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perfredlund

Post subject: Re: Patterns Posted: Thu Mar 01, 2012 3:48 pm 

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

Yet another ring pattern: 5 rings (5x5x5).This takes more turns than 6x6x6 equivalent And i'm sure it can be optimised! Per
_________________ "Life is what happens to you while you are busy making other plans" John Lennon, Beautiful Boy


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perfredlund

Post subject: Re: Patterns Posted: Fri Mar 02, 2012 8:36 am 

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

One more outstanding Gridlock variety: Grid  Locked Whirls.I think i achieved some good cancellation with this. But i still believe better can be found. It is symmetric and not too many pieces are involved Per
_________________ "Life is what happens to you while you are busy making other plans" John Lennon, Beautiful Boy


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perfredlund

Post subject: Re: Patterns Posted: Mon Mar 05, 2012 6:38 am 

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

This is a pattern i posted on speedsolving a long time ago: Both ways tiger stripes.It's getting harder to find good names Per
_________________ "Life is what happens to you while you are busy making other plans" John Lennon, Beautiful Boy


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perfredlund

Post subject: Re: Patterns Posted: Mon Mar 05, 2012 7:04 am 

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

Increasing opposite spots.I'm collecting all my old nice big cubes patterns here ... Per
_________________ "Life is what happens to you while you are busy making other plans" John Lennon, Beautiful Boy


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perfredlund

Post subject: Re: Patterns Posted: Tue Mar 06, 2012 8:16 am 

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

One of Walter's old favourites: Psychedelic waves. The start is his own contribution (less 4 twisted corners). 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: Thu Mar 08, 2012 2:11 pm 

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

I optimized your approach a little bit and saved 13 moves. Psychedelic WavesF R2 U' R2 U D B' D2 SR D2 F U' D' L2 U L2 B' TF' TR2 TU' TR2 TU2 TR' TU2 TF (25 btm) Here is another way to create 3 rings: 3 RingsNF R2 NF' NB' R2 NB WD NF R2 NF' NB' R2 NB WD' WD' MR U MR' WD MR U' MR' (22 btm or 21 btm actually)


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perfredlund

Post subject: Re: Patterns Posted: Fri Mar 09, 2012 2:56 pm 

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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perfredlund

Post subject: Re: Patterns Posted: Fri Mar 09, 2012 3:41 pm 

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

Waran wrote: I optimized your approach a little bit and saved 13 moves. Psychedelic WavesF R2 U' R2 U D B' D2 SR D2 F U' D' L2 U L2 B' TF' TR2 TU' TR2 TU2 TR' TU2 TF (25 btm) Here is another way to create 3 rings: 3 RingsNF R2 NF' NB' R2 NB WD NF R2 NF' NB' R2 NB WD' WD' MR U MR' WD MR U' MR' (22 btm or 21 btm actually) Nice improvement  due to better breakdown. I was lazy, simply adding twists to another pattern. 3 Rings can also be done on even sized cubes! 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: Sun Mar 11, 2012 11:17 am 

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

@ Per Fantastic patterns and as always I keep wondering how you find such short algorithms. This pattern looks similar to the 'Psychedelic Waves' above. However it isn't quite that extreme and only has 3 colors per face. Nevertheless it turned out to be tricky to build it. My current approach requires 114 moves. Can anyone see a way to further optimize it? 6x6x6 WavesF (R' D SR' F R F' L' D' F R' F' R2) F' VB' L2 VF VB L2 VF' WD VB' L2 VF VB L2 VF' WD' R F' (NU2 ND2 F U F' VU2 ND2 F U' F' MU2) F R' B L' (NU2 ND2 L D L' NU2 VD2 L D' L' MD2) L B' SD2 SR (NR NL' NF' NB NR' NL NF NB') (MF MU' MF' MB' MU MD MB MD') (MD NF NB' MD' NF' NB) (NU' ND MF NU ND' MF') SR' SD2 L' (MD' R D R' MD MU R D' R' MU') L B (MU' F' D' F MU MD F' D F MD') B' (114 btm) Fortunately a 4x4x4 version is much easier to achieve: 4x4x4 WavesD' B' L MF2 L' B L MF2 L' MF U B U' MF' U B' D MF D' F' D MF' D' F D' F' L2 D F SR SF L' U' F2 L U' D' F R' MF2 R F' R' MF2 R U' SD2 SR (MB' MU' MB MU) (MD MF MD' MF') SR' SD2 (58 btm)


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perfredlund

Post subject: Re: Patterns Posted: Mon Mar 12, 2012 7:02 am 

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

Maybe this was published here before. The thread is getting long. But i believe it should be an improvement nevertheless: 3 large rings (same slice).Constructed from 2 parts: N2R WU MF D (N2F2 MR2)2 D MF R2 WU N2R N2L WU R2 WU N2L (2 adjacent rings) N2L2 WU2 VL2 N2U2 MR2 VD2 (2 opposite rings  this might be new as well) I tried other approaches, but did not get any good cancellations. 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: Mon Mar 12, 2012 2:51 pm 

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

perfredlund wrote: I tried other approaches, but did not get any good cancellations. This solution is composed out of 3cyles. Part 1 draws the horizontal lines and part 2 the dots inbetween. 3 Large Rings (Same Slice)NU2 L2 F2 NU SF2 ND' B2 L2 NU2 R' MD' R' NF2 NB2 R MD R' NF2 NB2 R2 (20 btm) It might be possible to fuse these two parts to get a shorter sequence. I don't believe this is already an optimal solution.


