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perfredlund

Post subject: Re: Patterns Posted: Fri Jun 06, 2014 5:16 am 

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

This simple variety is also quite nice: 6X: 4 Long Slashes (v3) (Order 4) (27 btm).Alternative name would be 6X: ZigZag (Order 4) with surplus 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: Mon Jun 09, 2014 12:10 pm 

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


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perfredlund

Post subject: Re: Patterns Posted: Wed Jun 11, 2014 5:23 am 

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

I could not improve any of Walter's recent diagonal patterns, so I made up a new one instead 6X: 3 Cutout and Shifted Rings with Dots (32 btm).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: Thu Jun 12, 2014 5:39 am 

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


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Waran

Post subject: Re: Patterns Posted: Sun Jun 15, 2014 6:53 am 

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

For all who are interested to know how algorithms can be improved, here is a simple example: By analyzing Per's latest 'Impossible Huge Cube in a Cube' pattern you may discover that 3 algorithms have been used to construct it: R' (TU F2 TU' F' TL F2 TL' F) RR' (MD' F2 MD F' MR' F2 MR F) RR' (F' U T3B2 U' F U T3B2 U') R (30 btm) â€¦ Per then optimized it by canceling out 6 moves: 4x: 'Impossible' Huge Cube in a CubeR' (TU F2 TU' F' TL F2 TL' F) (MD' F2 MD F' MR' F2 MR U T3B2 U' F U T3B2 U') R (24 btm) For my solution I just arranged the 3 parts in a different order. And I also thought it looks nicer to write F2 D' F D F2 instead of T3B2 U' F U T3B2 in part 2: Step 1R' (MD' F2 MD F' MR' F2 MR F) RR' (F' U F2 D' F D F2 U') RR' (TU F2 TU' F' TL F2 TL' F) R (30 btm) Since all segments use the same set up moves, it can also be written like this: Step 2R' (MD' F2 MD F' MR' F2 MR F) ( F' U F2 D' F D F2 U') ( TU F2 TU' F' TL F2 TL' F) R (26 btm) â€¦ and it is even possible to cancel out 3 more moves: Final solutionR' MD' F2 MD F' MR' F2 MR U F2 D' F D F2 MU F2 TU' F' TL F2 TL' F R (23 btm)  1 move As you can see, optimizing algorithms can be very easy.


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Waran

Post subject: Re: Patterns Posted: Sun Jun 15, 2014 8:08 am 

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


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amarok

Post subject: Re: Patterns Posted: Sun Jun 15, 2014 8:41 am 

Joined: Mon Jun 09, 2014 10:02 am

I'd like to present several patterns of Bauhinia Dodecahedron which I recently made. All of them are fully simmetrical and base on swapping the pieces between opposite faces. Pattern 001  inverted centers: Attachment:
001.JPG [ 211.58 KiB  Viewed 881 times ]
Pattern 010  inverted triangles: Attachment:
010.JPG [ 213.38 KiB  Viewed 881 times ]
Pattern 011  inverted triangles and centers: Attachment:
011.JPG [ 209.31 KiB  Viewed 881 times ]
Pattern 100  inverted petals: Attachment:
100.JPG [ 207.97 KiB  Viewed 881 times ]
Pattern 101  inverted petals and centers: Attachment:
101.JPG [ 211.68 KiB  Viewed 881 times ]
Pattern 110  inverted petals and triangles: Attachment:
110.JPG [ 202.53 KiB  Viewed 881 times ]
Pattern 111  inverted petals, triangles and centers: Attachment:
111.JPG [ 207.38 KiB  Viewed 881 times ]


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Waran

Post subject: Re: Patterns Posted: Sun Jun 15, 2014 1:42 pm 

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

@ amarok The patterns look beautiful! Is there a similarity in the algorithms or did you need a different approach for each version?


