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 Post subject: Re: Patterns
PostPosted: Tue Jul 16, 2013 8:35 pm 
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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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 Post subject: Re: Patterns
PostPosted: Tue Jul 16, 2013 8:53 pm 
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Well. That pretty much seals it. The Curvy Copter Skewb will be my next Shapeways purchase. So beautiful.

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 Post subject: Re: Patterns
PostPosted: Sat Jul 20, 2013 3:06 am 
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After many days of effort......

Image

Image

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 Post subject: Re: Patterns
PostPosted: Sat Jul 20, 2013 10:42 am 
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Wow! Very well done. Did you document the sequence?

-d


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 Post subject: Re: Patterns
PostPosted: Sat Jul 20, 2013 10:52 am 
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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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 Post subject: Re: Patterns
PostPosted: Fri Sep 13, 2013 10:12 am 
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Snakes with Traiphum's 5x5x5

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 Post subject: Re: Patterns
PostPosted: Fri Sep 13, 2013 12:07 pm 
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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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 Post subject: Re: Patterns
PostPosted: Mon Sep 16, 2013 12:51 pm 
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1) Snake on a mirror cube:

Image

2) Snake on a void cube:

Image

The return alternation of colours of the snake is possible only due to void parity!!!


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 Post subject: Re: Patterns
PostPosted: Wed Oct 02, 2013 3:12 pm 
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@ Andrea and pytlivyj_1
Your snakes on the Traiphum' 5x5x5, Mirror Cube and Void Cube are awesome! 8-)

So, let's do another, exotic one with lots of colors:

5x: Triple Python
NU' 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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 Post subject: Patterns
PostPosted: Thu Oct 03, 2013 8:52 am 
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"12 axs" on CHIMERA 2x2+6x6 in comparison with "12 strips" on a cube 2Ń…2Ń…2:

Image

"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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 Post subject: Patterns
PostPosted: Thu Oct 03, 2013 9:01 am 
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"Snake" on CHIMERA 2x2+6x6:

Image

This snake has return alternation of colours too!


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 Post subject: Re: Patterns
PostPosted: Thu Oct 03, 2013 3:15 pm 
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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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 Post subject: Re: Patterns
PostPosted: Thu Oct 03, 2013 4:55 pm 
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Made with a dino dodecahedron!


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 Post subject: Re: Patterns
PostPosted: Sat Oct 05, 2013 11:49 am 
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Hi Walter,

A few patterns have been improved and I guess shorter solutions could still be found from better partitioning :wink:

5x: Triple Python
U2 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 Python
TB2 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: Python
TB2 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: :D

4x: Winding Hexagon
Edges:
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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 Post subject: Re: Patterns
PostPosted: Mon Oct 07, 2013 5:51 pm 
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There is my first hexaminx pattern! Fun to do and nice to watch ;)

Image

Image

Image


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 Post subject: Re: Patterns
PostPosted: Mon Oct 07, 2013 5:57 pm 
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That hexaminx pattern looks awesome.

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

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 Post subject: Re: Patterns
PostPosted: Mon Oct 07, 2013 6:23 pm 
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Thanks Andychilly! I'm quite proud of it 8-)

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 :P


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 Post subject: Re: Patterns
PostPosted: Thu Oct 10, 2013 6:17 am 
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Wow, that pattern is so cool, I love it! :)

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 Post subject: Re: Patterns
PostPosted: Mon Oct 14, 2013 2:57 pm 
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@ glazik
Fantastic optimization work! 8-)

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. :wink:

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 Anacondas
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 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 Anacondas
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 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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 Post subject: Re: Patterns
PostPosted: Tue Oct 15, 2013 3:02 am 
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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?

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 Post subject: Patterns
PostPosted: Tue Oct 15, 2013 1:46 pm 
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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. :D


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 Post subject: Re: Patterns
PostPosted: Fri Oct 18, 2013 3:13 am 
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@ 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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 Post subject: Re: Patterns
PostPosted: Fri Oct 18, 2013 7:56 am 
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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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 Post subject: Re: Patterns
PostPosted: Fri Oct 18, 2013 8:10 am 
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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.

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 Post subject: Re: Patterns
PostPosted: Fri Oct 18, 2013 9:50 am 
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The order 4 4U's on a 3x3 is an old pattern and I am not attempting to improve on http://www.randelshofer.ch/rubik/patterns/A410.03.html. But I found very simple sequences for the same pattern (only upside down because I like it more like that).

http://www.randelshofer.ch/cube/rubik/?(%5BR,U%5DCU)7

which can be marginally simplified to

http://www.randelshofer.ch/cube/rubik/?(RUR'TD')7

I like this because it is very simple to remember and it is a very rare case of algorithm that consists of a sevenfold repetition of a sequence. Also I am not claiming this sequence is original, but I haven't seen it before.

