' F2 NU' F2 F2 NU' WF2 ND' WF2 MR2 NU ND WR MR2 U2 WR' ND2 WR U2 WR' ND2 F2 5x: 4 Outlined Hearts (58 btm) 18 movesU2 R U' F L2 F' NL NR' F L2 F' U R' U' NR NL' TU' L2 NU2 B2 NU' NB NF' ND' NU NB' NF ND B2 NU2 L2 NU SR2 F2 NU F2 NU' F2 ND F2 ND' L2 NU R2 TD NB2 TD' NF2 MR' NF' R NF MR NF' R' NF' NU' NR' B NU TD2 TB R' NB MU2 NB' NR MU NR' MU R TB' TD2 NU' B' NR NU TU TR2 T3B2 S2D' TL MF TL TF2 TL' MF' TL T3D' 5x: Triple Python (89 btm) 6 movesI guess this last sequence could still be shortened down to at least 83 btm, by better partitioning... U2 R U' F L2 F' NL NR' F L2 F' U R' U' NR NL' TU' L2 NU2 B2 (NU' NB NF' ND' NU NB' NF ND) B2 NU2 L2 NU SR2 F2 NU F2 NU' F2 ND F2 ND' L2 NU R2 TD NB2 TD' NF2 MR' NF' R NF MR NF' R' NF' NU' NR' B NU TD2 TB R' NB MU2 NB' NR MU NR' MU R TB' TD2 NU' B' NR NU 5x: Double Python (77 btm) 6 movesTU' TB2 TU' NF S2U NF TD TB2 TD' NF' S2U' NF' TU2 S2R2 TB2 ND' TB2 ND TB2 NU' TB2 NU TR2 ND' TL2 L2 F2 VF' NR' VF WR' VD' NR VD WR F2 L2 TU' R' NU' MR NU2 MR' NU' R TU TU NR2 TU' VL2 TU NR2 TU' VL2 5x: 2 Rings (4x4x4) (52 btm) 9 movesA few simple patterns: 5x: New Pattern 1 (b,u,d,f) (8 btm) NR NU2 WF2 NR' NL' WF2 NU2 NL 5x: New Pattern 2 (b,u)(d,f) (8 btm) NR MU2 WF2 NL' NR' MU2 WF2 NL 5x: New Pattern 3 (d,u)(l,r)(b,f) (10 btm) NR2 WU2 NR2 NF NB' WU2 MU NB NF' MU' 5x: New Pattern 4 (d,l,b)(r,f,u) (8 btm) MR NU ND' WR' NU' ND NR NL' 5x: New Pattern 5 (d,f,r,u,b,l) (12 btm) NR2 NU2 ND2 NR2 NF NB' ND2 NU2 WR NB NF' WR' 5x: New Pattern 6 (d,u) (10 btm) MR2 WR NU2 WR' MR2 U2 WR NU2 WR' U2 5x: New Pattern 7 (d,u)(b,f) (6 btm) MR2 NU2 WR NU2 MR2 WR' 5x: New Pattern 8 (r,f,u)(d,l,b) (8 btm) NR MF' NR' NL' WF' MF NL WF 5x: New Pattern 9 (r,f,u)(d,l,b) (7 btm) NF' WR VF MR WR' MF' MR' I note that a rough estimate of the upper bound of God's number for 4x and 5x cubes can be obtained from the following assumptions:  1 move is gained by concatenating the algorithms of 2 consecutive phases  any orbit of edges or centers is solved in no more than 22 moves (extension of Jaap's results)  for cubes of odd order, corners + middle edges + true centers are solved in no more than 20 moves  for cubes of even order, corners are solved in no more than 11 moves This gives the following 'loose' upper bounds, which may be useful when designing pretty patterns: 20 + 22 + 22 + 22 3 = 83 moves (5x cube) 11 + 22 + 22 2 = 53 moves (4x cube), or... ...57  4 = 53 moves, as there are 5 phases in the 4x OBTM solver


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Zem

Post subject: Re: Patterns Posted: Sat Nov 09, 2013 6:17 pm 

Joined: Sat Sep 07, 2013 3:53 pm


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perfredlund

Post subject: Re: Patterns Posted: Tue Nov 12, 2013 4:37 am 

Joined: Fri May 06, 2005 10:13 am Location: Norway


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perfredlund

Post subject: Re: Patterns Posted: Tue Nov 12, 2013 6:37 am 

Joined: Fri May 06, 2005 10:13 am Location: Norway

Another easy contribution (not yet optimized!!) 3 "truncated" flips on 4x4x4 (43 btm).Per
_________________ "Life is what happens to you while you are busy making other plans" John Lennon, Beautiful Boy