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glazik

Post subject: Re: Patterns Posted: Tue Mar 13, 2012 4:13 pm 

Joined: Wed Oct 12, 2011 12:54 pm

@ Walter 3 Rings (f,l,r) (18 m)Part 2 can be replaced with a 9mover to gain 2 moves: NU2 L2 F2 NU SF2 ND' B2 L2 NU2 WF [MR' F MR', WF2] WF' 3 Rings (f,l,r) (18 m)Here are a few additional (unoptimized) algorithms of rings: 4 Rings (f,l)(r,b) (15 m)NU' WR2 NU2 WF2 NU' WR2 WF2 MF WR MF' SR' MF WR' MF' SR 4 Rings (f,l)(r,b) (15 m)4 Rings (f,b,l,r) (22 m)2 Rings (f,b) VR2 WU2 NR2 VD2 MR2 NU2 3 Rings (f,l,r) NU2 L2 F2 NU SF2 ND' B2 L2 NU2 WF MR' F MR' WF2 MR F' MR WF 4 Rings (f,b,l,r) = (f,b)(f,l,r) 4 Rings (f,b,l,r) (22 m)6 Rings (u,r,f,d,l,b) (13 m)6 Rings (u,r,f)(d,l,b) WR WF' WR' MR MF MR' MF' WF 2 Rings (d,u) WF2 VR2 NF2 MR2 VB2 NR2 6 Rings (u,r,f,d,l,b) = (u,r,f)(d,l,b) (d,u) = (u,r,f) (d,l,b,u) = (u,r,f) (u,d,l,b) = (u,r,f,d,l,b) 6 Rings (u,r,f,d,l,b) (13 m)


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Waran

Post subject: Re: Patterns Posted: Wed Mar 14, 2012 12:38 pm 

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

Excellent work! As you just proofed, it is indeed possible to build the '3 Rings (f,l,r)' with less then 20 moves. I couldn't find any shorter solutions for your other Ring patterns.


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glazik

Post subject: Re: Patterns Posted: Thu Mar 15, 2012 2:35 am 

Joined: Wed Oct 12, 2011 12:54 pm

Thank you for checking the algs. Continuing further, by slightly modifying the 2 parts of Per's algorithm of the '6 Rings (u,d)(r,l)(f,b)' pattern, a gain of 2 moves can be obtained: 12 Centers MR2 NF2 ND2 MR2 MF2 ND2 VF2 12 Bars VF2 WU2 NB2 NR2 WU2 WF2 NR2 Algorithm (11 moves) MR2 NF2 ND2 MR2 MF2 VU2 NB2 NR2 WU2 WF2 NR2 6 Rings (u,d)(r,l)(f,b) (11 m)


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perfredlund

Post subject: Re: Patterns Posted: Fri Mar 16, 2012 3:16 pm 

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

glazik wrote: @ Walter 4 Rings (f,l)(r,b) (15 m)NU' WR2 NU2 WF2 NU' WR2 WF2 MF WR MF' SR' MF WR' MF' SR 4 Rings (f,l)(r,b) (15 m)Slight improvement: 4 Rings (f,l)(r,b)(14m)Per
_________________ "Life is what happens to you while you are busy making other plans" John Lennon, Beautiful Boy


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perfredlund

Post subject: Re: Patterns Posted: Fri Mar 16, 2012 4:11 pm 

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

glazik wrote: Thank you for checking the algs. Continuing further, by slightly modifying the 2 parts of Per's algorithm of the '6 Rings (u,d)(r,l)(f,b)' pattern, a gain of 2 moves can be obtained: 12 Centers MR2 NF2 ND2 MR2 MF2 ND2 VF2 12 Bars VF2 WU2 NB2 NR2 WU2 WF2 NR2 Algorithm (11 moves) MR2 NF2 ND2 MR2 MF2 VU2 NB2 NR2 WU2 WF2 NR2 6 Rings (u,d)(r,l)(f,b) (11 m)This one can also be slightly improved. 6 Rings (u,d)(f,b)(r,l)(10m).Start with WF WU2 WF WU2 and add WU2 VL2 N2U2 MR2* VD2 N2L2 after that Then insert MR2 MF MR2 MF at the *. I hope to get back to Walter's new (3 colour/side) psychedelic waves. The 4x4x4 looks hardest to improve Per
_________________ "Life is what happens to you while you are busy making other plans" John Lennon, Beautiful Boy


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perfredlund

Post subject: Re: Patterns Posted: Sat Mar 17, 2012 8:52 am 

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

glazik wrote: 4 Rings (f,b,l,r) (22 m)2 Rings (f,b) VR2 WU2 NR2 VD2 MR2 NU2 3 Rings (f,l,r) NU2 L2 F2 NU SF2 ND' B2 L2 NU2 WF MR' F MR' WF2 MR F' MR WF 4 Rings (f,b,l,r) = (f,b)(f,l,r) 4 Rings (f,b,l,r) (22 m) One final improvement: 4 Rings (f,b,l,r) (21m).We are already pushing the limits now... 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: Sat Mar 17, 2012 10:21 am 

Joined: Wed Oct 12, 2011 12:54 pm

@ Per Good work done on optimizing the algs! It seems that algorithms of rings are indeed nearing the 20 moves border. As I was'nt able to found much info on the group of the 720 permutations of blocks of centers, I wrote a small program to find all cycles. Providing there were no errors, 33 cycles were found to be sufficient, up to symmetry + inversion. The list may be useful for adding cycles that don't still exist on Walter's website: (b, d) (d, u) (d, l, b) (l, u, d) (l, u) (b, d) (l, r) (d, u) (d, u) (b, l) (u, r) (d, l) (l, u, b, d) (l, u, d, b) (u, r, d, l) (u, r, l, d) (u, r) (d, l, b) (l, r) (d, u, b) (b, d) (u, r, l) (u, r, b, d, l) (u, r, b, l, d) (u, r, l, b, d) (r, f) (l, u) (b, d) (r, f) (d, u) (b, l) (b, f) (l, r) (d, u) (r, f) (l, u, b, d) (r, f) (l, u, d, b) (d, u) (r, f, b, l) (d, u) (r, f, l, b) (r, f, u) (d, l, b) (r, f, u) (b, l, d) (r, f, l) (d, u, b) (r, f, b, d, l, u) (r, f, b, l, d, u) (r, f, b, d, u, l) (r, f, d, b, l, u) (r, f, d, l, b, u) By pairing up 2 orbits of centers, distinct cycles can be obtained to give simple dual color patterns, such as: Dual Color Rings (r,f,u)(d,l,b)  (d,f,r)(l,u,b)