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perfredlund

Post subject: Re: Patterns Posted: Mon Jun 16, 2014 4:28 am 

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


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amarok

Post subject: Re: Patterns Posted: Mon Jun 16, 2014 1:47 pm 

Joined: Mon Jun 09, 2014 10:02 am

Waran wrote: @ amarok The patterns look beautiful! Is there a similarity in the algorithms or did you need a different approach for each version? I didn't used any special algorithm for making the patterns. I started with the solved puzzle and used algorithm for swapping 3 centers to setup the pattern 001. Each time when centers are swapped also triangles move to different faces. It is good to correct their positions immediately otherwise triangles start to migrate without the control and finally are completely scrambled. For this I used algorithm for swapping 3 triangles. After pattern 001 I made patterns 010 and 011 using the same routine. During making 100 I used algorithm for swapping 3 petals and in this time centers and triangles also were disturbed so I had to fix them as soon as possible. Creation of patterns 101, 110 and 111 from pattern 100 doesn't differ from making 001, 010 and 011 from solved puzzle. I know that this is not the most optimal way but for me was very enjoyable one.


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Waran

Post subject: Re: Patterns Posted: Sun Jun 22, 2014 7:28 am 

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

@ Per Excellent optimization work!!! Here is new and quite psychedelic looking pattern: 7x: 2 Outlined Crosses, 4 Twirled StripesSF' SD B' L2 U' D' L F2 SD R2 F' R' L' NU TR' TL' TF TU2 S2L TF2 TD' TF' TB' TU2 TL' S2U S2R TD2 S3B S3D T3B' T3L2 T3U' T3D' T3L T3F2 S3D T3R2 T3F' T3R' T3L' S2U2 NU' N3D D (45 btm) These are the shortest sequences I know to achieve these classic patterns: 4x: 2 RingsB' U' B L2 F' D MR2 MB2 TR2 MB2 R2 F' MB2 D' F2 ML2 TF2 TD' TF' TD TF' TL2 TF TD' TF' (25 btm) 5x: 2 RingsNR' F' NR NB2 NR' F NR NB2 L B' L NF' L' SF' L NF' L' F L NF2 NL2 (ND TF2)2 TL2 ND TL2 NU' TF2 NU TF2 ND2 TL2 (34 btm)


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perfredlund

Post subject: Re: Patterns Posted: Wed Jun 25, 2014 4:11 am 

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

Here is a slightly improved version of the 5X rings: 5X: 2 Rings (1) (33 btm).Done by postponing the U/D spots until the end 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: Wed Jun 25, 2014 2:03 pm 

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

I moved the U/D spots in the middle and gained another move: 5x: 2 RingsL B' L NF' L' SF' L NF' L' F L NF2 NL2 (ND TF2)2 L2 D' NR2 D NL2 D' NR2 TD TL2 NU' TF2 NU TF2 ND2 TL2 (32 btm) 1 move


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perfredlund

Post subject: Re: Patterns Posted: Wed Jun 25, 2014 5:29 pm 

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

Waran wrote: I moved the U/D spots in the middle and gained another move: 5x: 2 RingsL B' L NF' L' SF' L NF' L' F L NF2 NL2 (ND TF2)2 L2 D' NR2 D NL2 D' NR2 TD TL2 NU' TF2 NU TF2 ND2 TL2 (32 btm) 1 move I think I found the best insertion for the spots: 5X: 2 Rings (1) (31 btm).And now I believe this pattern algorithm is already optimal 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 Jun 26, 2014 3:46 pm 

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

@ Per Yep, it looks quite compact now! I didn't found a way to further improve it, but I was lucky on a very similar patterns: Waran wrote: 5x: 2 Rings (4x4x4)F2 R2 U' F' U R' U2 R U' NF TU TR' TU2 TR TU' TF TU TR2 TF2 NB' U' NR' MU NR U NR' MU' NR NB D2 NL2 D B' R B D' NL2 D B' R' B D (42 btm) 3 moves 5x: 2 Rings (4x4x4)F2 R2 U' F' U R' U2 R U' NF TU TR' TU2 TR TU' TF TU TR2 TF2 D2 NL2 D TB' U' NR' MD' NR U NR' MD NR NB R B D' NL2 D B' R' B D (41 btm) 1 move perfredlund wrote: Same pattern on V6 cube: 6X: 2 Rings (5x5x5) (32 btm).Much easier to obtain Per 6x: 2 Rings (5x5x5)F2 R2 U' F' U R' U2 R U' F' VR2 VF2 T3R2 VF2 NR2 MF2 T3R2 MF2 MR2 NF2 TF TU TR' TU2 TR TU' TF TU TR2 TF2 (30 btm) 2 moves


