Patterns

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

An improvement. Still much better could be found i'm sure ...

2 Square Yin - Yangs (6X) (20 btm).

Per

glazik · **Joined:** Wed Oct 12, 2011 12:54 pm

The algorithm of dots has been improved for better move cancellation.

New dots (with T3 moves)
(T3B2 NU2 N3L2 NU2 N3L2)2
Insert new dots at *
R2 T3B2 * VR2 T3B2 VR2 B2 T3U2 VL2 T3U2 T3R2
2 Square Yin-Yangs (6x) (17 btm)

Two patterns have been added on R/L faces.
The algorithm can of course be improved by taking into account symmetry properties of the whole pattern :wink:

2 Square Yin-Yangs F/B
R2 NU2 N3L2 NU2 N3L2 T3B2 NU2 N3L2 NU2 V3R2 T3B2 VR2 B2 T3U2 VL2 T3U2 T3R2
Insert Edges + Centers R/L
ND2 R2 N3B2 ND2 N3B2 ND2 R2 N3B2 ND2 NB2 VD2 WF2 D2 VF2 T3D2 VF2
4 Square Yin-Yangs (6x) (31 btm)

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

A major improvement and a variation:

4 Square Yin-Yangs (6X) (20 btm).

4 Square Yin-Yangs (v2) (6X) (20 btm).

Per

glazik · **Joined:** Wed Oct 12, 2011 12:54 pm

The two already short algs can be further improved as follows:

4 Square Yin-Yangs (6x) (19 btm)

4 Square Yin-Yangs (6x) (v2) (17 btm)

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

glazik wrote:

The two already short algs can be further improved as follows:

4 Square Yin-Yangs (6x) (19 btm)

4 Square Yin-Yangs (6x) (v2) (17 btm)

Ooopss. Something went wrong with the dots. I'm sure you can fix that easily ..

I was thinking about 6 Square Yin-Yangs. But not sure how to approach that yet ... (Challenge :wink:

)

Per

glazik · **Joined:** Wed Oct 12, 2011 12:54 pm

There was indeed something wrong with our last algs

Dots position has been corrected since (v2 alg may stiil be too long, though).

4 Square Yin-Yangs
Dots:
(T3U' L2 TF2) (N3F2 NU' ND N3F2 ND' NU) (TF2 L2 T3U)
Block 1:
T3U' L2 R2 T3U2 WR2 T3U'
Block 2:
R2 T3B2 VR2 T3B2 VR2 T5B2 T3R2
4 Square Yin-Yangs (6x) (20 btm)

4 Square Yin-Yangs (v2)
Dots:
NU T3R2 M2F2 T3R2 ND T3R2 N3B2 T3R2 ND' NU' T3R2 N3F2 T3R2
Block 1:
T3R2 B2 VR2 T3B2 VR2 T3B2 R2
Block 2:
T3U WR2 T3U2 R2 L2 T3U
4 Square Yin-Yangs (6x) (v2) (23 btm)

It seems pretty difficult to display 6 patterns on a 6x cube, maybe you could find a trick :wink:

A pattern variation with wide dots gives something that could look like masks:
4 Masks (6x)
Block 1:
L2 T3F2 VL2 T3F2 VL2 T5F2 T3L2
Dots (Eyes):
M2F2 NU' ND M2F2 ND' NU
Block 2:
T3U WR2 T3U2 R2 L2 T3U
4 Masks (6x) (18 btm)

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

A new obvious variety:

4 Masks (v2) (6X) (18 btm).

I'm quite certain the masks patterns could be improved !!

Per

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

New fairly simple contribution.

6 Orthogonal Whirls (6X) (24 btm).

This can be shortened to 20, but i like this compactness of notation :wink:

Per

glazik · **Joined:** Wed Oct 12, 2011 12:54 pm

Rings can also be "whirled" :wink:

6 Whirled Rings (6x)
This one seems to be too long, a shorter version should certainly exist.
Rings:
WF WD2 WF' V3L2 NU2 M2F M2R2 M2F' V3D2 NL2
Edges (shorter version?):
L2 D2 NF' NB' B2 NR' NL' B2 D2 B2 D2 NR NL D2 ND' NU' B2 L2 B2 L2 ND NU L2 B2 D2 L2 NF NB L2 D2
6 Whirled Rings (6x) (39 btm)

4 Whirled Rings (v2) (6x)
Edges:
L2 B2 ND' NU' B2 L2 B2 L2 ND NU L2 B2
Rings
B2 F2 M2U' M2F2 M2U M2F2 WU SF2 WU
4 Whirled Rings (v2) (6x) (19 btm)

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

Nice job as always :wink:

I could not find any obvious improvements.