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perfredlund

Post subject: Re: Patterns Posted: Sun Mar 18, 2012 7:18 am 

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

One more easy pattern: Dotpluszero.Quite easy construction. I will ezplain if needed Per
_________________ "Life is what happens to you while you are busy making other plans" John Lennon, Beautiful Boy


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perfredlund

Post subject: Re: Patterns Posted: Sun Mar 18, 2012 3:38 pm 

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

perfredlund wrote: A minor improvement. 4 Rings (f,u,b,d) (20 m).Per
_________________ "Life is what happens to you while you are busy making other plans" John Lennon, Beautiful Boy


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perfredlund

Post subject: Re: Patterns Posted: Sun Mar 18, 2012 4:06 pm 

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

perfredlund wrote: Yet another ring pattern: 5 rings (5x5x5).This takes more turns than 6x6x6 equivalent And i'm sure it can be optimised! Per I improved it, based on previous improvement: 5 Rings (u,b,d,f,r) (37 m).Surely better can be found  but probably not by me 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: Sun Mar 18, 2012 4:37 pm 

Joined: Wed Oct 12, 2011 12:54 pm

The algs have been slightly improved (but not yet optimized). Except the (5c), they are all less than 20 moves, so much work remains to be done on fivecycles! DotPlusZero (11 m)]MU' ND2 WF2, MR2] [MR', MU2] DotPlusZero (11 m)4 Rings (f,d,b,u) (19 m)8 Bars: ]NR WU2 NR2, WF2] 8 Centers: NU' MR2 NU MR' NU MR NU' MR NU' MR NU 4 Rings (f,d,b,u) (19 m)5 Rings (l,b,u,f,d) (31 m)(l,b,u,f,d) = (l,b,u,r,f,d)(f,r) (l,b,u,r,f,d): WR WF' WR' MR MF MR' MF' WF' VR2 NF2 MR2 VB2 NR2 (f,r): MU WR' D WR MU' WR' D' WR ND' WR' D2 WR NU ND WR' D2 WR NU' 5 Rings (l,b,u,f,d) (31 m)


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perfredlund

Post subject: Re: Patterns Posted: Mon Mar 19, 2012 8:25 am 

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

5 Rings (u,r,f,d,l) is essentially the same pattern as Glazik's last contribution. Saves 1 turn! 1. Same as Glazik start 2. Swap u and b rings 5 Rings (u,r,f,d,l) (30 m).Per Edit: Another essentially similar 5cycle of rings: 5 Rings (f,l,b,d,r) (25 m).I can probably delay the 6 spots and cancel even more turns. Quite a great optimization from the initial 39 turns, due to better breakdown of building blocks!! Edit 2: (I moved the 6spots and saved yet more 2 turns) 5 Rings (f,l,b,d,r) (23 m).I believe this one is now optimal!
_________________ "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: Tue Mar 20, 2012 4:27 pm 

Joined: Wed Oct 12, 2011 12:54 pm

Great optimization work! Here are additional (unoptimized) algorithms of 5cycles, slightly improved compared to those of Walter's website: 2 Rings (f,r) (18 m) (Alternate alg)[MU, WR' D WR] ND' WR' D2 WR NU ND WR' D2 WR NU' 2 Rings (f,r) (18 m) (Alternate alg)5 Rings (f,b)(u,r,l) (25 m)(f,b)(r,l) WF2 WU WF2 WU' MU MF2 MU' MF2 (r,u) [MF', WR' F WR] NF' WR' F2 WR NB NF WR' F2 WR NB' (f,b)(u,r,l) = (f,b)(r,l,u) = (f,b)(r,l)(r,u) WF2 WU WF2 WU' MU MF2 MU' MF2 [MF', WR' F WR] NF' WR' F2 WR NB NF WR' F2 WR NB' 5 Rings (f,b)(u,r,l) (25 m)5 Rings (l,r,b,f,u) (28 m)(l,r)(b,f) MR2 MU' MR2 MU WF2 WU WF2 WU' (b,u,l) WU [WU, MF' U MF] WU' [WU, NR B2 NL' NR' B2 NL] (l,r,b,f,u) = (l,r)(l,b,f,u) = (l,r)(b,f,u,l) = (l,r)(b,f)(b,u,l) MR2 MU' MR2 MU WF2 WU WF2 WU' WU [WU, MF' U MF] WU' [WU, NR B2 NL' NR' B2 NL] 5 Rings (l,r,b,f,u) (28 m)5 Rings (u,r)(d,b,l) (25 m)(u,f) [MR', WU' R WU] NR' WU' R2 WU NL NR WU' R2 WU NL' (u,f,r)(d,b,l) [ML', MF'] [WF', WR] (u,r)(d,b,l) = (u,f,f,r)(d,b,l) = (u,f)(u,f,r)(d,b,l) [MR', WU' R WU] NR' WU' R2 WU NL NR WU' R2 WU NL' [ML', MF'] [WF', WR] 5 Rings (u,r)(d,b,l) (25 m)And finally, to end this long list of long 5cycles, here is a simpler 'exotic' pattern on a 4x4x4 cube: 6 Small Dual Diagonals (f,l,b,u,r,d) (8 m)[WF2, ML' MR' MU'[ + shift: MR MU WF2 ML' MR' MU' WF2 ML 6 Small Dual Diagonals (f,l,b,u,r,d) (8 m)


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perfredlund

Post subject: Re: Patterns Posted: Wed Mar 21, 2012 5:42 am 

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

6 Rings (f,r)(b.l)(u,d) (18m).Construction: 1. ND WF2 (*)ND NU WF2 NU 2. WF2 VL2 N2F2 MR2 VB2 N2L2 (insert at *) And finally do the remaining centers: 3. MR WF MR SF MR WF MR SF Note that shorter solution for even sized cubes is possible based on my posted 6 spots 8mover Per Edit: 6 Rings 6x6x6 (f,r)(b,l)(u,d) (15m).(As already stated above)
_________________ "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 Mar 22, 2012 3:59 pm 