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perfredlund

Post subject: Re: Patterns Posted: Fri Jun 27, 2014 6:44 am 

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

Or even better: 6X: 2 Rings (5x5x5) (2) (28 btm).The middle corrective step improved to VR2 NF2 T3R2 VF2 NR2 N3F2 TR2 NF2 Per
_________________ "Life is what happens to you while you are busy making other plans" John Lennon, Beautiful Boy
Last edited by perfredlund on Sun Jun 29, 2014 3:42 pm, edited 1 time in total.


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perfredlund

Post subject: Re: Patterns Posted: Fri Jun 27, 2014 6:58 am 

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

And the 5X version could also be easily improved: 5X: 2 Rings (4x4x4) (9) (32 btm).Walter, you can easily work out how I did it Per
_________________ "Life is what happens to you while you are busy making other plans" John Lennon, Beautiful Boy


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robertpauljr

Post subject: Re: Patterns Posted: Fri Jun 27, 2014 9:10 am 

Joined: Sun Aug 12, 2007 8:28 pm Location: Northern Central California

The other day I put a 3x3x3 checkerboard pattern on a 6x6x6 cube, then left it where others in the family could see it and perhaps do something with it. Someone did. When I saw the pattern I was amazed. I tried to undo it, but couldn't figure it out, and ended up solving the cube with commutators. Can anyone explain how to make this pattern? Attachment:
SAM_0374.jpg [ 354.61 KiB  Viewed 628 times ]
Attachment:
SAM_0375.jpg [ 266.05 KiB  Viewed 628 times ]
The top checkerboard pattern in each picture is the same side of the cube.
_________________ Personal Blogâ€”Puzzles plus other interests Crazy 2face Planet Progress Log


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Waran

Post subject: Re: Patterns Posted: Fri Jun 27, 2014 2:17 pm 

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

@ robertpauljr Here is a solution how you can create checkerboard patterns on 4 faces: 6x: 4 CheckerboardsU2 MU2 ND2 R2 MR2 NL2 F2 MF2 NB2 R2 MR2 NL2 (12 btm) I guess you also tried to achieve a checkerboard pattern on ALL 6 faces. Unfortunately this isn't possible on cubes with an even amount of layers. â€¦ but at least this algorithm here comes pretty close: 6x: (almost) 6 CheckerboardsNU2 MD2 D2 R2 NF2 MB2 B2 R2 VL2 T3D2 VR2 T3U2 M2R2 MF MB SD' F2 SD VF' VB' SD' F2 SD NF NB (25 btm) @ Per I also had a short solution for the 5x Rings pattern, but wasn't able to post it earlier. However, your solution is much better anyway! Excellent work, Per! As you can see my approach goes in a similar direction: 5x: 2 Rings (4x4x4)F2 R2 U' F' U R' U2 R U' F' NF2 R2 NF2 TR2 NF2 NR2 TF TU TR' TU2 TR TU' TF TU TR2 TF2 NR' NL' MD2 NR NL U NR NL MD2 NR' NL' U' (38 btm)


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perfredlund

Post subject: Re: Patterns Posted: Fri Jun 27, 2014 3:02 pm 

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

@ Walter: You could have easily saved 5 turns with a more efficient finish! 5X: 2 Rings(4x4x4) (33 btm).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 Jun 27, 2014 3:31 pm 

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

And here is the 4X version: 4X: 2 Rings (3x3x3) (25 btm).Per
_________________ "Life is what happens to you while you are busy making other plans" John Lennon, Beautiful Boy