And now the missing version:

2 Whirled Rings (6x) (22 btm).

Hmm. A combination of 2 whirls and 4 whirls might work to achieve an improvement to the first varietey I will have a go later

Per

glazik · **Joined:** Wed Oct 12, 2011 12:54 pm

Continuing to whirl...

In the following, edges are processed separately and already known ring algorithms are re-used, probably not an optimal way of doing things.

2 Whirled Rings (6x)
This is an alternate solution to yours, still same length though.
Edges:
SR' ND NU SR D2 SR' NU' ND' NF NB SR F2 SR' NB' NF' SR F2 D2
Rings:
D2 (WF2 V3D2 NF2 M2U2 V3B2 ND2) D2
2 Whirled Rings (6x) (22 btm)

4 Whirled Rings (6x)
Edges (may still be too long):
SR' NU ND SR U2 SR' NU' ND' SR U2
U2 SF' ND NU SF U2 SF' ND' NU' SF
R2 B2 NU' ND' B2 R2 B2 R2 NU ND R2 B2
Rings:
B2 F2 M2U' M2F2 M2U M2F2 WU SF2 WU
4 Whirled Rings (6x) (37 btm)

2 Whirled Rings (v2) (6x)
Edges:
SR NF NB SR' F2 SR NF' NB' SR' F2
Rings:
WF2 V3D2 NF2 M2U2 V3B2 ND2
2 Whirled Rings (v2) (6x) (15 btm)

4 Connected Rings (6x)
Edges:
F B NR NL SF' R2 SF NR' NL' SF' R2 B2
Rings:
B2 F2 M2U' M2F2 M2U M2F2 WU SF2 WU
4 Connected Rings (6x) (19 btm)

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

I made an improvement to the following:

4 Whirled Rings (6x) (30 btm).

And also:

4 Connected Rings (6x) (17 btm).

Further improvements should certainly still be possible to find :roll:

Per

wwwmwww · **Posted:** Fri Nov 30, 2012 6:35 pm

Can someone point me to a definition of the word mezon? From context I have a good idea what it means but I can't find it in the dictionary and google isn't even much help aside from pointing me to a few pictures of twisty puzzles. Was this a term coined here or by some member of the puzzle community? Its been used more in this thread then any other I've seen so I figured this was a good place to ask. I'm rather curious where it originated as I can't seem to find any indication that its even a word yet a large number of twisty puzzle members use it and its quite clear from context everyone has the same understanding as to its definition. So how did that happen? What am I missing? Is it actually some obscure mathematical or scientific term I'm just not familar with? Even if so I would have thought google would have turned up something rather easily and I'm just not finding it.

Carl

Doug Roth · **Joined:** Sun May 29, 2011 2:56 pm **Location:** New York

wwwmwww wrote:

Can someone point me to a definition of the word mezon? From context I have a good idea what it means but I can't find it in the dictionary and google isn't even much help aside from pointing me to a few pictures of twisty puzzles. Was this a term coined here or by some member of the puzzle community? Its been used more in this thread then any other I've seen so I figured this was a good place to ask. I'm rather curious where it originated as I can't seem to find any indication that its even a word yet a large number of twisty puzzle members use it and its quite clear from context everyone has the same understanding as to its definition. So how did that happen? What am I missing? Is it actually some obscure mathematical or scientific term I'm just not familar with? Even if so I would have thought google would have turned up something rather easily and I'm just not finding it.

Carl

Maybe this: "A pattern which makes a puzzle look like a completely different puzzle."

-Doug

bmenrigh · **Posted:** Fri Nov 30, 2012 6:47 pm

I assumed it was a misspelling of meson and implied something was in a middle / intermediate twist state. The mezon pattern for the Helicopter Cube has about half the puzzle in the right state and the other half mid-turn.

I'd like to know too

wwwmwww · **Posted:** Fri Nov 30, 2012 6:52 pm

Doug Roth wrote:

Maybe this: "A pattern which makes a puzzle look like a completely different puzzle."

Oh I take it that it means something along the lines of twisting a corner of a puzzle that's not just a trivial twist. I'm really not so worried about the exact definition as I think I can get a pretty good idea from the pictures which have been posted. I'm really more curious how this word got adopted/created for this purpose.