Joined: Wed Oct 12, 2011 12:54 pm

Another 4ring pattern: 4 Rings (u,d)(r,f) (23 m)(u,d)(r,l) MR2 MF MR2 MF' WF' WR2 WF WR2 (r,l,f) NU2 L2 F2 NU SF2 ND' B2 L2 NU2 WF MR' F MR' WF2 MR F' MR WF (u,d)(r,f) = (u,d)(r,l,l,f) = (u,d)(r,l)(r,l,f) NU2 L2 F2 NU SF2 ND' B2 L2 NU2 WF MR' F MR' WF2 MR F' MR MR2 MF MR2 MF' WF WF' WR2 WF WR2 4 Rings (u,d)(r,f) (23 m)An attempt to solve the 4x4x4 Waves pattern (unoptimized alg), with a reduction of 23 moves! 4x4x4 Waves (35 m)Basic Edge 4(3c) [U' ML2 U D ML2 D', SL] Edges 8(3c) WF [U' ML2 U D ML2 D', SL] [SL, U' MR2 U D MR2 D'] WF' WF U' ML2 U D ML2 D' SL D ML2 D' U' ML2 MR2 U D MR2 D' SL' D MR2 D' U' MR2 U WF' Centers (WF WR') (ML MD MR' MD') (MU' ML' MU MR) (WR WF') 4x4x4 Waves (35 m)


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Waran

Post subject: Re: Patterns Posted: Fri Mar 23, 2012 5:19 pm 

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

@ perfredlund and galzik Wow, you did a lot of awesome contributions! Here is a new approach for the 6x6x6 Wave which saves 31 moves: 6x6x6 Waves: D B D2 L B2 D L2 D2 B2 U B' WR' B' WR U' WF (U' MR2 U D MR2 D' SL D MR2 U' D' VR2 NL2 U D NR2 NL2 D' SL' D NR2 NL2 U' D' NR2 NL2 U) WF' VB' L2 VF VB L2 VF' WD VB' L2 VF VB L2 VF' WD' SD2 SR (NR NL' NF' NB NR' NL NF NB') (MF MU' MF' MB' MU MD MB MD') (MD NF NB' MD' NF' NB) (NU' ND MF NU ND' MF') SR' SD2 (90 btm or 83 btm actually)


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perfredlund

Post subject: Re: Patterns Posted: Wed Mar 28, 2012 4:52 am 

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

I tried to improve the 4x4x4 and 6x6x6 waves by using cotransportation, but i was unsuccessful. I did not get the edges into the correct configuration without long combinations. So, instead i now post waves on the 5x5x5 cube. But due to centre restrictions, the waves must be reflexive  unlike on evensized cubes. 5x5x5 reflexive waves.1. CU WR2 U WF2 U2 WR2 D F WU2 F2 WR WF WR F (first step edges) 2. CU MR2 TU MF2 TU2 MR2 TD TF MU2 TF2 MR MF MR TF (second step edges) 3. SF NL NU NL NU NR ND NR ND SF (centres) Unoptimized ... Per
_________________ "Life is what happens to you while you are busy making other plans" John Lennon, Beautiful Boy
Last edited by perfredlund on Wed Mar 28, 2012 8:20 am, edited 1 time in total.


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perfredlund

Post subject: Re: Patterns Posted: Wed Mar 28, 2012 8:17 am 

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

I got in the mood for some serious cubeincube stuff. CubeInCubeWaves (44 m).3 obvious parts. No slice turns for this one Per
_________________ "Life is what happens to you while you are busy making other plans" John Lennon, Beautiful Boy


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perfredlund

Post subject: Re: Patterns Posted: Fri Mar 30, 2012 12:46 pm 

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

3 swapped pairs of Rings (35 m).This was the worst case scenario of permuted rings on 5x5x5 I could think of. My solution is not elegant, and I just reuse old stuff already posted. Please improve me 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: Sat Mar 31, 2012 9:35 am 

Joined: Wed Oct 12, 2011 12:54 pm

Here is an alternate way of composing already existing permutations, not a great gain though (1 move only). Shorter solutions do not seem to be quite obvious. (f,d,l,b,u,r): WR WF' WR' MR MF MR' MF' WF' VR2 NF2 MR2 VB2 NR2 (l,f,u): WD2 MF' U' MF WD' MF' U MF NR' F2 NL NR F2 NL' WD' NR' F2 NL NR F2 NL' (f,d)(l,b)(u,r) = (f,d,l,b,u,r) (l,f,u): WR WF' WR' MR MF MR' MF' WF' VR2 NF2 MR2 VB2 NR2 WD2 MF' U' MF WD' MF' U MF NR' F2 NL NR F2 NL' WD' NR' F2 NL NR F2 NL' 6 Rings (f,d)(l,b)(u,r) (34 m)
Last edited by glazik on Sat Mar 31, 2012 3:47 pm, edited 1 time in total.


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Waran

Post subject: Re: Patterns Posted: Sat Mar 31, 2012 11:23 am 

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

This solution isn't a breakthrough either, I just canceled out another move: 6 Rings (u,l) (r,b) (f,d)WF' WR' WF MF' MR MF MR' WR' VB2 NR2 MF2 VL2 NB2 NB D2 NF' NB' D2 NF WR NB D2 NF' NB' D2 NF WR2 MD L MD' WR MD L' MD' (34 btm or 33 btm actually)


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Waran

Post subject: Re: Patterns Posted: Wed Apr 11, 2012 3:18 pm 

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

Those images below inspired me to create PacMan Monsters on a 7x7x7: 4 PacMan Monsters with small eyes: TR2 S2F2 TL2 D TR2 S2F2 TL2 U R2 SF2 L2 ND R2 SF2 L2 NU T3R2 NF2 MF2 NB2 T3R2 D T3L2 NF2 MF2 NB2 T3L2 D' NF2 MR2 NF2 V3R2 VF2 M2U2 VF2 VR2 M2U2 N3F N3L N3B N3R MD N3R' N3B' N3L' N3F' MD' (47 btm) 4 PacMan Monsters with large eyes: TR2 S2F2 TL2 D TR2 S2F2 TL2 U R2 SF2 L2 ND R2 SF2 L2 NU T3R2 NF2 MF2 NB2 T3R2 D T3L2 NF2 MF2 NB2 T3L2 D' NF2 MR2 NF2 V3R2 VF2 M3D2 VF2 VR2 M3D2 N3F N3L N3B N3R MD N3R' N3B' N3L' N3F' MD' (47 btm)