Roberto

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 Post subject: Re: Patterns
PostPosted: Sun Oct 20, 2013 2:15 pm 
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First is my HOT cube ;)

Secondly is my Orthogonal H's

Apologies for the discolored plastic

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 Post subject: Re: Patterns
PostPosted: Tue Oct 22, 2013 6:14 pm 
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@ mocenigo
Nice algorithm! Algorithms with a sevenfold repetition can't be found often indeed!


@ glazik
Great algorithms! 8-)

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 Rings
F2 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 Anaconda
L2 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 Triangles
MR' 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 Diagonals
TR
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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 Post subject: Re: Patterns
PostPosted: Wed Oct 23, 2013 8:52 am 
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A few sequences, not far from the lower bound, have again been slightly improved :wink:

WU2 L2 F2 D2 MF2 MR2 TF2 D2 ML2 F2 MR2 D2 L2
L' MF' D2 MF D' ML' D2 ML D L
TL' MD' TB TD2 TF' MD TF TD2 TB' TL
4x: Double Anaconda (31 btm)

4x: 4 Peaks, 6 Diagonals (34 btm)

4x: Winding Anaconda (28 btm)

CU' CR2 U2 R2 WF2 L B' L2 U2 B U2 F L WU2 F' WU F' L2 U2
U2 L2 B' F' (ML MD' ML' MD) F B L2 U2
4x: 2 Corner Triangles 6 Triangles (21 btm)


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 Post subject: Re: Patterns
PostPosted: Fri Oct 25, 2013 3:28 am 
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Hi leRAFs,

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


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 Post subject: Re: Patterns
PostPosted: Fri Nov 01, 2013 3:36 pm 
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Here are a couple of more improved 4x4 patterns.
A total of 23 moves have been gained:

4x: 2 Triangles
SF' 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 Peak
TR' (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 Cube
R' 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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 Post subject: Re: Patterns
PostPosted: Sat Nov 02, 2013 12:00 pm 
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This colorful pattern reminds a little bit on Oskar van Deventer's Gear Cubes: :wink:

5x: Gear Cube
D 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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 Post subject: Re: Patterns
PostPosted: Sat Nov 02, 2013 3:45 pm 
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@ Walter,

A few sequences have been improved...again :wink:

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 move

Edges (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 moves

Edges
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 moves

All present 4x sequences should now be below the published 57 obtm upper bound, although the actual btm bound may well be about 53-54 btm. :D

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 moves

5x: 6 Sieves (u,d,r,l) (14 btm)

5x: 6 Sieves (d,u)(l,f,r,b) (10 btm)


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 Post subject: Re: Patterns
PostPosted: Sun Nov 03, 2013 9:49 am 
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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 53-54 btm. :D

Even better! By improving another algorithm, all 4x sequences are now below 55 moves:

4x: Winding Hexagon
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 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 Whirls
MR' 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. :shock:
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. :wink:

5x: 4 Outlined Hearts
F' 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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 Post subject: Re: Patterns
PostPosted: Sat Nov 09, 2013 4:11 pm 
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All 4x sequences should now be 53 moves long or less :D :

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 move

MR 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 moves


5x sequences have again been shortened :wink:

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 moves

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
TU TR2 T3B2 S2D' TL MF TL TF2 TL' MF' TL T3D'
5x: Triple Python (89 btm) -6 moves
I 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 moves

TU' 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 moves


A 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 :mrgreen:


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 Post subject: Re: Patterns
PostPosted: Sat Nov 09, 2013 6:17 pm 
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Some interesting checkerboard pattern combinations on my Super OctoCube (don't mind the places where the stickers have fallen off):

Image

Image

Image

Image

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 Post subject: Re: Patterns
PostPosted: Tue Nov 12, 2013 4:37 am 
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A more traditional pattern on the 6x6x6:

Small and large ring (opposite ways) (28 btm).

Or without physical cube rotation:

Small and large ring (opposite ways) (28 btm).

Cheers :D

Per Kristen

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 Post subject: Re: Patterns
PostPosted: Tue Nov 12, 2013 6:37 am 
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Another easy contribution (not yet optimized!!)

3 "truncated" flips on 4x4x4 (43 btm).

Per :)

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 Post subject: Re: Patterns
PostPosted: Wed Nov 13, 2013 4:46 am 
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Hi Per,

Here is an attempt at optimizing the truncated block flip pattern:

U2 L' WU2 L2 WU L' U' L MU' F2 MU L2 MU' L2 MD2 F2 MD F2 MD' F2 L2 MU2 L U'
TU R' F MR' MB2 MR F' R MF TR' MB2 TR MF' TU'
4x: 3 Truncated Block Flips (37 btm)


A few more (unoptimized) block flip patterns:

F R U' R U' SF' L' F U' R D F R2 F2 SR' U'
U2 B2 R L MU' WF MD MB WU MF' L' R' B2 U2
4x: 6 Truncated Block Flips (29 btm)

F WR2 B WR2 U2 WR U2 B' U2 WR' U2 F'
WF' WR' WF MD' R2 WF' WR WF R2 MD
4x: 4 Truncated Block Flips (Type 2) (21 btm)

MD2 TR MB TR' TF2 TR MB' TR MD TR2 TF2 MD2
F' MD' MF2 MD F MD' MF2 MD
4x: Truncated Block Flip (Type 2) (20 btm)

More truncated block flips patterns could certainly be found...