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robertpauljr

Post subject: Re: Patterns Posted: Sat Jun 28, 2014 1:51 am 

Joined: Sun Aug 12, 2007 8:28 pm Location: Northern Central California

Waran wrote: @ robertpauljr Here is a solution how you can create checkerboard patterns on 4 faces: 6x: 4 CheckerboardsU2 MU2 ND2 R2 MR2 NL2 F2 MF2 NB2 R2 MR2 NL2 (12 btm) Thanks Waran. I am on a borrowed computer that is not set up to view the link you sent. Another thing: I know what U, D, R, and L are in your algorithm above (if they mean the same thing they do with a 3x3 cube, but what are M and N on a 6x6 cube? Waran wrote: I guess you also tried to achieve a checkerboard pattern on ALL 6 faces. Unfortunately this isn't possible on cubes with an even amount of layers. â€¦ but at least this algorithm here comes pretty close: I already knew from experience with a 4x4 cube that even numbered cubes can not be checker boarded on all 6 sides at once. That is why I put a 3x3 cube checkerboard pattern on it. In other words I checker boarded it two layers at a time so that it was checker boarded on all 6 sides but looked like a 3x3 cube. Waran wrote: (almost) 6 Checkerboards NU2 MD2 D2 R2 NF2 MB2 B2 R2 VL2 T3D2 VR2 T3U2 M2R2 MF MB SD' F2 SD VF' VB' SD' F2 SD NF NB (25 btm) Once I find out what exactly all of this means, I'll try it. But in the meantime, perhaps you, or Per, or someone, could take a look at the pics I posted above and see if you can duplicate it. You see, the blue and green sides are solid. The white and yellow sides are checkerboards. But the red and orange sides are the ones that baffle me. They are half checkerboard and half stripes. How does that work? After I put the 3x3 checkerboard pattern on it, my daughterinlaw picked it up after I had left the room and fiddled with it some. Then she put it down. She is not an avid cuber. Later I came back in and saw it as it is pictured above. What? How'd you do that? She couldn't tell me. So I posted the pictures on the Puzzle Photography page on Facebook. Several people responded, but no one could explain the redorange sides. Then I remembered the Patterns thread on the twistypuzzles forum. I thought someone would say, oh that is easyâ€”just do... I guess my job today will be to play with the 6x6 cube, seeing what i can learn about patterns.
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robertpauljr

Post subject: Re: Patterns Posted: Sat Jun 28, 2014 4:29 am 

Joined: Sun Aug 12, 2007 8:28 pm Location: Northern Central California

Referring to my post above: I got close to my pictured pattern, but by the time I got there I had no idea exactly how I did it. So after trying other ideas and just getting further away from the goal, I solved the cube and tried U2 MU2 ND2 R2 MR2 NL2 F2 MF2 NB2 R2 MR2 NL2. I guessed that M was the layer in from L and N was the next layer in. But when I got to R2 MR2 I realized I was not interpreting it correctly, since R2 MR2 would just equal M. So now I wonder if MR2 = (MR)2. Tried it. R2 MR2 still makes no sense, since M and R are parallel.
_________________ Personal Blogâ€”Puzzles plus other interests Crazy 2face Planet Progress Log


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Waran

Post subject: Re: Patterns Posted: Sat Jun 28, 2014 4:42 am 

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


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robertpauljr

Post subject: Re: Patterns Posted: Sat Jun 28, 2014 8:12 am 

Joined: Sun Aug 12, 2007 8:28 pm Location: Northern Central California


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perfredlund

Post subject: Re: Patterns Posted: Sat Jun 28, 2014 3:41 pm 

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


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Waran

Post subject: Re: Patterns Posted: Sun Jun 29, 2014 9:10 am 

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

@ robertpauljr Anytime, if you have another mystery or nice pattern to solve. By slightly modifying Per's algorithm it is even possible to show the half checkerboard half stripe pattern on all 4 faces: 6x: 4 CheckerboardStripesNU2 MD2 D2 T3R2 B2 MB2 T3R2 T3F2 NR2 T3F2 (10 btm)


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Waran

Post subject: Re: Patterns Posted: Sun Jun 29, 2014 9:22 am 

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

Any good ideas to do this pattern more efficiently? In this solution part 1 does the edges and all the rest is used for the centers. 5x: Double PythonU2 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 NF NB D' MR' ND' MR2 ND MR' D NB' NF' NR NL U MF NU' MF2 NU MF U' NL' NR' (54 btm)


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Pithecanthropus

Post subject: Re: Patterns Posted: Tue Jul 01, 2014 6:03 pm 

Joined: Sun Feb 09, 2014 5:24 am

Here's a pattern I did on Eitan's Star. Attachment:
pattern3.jpg [ 176.86 KiB  Viewed 436 times ]
Attachment:
pattern4.jpg [ 191.24 KiB  Viewed 436 times ]
Attachment:
pattern6.jpg [ 162.22 KiB  Viewed 436 times ]
_________________ I've never wished I played the flute so I wouldn't take that bet if I were you.