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glazik

Post subject: Re: Patterns Posted: Wed Nov 13, 2013 4:46 am 

Joined: Wed Oct 12, 2011 12:54 pm


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perfredlund

Post subject: Re: Patterns Posted: Thu Nov 14, 2013 5:03 am 

Joined: Fri May 06, 2005 10:13 am Location: Norway

Waran wrote: The patterns on the Chimera 2x2+6x6 are impressing! Since I don't have such smashing cubes, I am using a humble 5x5 for another snake. It's a sort of a single path Python that meanders close to the boundaries of the cube: 5x: Python on the edge(MR2 ND L2 ND')2 TB2 ND TB2 ND' TB2 NU TB2 NU' TR2 NU TR2 TU' B2 TU TD NB TU' TD' B2 TU TD NB' TD' ND' B' ND' NR ND NR' ND NB' ND' TB ND D' MR2 D NR NB D' MR2 D NB' NR' (52 btm) That one can be done much shorter: 5X: Python on the edge (26 btm).Per
_________________ "Life is what happens to you while you are busy making other plans" John Lennon, Beautiful Boy


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glazik

Post subject: Re: Patterns Posted: Thu Nov 14, 2013 12:42 pm 

Joined: Wed Oct 12, 2011 12:54 pm

4 more moves gained by optimizing the sequence: R MU' R' NB2 R MU R' NB2 B2 ND' F2 NU L2 NU' L2 ND L2 ND' L2 SF2 TD NB2 TD' 5x: Python on the Edge (22 btm)An easy variation: R MU' R' NB2 R MU R' NB2 B2 ND' F2 NU L2 NU' L2 ND L2 ND' L2 SF2 TD NB2 TD' TD TB2 T3R2 S2U' TF MR' TF TL2 TF' MR TF T3U' 5x: Fat Python (31 btm)


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perfredlund

Post subject: Re: Patterns Posted: Fri Nov 15, 2013 4:48 am 

Joined: Fri May 06, 2005 10:13 am Location: Norway

_________________ "Life is what happens to you while you are busy making other plans" John Lennon, Beautiful Boy


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glazik

Post subject: Re: Patterns Posted: Fri Nov 15, 2013 8:41 am 

Joined: Wed Oct 12, 2011 12:54 pm


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perfredlund

Post subject: Re: Patterns Posted: Mon Nov 18, 2013 6:46 am 

Joined: Fri May 06, 2005 10:13 am Location: Norway


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perfredlund

Post subject: Re: Patterns Posted: Tue Nov 19, 2013 6:12 am 

Joined: Fri May 06, 2005 10:13 am Location: Norway


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glazik

Post subject: Re: Patterns Posted: Tue Nov 19, 2013 9:51 am 

Joined: Wed Oct 12, 2011 12:54 pm

Using the 3x 16move superflip sequence and a short algorithm for centers, a gain of 42 moves has been obtained for the Fat Helicopter Superflip pattern (corrected): CD CR2 M2R2 TU' TR2 TD' M2F M2R2 TU M2R TU2 TF2 TD' M2F M2R2 TU' TR2 TU' TU TR' TF N3L M2U' N3L' N3F N3B U2 N3R2 N3F2 N3R2 N3F2 U2 N3R2 N3F2 M2U M2F N3R2 TF' TR TU' 6x: Fat Helicopter Superflip (35 btm)The following pattern may be new: Insertion + face twists applied to: NR2 NB NF' ND NU' NF2 NR2 U2 NF2 NR2 NF2 NR2 U2 NB' NF' NL NU ND' NL' VL VD VU' VL' VF VB U2 VR2 VF2 VR2 VF2 U2 VR2 VF2 VU VD' VF VB' VR2 6x: 6 Crosses (36 btm)I'm still working on the other patterns...