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glazik

Post subject: Re: Patterns Posted: Sat Apr 14, 2012 7:19 am 

Joined: Wed Oct 12, 2011 12:54 pm

Here is a way of cancelling a few moves (still improvable): 1 Replace the first 16mover with this 14mover TU R2 SF2 L2 ND R2 SF2 NL2 S2F2 TR2 D TL2 S2F2 TR2 2 Insert (V3F2 VR2 M2U2 VR2 VF2 M2U2 NR2 MF2 NR2) at * TU * R2 SF2 L2 ND R2 SF2 NL2 S2F2 TR2 D TL2 S2F2 TR2 T3R2 NF2 MF2 NB2 T3R2 D T3L2 NF2 MF2 NB2 T3L2 D' N3F N3L N3B N3R MD N3R' N3B' N3L' N3F' MD' 4 PacMan Monsters with small eyes (43 m)The following (unoptimized) algorithms are new or have been slightly improved: 4x4x4 Waves (31 m)6 Rings (f,l)(r,d)(b,u) (31 m)4 Rings (f,r)(b,u) (30 m)4 Rings (u,d)(f,r) (22 m)4 Rings (f,l,b,r) (18 m)4 Rings (f,b,u,r) (25 m)5 Rings (u,d)(l,r,f) (22 m)5 Rings (u,f)(d,l,b) (24 m)5 Rings (u,d,r,l,f) (25 m)5 Rings (u,f,d,b,l) (22 m)6 Rings (u,d)(f,r,b,l) (19 m)6 Rings (u,d)(f,b,l,r) (25 m)6 Rings (d,f)(u,l,b,r) (27 m)6 Rings (d,f)(u,b,r,l) (23 m)6 Rings (b,f,l,d,r,u) (24 m)I guess there are still 8 ring algorithms to be found to complete the group of 33 permutations: (l, u, b, d) (b, d) (u, r, l) (u, r, b, l, d) (r, f, u) (b, l, d) (r, f, l) (d, u, b) (r, f, b, l, d, u) (r, f, b, d, u, l) (r, f, d, b, l, u)


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perfredlund

Post subject: Re: Patterns Posted: Mon Apr 16, 2012 6:36 am 

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

@ Glazik: Now i know how you spent your Easter vacation It's not all that interesting anymore, but we have to complete the 5x5x5 rings variations When I get the time ... 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: Sun Apr 22, 2012 7:44 am 

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

Let's make an overview of the already known Ring patterns and let's see what's missing. I am just posting the shortest algorithms and exclude invers versions: 2 Rings2 Rings (u,d)NR2 WF2 VR2 NF2 MR2 VB2 (6 btm) 2 Rings (r,f)MD' WR' D WR MD WR' D' WR ND' WR' D2 WR NU ND WR' D2 WR NU' (18 btm) 3 Rings3 Rings (u,r,f)WD2 MF U MF' WD MF U' MF' NL F2 NR' NL' F2 NR WD NL F2 NR' NL' F2 NR (21 btm) 3 Rings (r,f,l)NU2 L2 F2 NU SF2 ND' B2 L2 NU2 WF MR' F MR' WF2 MR F' MR WF (18 btm) I guess the groups of 2 and 3 Rings can be regarded as complete.


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glazik

Post subject: Re: Patterns Posted: Sun Apr 22, 2012 2:02 pm 

Joined: Wed Oct 12, 2011 12:54 pm

@ Walter and Per
Here is a compiled (yet unchecked) list of the 33 cycles for which algorithms are either already known or unknown:
(d, u)  (6 moves)
(d, l, b)  (21 moves) (l, u, d)  (18 moves)
(l, u) (b, d)  (30 moves) (l, r) (d, u)  (8 moves) (d, u) (b, l)  (22 moves) (u, r) (d, l)  (14 moves)
(l, u, b, d)  (UNKNOWN) (l, u, d, b)  (25 moves) (u, r, d, l)  (18 moves) (u, r, l, d)  (21 moves)
(u, r) (d, l, b)  (24 moves) (l, r) (d, u, b)  (22 moves) (b, d) (u, r, l)  (UNKNOWN)
(u, r, b, d, l)  (22 moves) (u, r, b, l, d)  (UNKNOWN) (u, r, l, b, d)  (25 moves)
(r, f) (l, u) (b, d)  (31 moves) (r, f) (d, u) (b, l)  (18 moves) (b, f) (l, r) (d, u)  (10 moves)
(r, f) (l, u, b, d)  (27 moves) (r, f) (l, u, d, b)  (23 moves) (d, u) (r, f, b, l)  (25 moves) (d, u) (r, f, l, b)  (19 moves)
(r, f, u) (d, l, b)  (8 moves) (r, f, u) (b, l, d)  (UNKNOWN) (r, f, l) (d, u, b)  (UNKNOWN)
(r, f, b, d, l, u)  (24 moves) (r, f, b, l, d, u)  (UNKNOWN) (r, f, b, d, u, l)  (UNKNOWN) (r, f, d, b, l, u)  (UNKNOWN) (r, f, d, l, b, u)  (13 moves)
It happens that (yet unknown) cycle (l, u, b, d) could be used to get a few other unknown cycles, simply by composing cycles.
As many patterns are built from doubleline subpatterns, I searched for a few new/shorter/alternate algorithms of doublelines and found these ones, that may possibly be useful:
(f, r) (10 moves) ND' WR' D2 WR NU ND WR' D2 WR NU' ND' WR' D2 WR VU VD WR' D2 WR NU' VD' WR' D2 WR NU ND WR' D2 WR VU' VD' WR' D2 WR VU VD WR' D2 WR VU'
(d, f, u, b) (8 moves) NR WU WF2 WU NR' WU' WF2 WU'
(d, u) (l, r) (b, f) (7 moves) VU2 WR2 NU2 WF WR2 MU2 WF' WU2 MR2 WF VR2 WU2 NR2 WF' VR2 WU2 NR2 WF MR2 WU2 WF' VL2 WF2 NR2 NU2 WR2 WF2 NU2
(b, d) (l, r) (u, f) (8 moves) NR WU2 NL' NR' NF2 WU2 NF2 NL
(b, f) (d, l, u, r) (10 moves) NR WU2 NL' NR' WU2 NR WU NL NR' WU'
(u, f, l, d, b, r) (8 moves) NL' NR' NF2 WU' NF2 NL NR WU