Carl

wwwmwww · **Posted:** Fri Nov 30, 2012 7:12 pm

bmenrigh wrote:

I assumed it was a misspelling of meson and implied something was in a middle / intermediate twist state.

The only connection I see between "intermediate" and "meson" is here, and off the top of my head I don't even know what it means to say a meson is an intermediate mass particle. Still that seems quite a jump from subatomic partices to states of a Rubik's cube. And I don't think its just any old intermediate state. It seems to imply a corner twist on a non-corner turning puzzle. Most of the pictures seem to be 3x3x3's or helicopter cubes which are face and edge turning. Subatomic particles and Rubik's cubes both have strong ties to group theory... just thinking out loud... I still feel I'm missing something.

Carl

Doug Roth · **Joined:** Sun May 29, 2011 2:56 pm **Location:** New York

wwwmwww wrote:

Oh I take it that it means something along the lines of twisting a corner of a puzzle that's not just a trivial twist. I'm really not so worried about the exact definition as I think I can get a pretty good idea from the pictures which have been posted. I'm really more curious how this word got adopted/created for this purpose.

Carl

Hmmm not exactly sure what you mean by this. I always just assumed that a mezon was a illusion state.

Examples:
A Helicopter Dodecahedron in a FTD mezon

A Helicopter Cube in a VTC mezon

A Helicopter Cube in a different type of VTC mezon

A Helicopter Cube in a FTC mezon

A Bermuda Cube in a VTC mezon

A AI 4x4x4 Cube in a VTC mezon

An FTO in a VTO mezon

A mosaic cube in a different type of VTC mezon

Even this could be considered a Rex Cube in a FTC mezon

-Doug

wwwmwww · **Posted:** Fri Nov 30, 2012 7:25 pm

Doug Roth wrote:

Hmmm not exactly sure what you mean by this. I always just assumed that a mezon was a illusion state.

Examples:
A Helicopter Dodecahedron in a FTD mezon

A Helicopter Cube in a VTC mezon

A Helicopter Cube in a different type of VTC mezon

A Helicopter Cube in a FTC mezon

A Bermuda Cube in a VTC mezon

A AI 4x4x4 Cube in a VTC mezon

An FTO in a VTO mezon

A mosaic cube in a different type of VTC mezon

Even this could be considered a Rex Cube in a FTC mezon

Looking at those pics the only ones I see called mezon by their original posters are those with what appear to be vertex turns. I agree that making an apparent face turn on a non-face turn puzzle is something very closely related but at the moment you are the only one that seems to be useing the term mezon in those cases. So how do I know you are using it correctly? You may be... I just don't know. This is one of the main reasons for my initial question.

Carl

P.S. I spoke too soon. I see schuma used it that way in one of his posts. So you aren't the only one. Still I am looking for something official or a post where someone says they are coining the term "mezon" to mean bla bla bla... Say the way Bram coined the use of the word doctrinaire as it applies to twisty puzzles.

Doug Roth · **Joined:** Sun May 29, 2011 2:56 pm **Location:** New York

wwwmwww wrote:

Doug Roth wrote:

Hmmm not exactly sure what you mean by this. I always just assumed that a mezon was a illusion state.

Examples:
LINKS

Looking at those pics the only ones I see called mezon by their original posters are those with what appear to be vertex turns. I agree that making an apparent face turn on a non-face turn puzzle is something very closely related but at the moment you are the only one that seems to be useing the term mezon in those cases. So how do I know you are using it correctly? You may be... I just don't know. This is one of the main reasons for my initial question.

Carl

Well I'm not so sure either. I guess I am just assuming that a mezon state isn't restricted to "fake" vertex turns. If it is, then what would the patterns that are not "fake vertex" turning be called? Simply a pattern?

-Doug

bmenrigh · **Posted:** Fri Nov 30, 2012 7:29 pm

wwwmwww wrote:

bmenrigh wrote:

I assumed it was a misspelling of meson and implied something was in a middle / intermediate twist state.

The only connection I see between "intermediate" and "meson" is here, and off the top of my head I don't even know what it means to say a meson is an intermediate mass particle. Still that seems quite a jump from subatomic partices to states of a Rubik's cube. And I don't think its just any old intermediate state. It seems to imply a corner twist on a non-corner turning puzzle. Most of the pictures seem to be 3x3x3's or helicopter cubes which are face and edge turning. Subatomic particles and Rubik's cubes both have strong ties to group theory... just thinking out loud... I still feel I'm missing something.