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

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 Post subject: Re: Patterns
PostPosted: Thu Nov 14, 2013 12:42 pm 
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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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 Post subject: Re: Patterns
PostPosted: Fri Nov 15, 2013 4:48 am 
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New contribution:

4X: 4 Helicopter flips (18 btm).

Per :)

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 Post subject: Re: Patterns
PostPosted: Fri Nov 15, 2013 8:41 am 
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A slight improvement:
L2 NU' WF2 NU2 WF2 NU' L2
B2 MU MD B2 MU MD R2 MU MD R2
4x: 4 Helicopter Flips (17 btm)


A few additional patterns:
MU T3F2 MU MD T3F2 MU2 MD'
4x: 2 Helicopter Flips (7 btm)

MD2 TR MB TR' TF2 TR MB' TR MD TR2 TF2 MD2
F' MR MF' MR' F MR MF MR'
4x: Truncated Block Flip (20 btm)

MD2 TR MB TR' TF2 TR MB' TR MD TR2 TF2 MD2
F2 R WF MR' WF' R2 WF MR WF' R F2
4x: Large Block Flip (23 btm)


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 Post subject: Re: Patterns
PostPosted: Mon Nov 18, 2013 6:46 am 
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New contribution:

6X: Helicopter Superflip (83 btm).

For sure this could be improved :wink:

EDIT:

I missed out some notational simplifications :oops:

6X: Helicopter Superflip (77 btm).

Per :solved:

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 Post subject: Re: Patterns
PostPosted: Tue Nov 19, 2013 6:12 am 
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perfredlund wrote:
New contribution:

6X: Helicopter Superflip (83 btm).

For sure this could be improved :wink:

EDIT:

I missed out some notational simplifications :oops:

6X: Helicopter Superflip (77 btm).

Per :solved:


And the very similar:

6X: Small Helicopter Superflip (77 btm).

This one is easier to optimize further, for example by 20 turn 3x3x3 superflip followed by clever center manipulation :wink:

EDIT:

Another easy variation (corrected):

6X: Fat Helicopter Superflip (77 btm).

Per :solved:

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Last edited by perfredlund on Fri Nov 22, 2013 4:48 am, edited 2 times in total.

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 Post subject: Re: Patterns
PostPosted: Tue Nov 19, 2013 9:51 am 
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Using the 3x 16-move superflip sequence and a short algorithm for centers, a gain of 42 moves has been obtained for the Fat Helicopter Superflip pattern (corrected): :D
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... :wink:


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 Post subject: Re: Patterns
PostPosted: Fri Nov 22, 2013 6:59 am 
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glazik wrote:
Using the 3x 16-move superflip sequence and a short algorithm for centers, a gain of 42 moves has been obtained for the Fat Helicopter Superflip pattern (corrected): :D
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... :wink:


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 :solved:

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 Post subject: Re: Patterns
PostPosted: Fri Nov 22, 2013 12:09 pm 
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Thanks Per,

The algorithm has been corrected and is now 35 moves long: :wink:

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)

A few additional patterns:
U F R' VL WU' VL' NF NB N3L M2U N3L' N3R2 M2F' M2U' N3F2 N3R2 U2 N3F2 N3R2 N3F2 NR2 VF2 VR2 VF2 U2 VR2 VF2 WU WF VR2 R F' U'
6x: 6 4-Color Rings (33 btm)

T3F2 NU' ND T3F2 NU2 T3R2 ND2 T3R2 ND2
6x : 4 Deep Double Edge Flips (9 btm)

T3F2 M2U' T3F2 N3U2 T3R2 N3D2 T3R2 N3D2
6x : 4 Block Flips (8 btm)

This last one may be too long:
WF2 SR2 N3D' VR2 N3D L' N3D' WR2 N3D R N3D' VL2 N3D SR WF2
N3U T3F2 N3U N3D T3F2 N3U2 N3D'
6x: 2 Helicopter Flips (22 btm)


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 Post subject: Re: Patterns
PostPosted: Fri Nov 22, 2013 2:50 pm 
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The following has been improved:

6X: 2 Helicopter Flips (18 btm).

Per :solved:

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 Post subject: Re: Patterns
PostPosted: Sat Nov 30, 2013 4:36 pm 
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Here are some 5x5 patterns that have been improved:

5x: 4 Small Diagonals
NU 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 U
WF' (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 Cube
R 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 Cube
R 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 Waffle
NB' NR' ND' NR2 ND NR' NB
NF2 NR2 NF NR2 NF2 NU NR NL ND NB (17 btm) -1 move

5x: 4 Enhanced Edge Flips
U' 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 Triangles
SF 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 Cube
SF' 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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