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perfredlund

Post subject: Re: Patterns Posted: Mon Apr 23, 2012 4:51 am 

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

@ Glazik: Let us not forget this simple (f,r)(b,l) stripes version. 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: Tue Apr 24, 2012 2:45 pm 

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

It seems that the group of 4 Rings has more then just 8 members: 4 Rings4 Rings (r,l) (f,b) > (l,r) (d,u) WD WR2 WD' WR2 MR2 MD MR2 MD' (8 btm) 4 Rings (r,b) (f,l) > (u,r) (d,l) ND' WR2 NU ND WR2 NU' MF WR MF' SR' MF WR' MF' SR (14 btm) 4 Rings (u,d) (r,f) > (d,u) (b,l) MD' WR' D WR MD WR' D' WR ND' WR' TD2 VL2 MD2 NR2 VD2 WR' VU VD WR' D2 WR NU' (22 btm) 4 Rings (u,r) (f,d) > (l,u) (b,d) WF' R' WF NF WD' F2 NB' L2 NB WD NF' NB' WD' NF L2 F2 NF' WD NB MR' WF' R WF WD' MR U MR' WD MR U' (30 btm) 4 Rings (u,f) (r,d) > new WR F WR' NR' WD R2 NL B2 NL' WD' NR NL WD NR' B2 R2 NR WD' NL' MF WR F' WR' WD MF' U' MF WD' MF' U (30 btm) 4 Rings (r,f,l,b) > (u,r,u,l) NR' MD2 NR MD' NR MD NR' WR2 ND2 WF2 ND' WR2 ND2 WF2 VD NR' MD NR (18 btm) 4 Rings (r,f,b,l) > (u,r,l,d) VL2 MD2 NR2 VU2 T4L2 F2 NU SF2 ND' B2 L2 NU2 WF MR' F MR' WF2 MR F' MR WF (21 btm) 4 Rings (u,r,f,d) > (l,u,d,b) NF2 VL2 MF2 NR2 VF2 MD' R' MD WR MD' R MD NB' D2 NF NB D2 NF' WR NB' D2 NF NB D2 NF' (25 btm) 4 Rings (u,f,r,d) > new NR2 VB2 MR2 NF2 VR2 MD F MD' WF' MD F' MD' NL D2 NR' NL' D2 NR WF' NL D2 NR' NL' D2 NR (25 btm) 4 Rings (u,r,d,f) > new NF' WD B2 WD' Â· NF NB Â· WD B2 WD' NB' WD B' WD' MF' WD B WD' MF NF R2 Â· NF' NB' Â· R2 NB WD NF R2 Â· NF' NB' Â· R2 NB MR' U' MR WD MR' U MR WD2 (39 btm) 4 Rings (u,f,d,r) > (l,u,b,d) NR WD' L2 WD Â· NR' NL' Â· WD' L2 WD NL WD' L WD MR WD' L' WD MR' NR' F2 Â· NR NL Â· F2 NL' WD' NR' F2 Â· NR NL Â· F2 NL' MF U MF' WD' MF U' MF' WD2 (39 btm)


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Waran

Post subject: Re: Patterns Posted: Tue Apr 24, 2012 4:19 pm 

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

Maybe the group of 5 Rings has more than 6 variations as well: 5 Rings5 Rings (u,r,b,l,f) > new WD WR WD' ND2 F2 L2 ND SR2 NU' R2 F2 ND2 WR' MD' MF MD L MF WR2 MF' L' MF' WR2 (23 btm) 5 Rings (u,r,f,l,b) > (u,r,b,d,l) NR2 U2 F2 NR SF2 NL' B2 U2 NR2 WF MD' F MD' WF2 MD F' WD MF MD NF NB' WD' (22 btm) 5 Ringe (u,r,l,f,b) > (u,r,l,b,d) MR2 WD' WR2 WD MD' MR2 R MD WR' MD' R' MD NB U2 NF' NB' U2 NF WR' NB U2 NF' NB' U2 NF (25 btm) 5 Rings (u,r,b,l,d)unknown 5 Rings (l,b) (u,r,f) > (u,r) (d,l,b) NL WD' R2 WD NR' NL' WD' R2 WD NR WD' R WD MR' WD' R' WD WR MF' MR WF' MF WR' WF (24 btm) 5 Rings (f,b) (u,r,l) > (l,r) (d,u,b) NF2 R2 U2 NF SD2 NB' D2 R2 NF2 WD' MR U MR NB2 VD2 MF2 NU2 VB2 MR' U' MR' WD' (22 btm) 5 Rings (u,b) (r,f,l) > (b,d) (u,r,l) NU2 L2 F2 NU SF2 ND' B2 L2 NU2 WF MR' F MR' WF2 MR F' MR WF MR' WF R WF' MR WF R' WF' NR' WF R2 WF' NL NR WF R2 WF' NL' (36 btm)
Last edited by Waran on Tue Apr 24, 2012 5:00 pm, edited 1 time in total.