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perfredlund

Post subject: Re: Patterns Posted: Fri Nov 22, 2013 6:59 am 

Joined: Fri May 06, 2005 10:13 am Location: Norway

glazik wrote: Using the 3x 16move superflip sequence and a short algorithm for centers, a gain of 42 moves has been obtained for the Fat Helicopter Superflip pattern (corrected): CD CR2 M2R2 TU' TR2 TD' M2F M2R2 TU M2R TU2 TF2 TD' M2F M2R2 TU' TR2 TU' TU TR' TF N3L M2U' N3L' N3F N3B U2 N3R2 N3F2 N3R2 N3F2 U2 N3R2 N3F2 M2U M2F N3R2 TF' TR TU' 6x: Fat Helicopter Superflip (35 btm)The following pattern may be new: Insertion + face twists applied to: NR2 NB NF' ND NU' NF2 NR2 U2 NF2 NR2 NF2 NR2 U2 NB' NF' NL NU ND' NL' VL VD VU' VL' VF VB U2 VR2 VF2 VR2 VF2 U2 VR2 VF2 VU VD' VF VB' VR2 6x: 6 Crosses (36 btm)I'm still working on the other patterns... Hi Glazik! Your improvement was not quite correct, so i added 2 center cycles to make it corect: 6X: Fat Helicopter Superflip (54 btm).Could be improved by insertion Per
_________________ "Life is what happens to you while you are busy making other plans" John Lennon, Beautiful Boy


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glazik

Post subject: Re: Patterns Posted: Fri Nov 22, 2013 12:09 pm 

Joined: Wed Oct 12, 2011 12:54 pm


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perfredlund

Post subject: Re: Patterns Posted: Fri Nov 22, 2013 2:50 pm 

Joined: Fri May 06, 2005 10:13 am Location: Norway

The following has been improved: 6X: 2 Helicopter Flips (18 btm).Per
_________________ "Life is what happens to you while you are busy making other plans" John Lennon, Beautiful Boy


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Waran

Post subject: Re: Patterns Posted: Sat Nov 30, 2013 4:36 pm 

Joined: Sat Jan 28, 2006 6:04 am Location: Switzerland

Here are some 5x5 patterns that have been improved: 5x: 4 Small DiagonalsNU L2 (T3F2 MD' MF2 WD NF2 NU ND' F2) L2 NU' (12 btm) 2 moves 5x: 4 Woven Diagonals(TF TB TR TL)2 TF TB NR NL F' B' (R' L' F' B')2 (22 btm) 2 moves 5x: I Love UWF' (WR2 NF2 WR2 WD2 VF2 WD MF2 WD) VF L NB' NR2 NB L' NB' TR2 MF' NL2 MF R2 MF' NL2 MF (24 btm) 1 move 5x: 2 Cube in a Cube in a Cube in a Cube in a CubeR U' L F U' R2 U2 R U R' U2 D' L D F2 L2 U MR TB2 MR' MD' TB' S2D2 TB TR' MD MF TL MF' TU2 (30 btm) 2 moves 5x: 2 Angry CubeR U' L F U' R2 U2 R U R' U2 D' L D F2 L2 U MR TB2 MR' MD' TB' S2D2 TB TR' MD MF TL MF' TU2 F SR' SF SR' SF' SD2 SR B' (38 btm) 3 moves 5x: Awful WaffleNB' NR' ND' NR2 ND NR' NB NF2 NR2 NF NR2 NF2 NU NR NL ND NB (17 btm) 1 move 5x: 4 Enhanced Edge FlipsU' B2 WR B2 WR2 U WR2 B2 NR' ND' VL ND B2 ND' VL' ND VL L2 VF' ND' VF ND L2 ND' VF' ND VF F2 VR' ND' VR ND F2 ND' VR' ND VR R2 VB' ND' VB ND R2 ND' VB' ND VB (47 btm) 3 moves 5x: 4 Enhanced Edge Flips (Version 2)U' B2 WR B2 WR2 U WR2 B2 WR' B WD NB WD' B WD NB' WD' R' WD NR WD' R WD NR' WD' F' WD NF WD' F WD NF' WD' L' MD NL MD' L MD NL' VU NL' NU' L NU NL NU' L' (48 btm) 1 move 5x: 2 TrianglesSF L2 B2 (SR U' NL2 U SR' U' NL2 U) B2 L2 F2 U D L2 (MF NU' MF' NU NF MD NF' MD') L2 D' U' B F (30 btm) 2 moves 5x: 2 Marked Cube in a CubeSF' U2 F2 (L' NU2 L SU' L' NU2 L SU) F2 U2 B2 L2 U2 (ND' NR' ND NR) U2 L2 B L2 F D' R2 D F' L2 F D' R2 D (34 btm) 4 moves


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