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perfredlund

Post subject: Re: Patterns Posted: Wed Jul 02, 2014 3:53 am 

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

The threfold mezon on the mosaic cube looks cool It is also possible to have the mezons all rotate "the same way". Or only on 3 of the 6 faces ... 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 Jul 02, 2014 5:55 am 

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

@ Walter: Here is my 6X version of Double Python: 6X: Double Python (46 btm).Step1: CR2DL2FWUFWUWR2WUFWUFR2U ("edges" with dots) (3x3x3=141) Step2: VUR2VU2F2VU(VLWU2VLVRWU2VRN3RM2U2N3RN3LM2U2N3L)VUF2VU2R2VU (4 4x4 sized rings) Step3: TUTR2TFM2UTFM2UM2R2M2UTFM2UTFTL2 DCR2 (inverse of step 1 but with 222 layering) This was cool to do, same approach for odd sized cubes will not work because there is no easy equivalent to VUR2VU2F2VU ("block center swap") 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: Wed Jul 02, 2014 5:07 pm 

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

@ Per Wow, that's a very clever solution! I very much like Step 2 where you found an incredibly efficient algorithm to build 4 Rings! Here is a slightly optimized approach: 6x: Double PythonVU' R2 VU2 F2 VD' WF WD WF' VU F2 VU2 R2 T3U L2 B' WD B SR2 F' WD' F R2 NU TR2 TF' M2D TF S2R2 TB' M2D' TB TL2 T3U' TR2 MU2 TF2 MU' M2F M2D' M2F' MD TF2 MU2 TR2 MU (45 btm) 1 move


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Waran

Post subject: Re: Patterns Posted: Thu Jul 03, 2014 2:59 pm 

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

For this 5x5x5 version I used the same approach as above. The algorithm for the 6 Rings (part 1, 2 and 3) can certainly be done much more efficiently. 5x: Double PythonWF2 WD NL' B2 Â· NR NL Â· B2 NR' WF2 WD' NL' B2 Â· NR NL Â· B2 TR' MD' Â· F MF Â· WD' MF' SD' MF WD MF' SD Â· F' MF2 Â· MD MF2 R U L2 B' WD B SR2 F' WD' F R2 NU TR2 TF' MD TF S2R2 TB' MD' TB TL2 TU' (52 btm) 2 moves


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perfredlund

Post subject: Re: Patterns Posted: Fri Jul 04, 2014 2:35 pm 

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

Here is my best effort so far: 5X: Double Python (2) (50 btm).I achieved this using insertion 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 Jul 21, 2014 3:27 pm 

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

These are two new contributions â€¦ I am pretty sure they can be further improved: 7x: 2 Stripe CubesD' F2 U L2 U' R2 U SR B' R' SF' L2 F2 U R2 F2 D WR N3F' N3B WR' N3F N3B' D' R B' U R' N3F2 N3B2 R U' B R' U N3F2 N3B2 B2 U' N3F N3B' U B U' N3F' N3B U B F2 D N3F N3B' D' F' D N3F' N3B D' F' (59 btm) The second one is a rather unusual snake pattern. On its way around the cube it comes along each face twice. Almost like a Boa constrictor that tightly wraps around a cube: 7x: Boa constrictorCF' CD' WR V3F (N3D NB' ND N3B' VD') (VF' N3U' NF NU' N3F VU) (MD N3F' N3B MD' N3F N3B') (M3U' MF' M3U MF) WF' WR' T3L T3R2 T3U' T3F2 T3R T3U MR' MF T3D' T3F' T3R2 T3D T3F2 T3B' (39 btm)


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