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glazik

Post subject: Re: Patterns Posted: Tue Apr 24, 2012 4:53 pm 

Joined: Wed Oct 12, 2011 12:54 pm

There are 720 items in the group of permutations of face patterns, indexed by the 6 letters {f,r,u,l,d,b}, provided that face pattern twists are not taken into account, ie. are considered the same, which is the case for rings. From these 720 items, only 33 representatives should be considered, from which all remaining permutations can be computed by inversion and symmetry (48 cases). So, (u,r)(f,d) and (u,f)(r,d) are strictly equivalent, because (u,f)(r,d) can be obtained from (u,r)(f,d) by rotation CF2 CU plus Point Reflection, or equivalently by applying transformation: F > R' R > F' U > U' L > B' D > D' B > L' I think the challenge would be to find algorithms shorter than say 30 moves for the missing representatives.


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perfredlund

Post subject: Re: Patterns Posted: Wed Apr 25, 2012 6:04 am 

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

Hi! I have been working one of the missing 6 rings patterns for a few days now. It is the case 6 rings (f,r,l)(b,u.d)(34 m).My solution is just slightly shorter than the trivial 36 move solution (3 rings done twice). I have not found any way to cancel out turns by that trivial way. So instead i found a new way to do only the missing centers after doing 6 stripes. The sequence i found was: B SU MF L MF NR NL MU NR NL MU MF L MF SU B. Which is [NR NL,MU] conjugated with B SU MF L MF. I am sure further optimisations can be found Per
_________________ "Life is what happens to you while you are busy making other plans" John Lennon, Beautiful Boy


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perfredlund

Post subject: Re: Patterns Posted: Wed Apr 25, 2012 6:43 am 

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

Another missing ring variation. 6 Rings (u,f,r)(d,l,b) (24 m).Per (Edited because found shorter sequence ... )
_________________ "Life is what happens to you while you are busy making other plans" John Lennon, Beautiful Boy


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perfredlund

Post subject: Re: Patterns Posted: Thu Apr 26, 2012 1:03 pm 

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

And a minor improvement on an already found ring variation: 4 Rings (u,r)(f,d) (29m).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: Thu Apr 26, 2012 2:21 pm 

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

This list of 6 Ring patterns already contains Per's recent algorithms: 6 Rings6 Rings (u,d) (r,l) (f,b) > (b,f) (l,r) (d,u) WF WD2 WF' VL2 NU2 MF MR2 MF' VD2 NL2 (10 btm) 6 Rings (u,d) (r,b) (f,l) > (r,f) (d,u) (b,l) ND' VB2 NL2 MF2 VR2 NB2 NU ND WR2 NU' MF WR MF' SR' MF WR' MF' SR (18 btm) 6 Rings (u,b) (r,d) (f,l) > (r,f) (l,u) (b,d) WF' VL B2 NR' NL' B2 NL WD NR B2 NR' NL' B2 NL WD2 MF' U MF WD MF' U' WF MR MF MR' WR' VB2 NR2 MF2 VL2 NB2 (31 btm) 6 Rings (u,r,f) (d,l,b) > (r, f, u) (d, l, b) WR WF' WR' NF NB' MR MF MR' (8 btm) 6 Rings (u,r,f) (d,b,l) > (r,f,u) (b,l,d) NF' U2 NF2 R2 NF' WD WF WD' VB R2 NF2 U2 NF MD' MR' MD MR2 U MR' WD' MR U' MR' WD (24 btm) 6 Rings (u,b,d) (r,f,l) > (r,f,l) (d,u,b) B SD' MF' L MF MD' NR' NL MD NR NL' MF' L' MF SD B' NU2 L2 F2 NU SF2 ND' B2 L2 NU2 NR2 D2 B2 NR SF2 NL' F2 D2 NR2 (34 btm) 6 Rings (u,d) (r,f,l,b) > (d,u) (r,f,l,b) NU' WR2 NU ND WR2 ND' MF WR' MF' SR MF WR' MR2 WF' WR2 WF MF' MR2 SR' (19 btm) 6 Rings (u,d) (f,b,l,r) > (d,u) (r,f,b,l) VL2 MD2 NR2 VU2 T4L2 F2 NU SF2 ND' B2 L2 NU2 WF MR' F MR' NU2 VF2 MD2 NB2 VU2 MR F' MR WF (25 btm) 6 Rings (l,b) (u,r,d,f) > (r,f) (l,u,b,d) WF2 WD WR WD' MD MR' MD' WR' F MR WF' MR' F' MR NU L2 NU' ND' L2 ND WF' NU L2 NU' ND' L2 ND (27 btm) 6 Rings (l,b) (u,d,r,f) > (r,f) (l,u,d,b) NR2 D2 B2 NR SF2 NL' F2 D2 NR2 WF' MD B MD WF2 MD' B' MD2 WD MF' MD NB NF' WD' (23 btm) 6 Rings (u,b,r,d,f,l) > (r,f,d,l,b,u) WF' WR' WF MF' MR MF MR' WR' VB2 NR2 MF2 VL2 NB2 (13 btm) 6 Rings (u,r,l,b,d,f) > (r,f,b,d,l,u) WF WD WF' MF MD' MF' WD' WF' D WF MD WF' D' WF ND' WF' D2 WF NU ND WF' D2 WF NU' (24 btm) 6 Rings (r,f,b,l,d,u)unknown 6 Rings (r,f,b,d,u,l)unknown 6 Rings (r,f,d,b,l,u)unknown


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Waran

Post subject: Re: Patterns Posted: Thu Apr 26, 2012 2:29 pm 

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

A minor improvement can be done on this 4 Ring pattern: 4 Rings (u,f,d,r)NR WD' L2 WD NR' NL' WD' L2 WD NL WD' L WD MR WD' L' WD VR' F2 NR NL F2 NL' WD' NR' F2 NR NL F2 NL' MF U MF' WD' MF U' MF' WD2 (38 btm)


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glazik

Post subject: Re: Patterns Posted: Fri Apr 27, 2012 4:04 am 

Joined: Wed Oct 12, 2011 12:54 pm

Here are additional new/improved/alternate algorithms of rings: 6 Rings (l,r,f) (d,u,b)(l,r,f) (d,u,b)  Double Lines (18 m) NU2 L2 F2 NU SF2 ND' B2 L2 NU2 NR2 D2 B2 NR SB2 NL' F2 D2 NR2 (l,r,f) (d,u,b)  MidgeCenters (15 m) WF' MU' B MU' MR' B MR' WF2 MR B' MR MU B' MU WF' 6 Rings (l,r,f) (d,u,b) (33 m)6 Rings (f,b,d,u,l,r)(f,b)(d,u)(l,r) WF' NR2 VU2 MF MR2 MF' ND2 VR2 WF WU2 (l,f,d) WU2 MF D MF' WU MF D' MF' NR F2 NL' NR' F2 NL WU NR F2 NL' NR' F2 NL (f,b,d,u,l,r) = (f,b)(f,d,u,l,r) = (f,b)(d,u,l,r,f) = (f,b)(d,u)(d,l,r,f) = (f,b)(d,u)(l,r,f,d) = (f,b)(d,u)(l,r)(l,f,d) 6 Rings (f,b,d,u,l,r) (29 m)4 Rings (u,r)(f,d)  Alternate solution to Per's algorithm[WU' WR2, NF R2 NF' NB' R2 NB] MR MF' ND NU' MF2 U MF ND' NU MF' U' MF' MR' 4 Rings (u,r)(f,d) (29 m)4 Rings (u,f,d,r)(u,f) MR' WU' R WU MR WU' R' WU NR' WU' R2 WU NL NR WU' R2 WU NL' (u,d,r) WR' MU' R' MU' WR2 MU R MU WR' NF2 U2 R2 NF' SR2 NB L2 U2 NF2 (u,f,d,r) = (u,f)(u,d,r) 4 Rings (u,f,d,r) (35 m)4 Rings (b,d)(u,r,l)  Alternate solution to Walter's algorithm(b,d) MR' WU R WU' MR WU R' WU' NR' WU R2 WU' NL NR WU R2 WU' NL' (u,r,l) WU MR U MR WU2 MR' U' MR' WU NF2 R2 U2 NF SU2 NB' D2 R2 NF2 (b,d)(u,r,l) MR' WU R WU' MR WU R' WU' WU MR U MR WU2 MR' U' MR' WU NR' WU R2 WU' NL NR WU R2 WU' NL' NF2 R2 U2 NF SU2 NB' D2 R2 NF2 4 Rings (b,d)(u,r,l) (34 m)Shorter solutions should certainly be found, because these are based on composition of already existing algorithms. Anyway, this gives at least an upper bound.


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glazik

Post subject: Re: Patterns Posted: Fri Apr 27, 2012 3:44 pm 

Joined: Wed Oct 12, 2011 12:54 pm

By adding the following algorithms, I think all 33 representatives are now done... These could of course be further optimized if algorithms of length lower than 30 moves is what would be searched for. 4 Rings (u,f,d,r)(d,u) NF2 MR2 VB2 NR2 WF2 VR2 (d,f)(u,r) WD WR2 NB' R2 NF NB R2 NF' WR2 WD' NB' R2 NF NB R2 TF' MD' MR' L WD' MR SD' MR' WD MR SD L' MD F (u,f,d,r) = (u,f,d)(u,r) = (d,u,f)(u,r) = (d,u)(d,f)(u,r) NF2 MR2 VB2 NR2 WF2 VR2 WU' WR2 NB' R2 NF NB R2 NF' WR2 WU NB' R2 NF NB R2 TF' MU MR' L WU MR SD' MR' WU' MR SD L' MU' F 4 Rings (u,f,d,r) (33 m)5 Rings (r,b,l,d,u)(r,b,l) ND2 L2 B2 ND SB2 NU' F2 L2 ND2 WF' MR' B MR' WF2 MR B' MR WF' (r,d,u) NF2 D2 R2 NF SR2 NB' L2 D2 NF2 WR MU' R MU' WR2 MU R' MU WR (r,b,l,d,u) = (r,b,l)(r,d,u) ND2 L2 B2 ND SB2 NU' F2 L2 ND2 WF' MR' B MR' WF2 MR B' MR WF' NF2 D2 R2 NF SR2 NB' L2 D2 NF2 WR MU' R MU' WR2 MU R' MU WR 5 Rings (r,b,l,d,u) (36 m)6 Rings (u,r,f,d,b,l)(u,r,f)(d,b,l) MU MR' MU' MR2 U MR' WU MR U' MR' WU' NF' U2 NF2 R2 NF' WU' WF WU VB R2 NF2 U2 NF (d,u) NF2 MR2 VB2 NR2 WF2 VR2 (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) MU MR' MU' MR2 U MR' WU MR U' MR' WU' NF' U2 NF2 R2 NF' WU' WF WU VB R2 NF2 U2 NF NF2 MR2 VB2 NR2 WF2 VR2 6 Rings (u,r,f,d,b,l) (29 m)6 Rings (f,b,l,d,u,r)(f,b)(r,l)(d,u) WF WD2 WF' VL2 NU2 MF MR2 MF' VD2 NL2 (d,r)(l,f) WR' WD2 NB' D2 NF NB D2 NF' WD2 WR NB' D2 NF NB D2 TF' MR MD' U WR MD SL' MD' WR' MD SL U' MR' F (f,b,l,d,u,r) = (f,b)(r,l)(d,u)(d,r)(l,f) WF WD2 WF' VL2 NU2 MF MR2 MF' VD2 NL2 WR' WD2 NB' D2 NF NB D2 NF' WD2 WR NB' D2 NF NB D2 TF' MR MD' U WR MD SL' MD' WR' MD SL U' MR' F 6 Rings (f,b,l,d,u,r) (39 m)


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perfredlund

Post subject: Re: Patterns Posted: Sat Apr 28, 2012 7:32 am 

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

Hi! I managed to improve a previous contribution. I base it on a 4 Rings sequence : (u,r)(f,d). I do another 4 Rings : (f,b)(r,l) inserted in two parts. The result is: 6 Rings (f,b,d)(r,l,u) (31 m).Per
_________________ "Life is what happens to you while you are busy making other plans" John Lennon, Beautiful Boy


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