Carl

Well I was thinking of the Latin root word medianus meaning "middle" which gets turned into words like mezzanine, meson, etc. The prefix is "meso" as in mesomorph, mesosphere, mesozoic, etc.

The first reference I can find on the forum to mezon is this post by pytlivyj_1 who I think is Russian. Perhaps he translated Мезон to "mezon" instead of "meson"?.

wwwmwww · **Posted:** Fri Nov 30, 2012 7:53 pm

bmenrigh wrote:

Well I was thinking of the Latin root word medianus meaning "middle" which gets turned into words like mezzanine, meson, etc. The prefix is "meso" as in mesomorph, mesosphere, mesozoic, etc.

The first reference I can find on the forum to mezon is this post by pytlivyj_1 who I think is Russian. Perhaps he translated Мезон to "mezon" instead of "meson"?.

Nice... that helps alot. But the date of that post is 2010. I think the term has been used far longer then that but maybe it is a misspelling after all. Here is a link:

http://www.usna.edu/Users/math/wdj/rubik/patterns.html

Last updated in January 2006 that uses the term "meson". And I can't say I've seem the checker board state called "pons asinorum" before which in latin means something rather funny. My guy tells me that there may be one of the very early solution books for the Rubik's cube that described some interesting states of the 3x3x3 and that used this term and the term may be almost as old as the Rubik's cube itself. But how is it that even if everyone here first saw the word misspelled by a Russian poster... that everyone just jumps to applying it to what appear to be illegal turns on a puzzle? I'll keep digging.

Carl

wwwmwww · **Posted:** Fri Nov 30, 2012 8:06 pm

Oh I just LOVE it when my gut is correct. I think I've found it. Check out the book "Metamagical Themas: Questing for the Essence of Mind and Pattern" By Douglas R. Hofstadter copyright 1985. Check this out:

Attachment:

Meson.png [ 402.05 KiB | Viewed 3229 times ]

So a meson really is a quark antiquark pair. And we have Douglas R. Hofstadter to thank for this term. Odd that the key to finding this was "pons asinorum"...

So I guess this means everyone should stop using the incorrect spelling.

Carl

bmenrigh · **Posted:** Fri Nov 30, 2012 8:08 pm

wwwmwww wrote:

http://www.usna.edu/Users/math/wdj/rubik/patterns.html

Last updated in January 2006 that uses the term "meson".

Alright this goes back to 2003:
http://www.madore.org/~david/.misc/rubik-meson/

Attachment:

rubiks_meson.png [ 123.79 KiB | Viewed 3227 times ]

Finding the first reference could be hard but clearly it's old.

I checked the "Cube Lovers" archive and found the first reference to "meson" on the mailing list in this post:

Code:

From cube-lovers-errors@curry.epilogue.com  Fri Apr  4 11:35:52 1997
Return-Path: cube-lovers-errors@curry.epilogue.com
Received: from curry.epilogue.com (localhost [127.0.0.1]) by curry.epilogue.com (8.6.12/8.6.12) with SMTP id LAA04602; Fri, 4 Apr 1997 11:35:52 -0500
Precedence: bulk
Errors-To: cube-lovers-errors@curry.epilogue.com
Date: Fri, 4 Apr 1997 09:28:08 -0500 (EST)
From: Jiri Fridrich <fridrich@binghamton.edu>
X-Sender: fridrich@bingsun2
To: Cube-Lovers@ai.mit.edu
Subject: Pretty patterns with Kociemba (help)
Message-ID: <Pine.SOL.L3.93.970404092400.8134A-100000@bingsun2>
MIME-Version: 1.0
Content-Type: TEXT/PLAIN; charset=US-ASCII

I would like to ask for your help to find short algorithms for some
pretty patterns below. The algorithms are just working algorithms and
are probably too long. Can anybody apply Kociemba's algorithm to 
those positions? 

The patterns form a small portion of a very large collection of
pretty patterns found by Mirek Goljan and Peter Nanasy from Czech
Republic. The algorithms below are the awkward "outliers" for which
we were unable to find a reasonably short "logical" algorithm. It
looks like Kociemba's algorithm is the only chance. 

Thanks in advance for your help!

Jiri Fridrich

P.S.: Visit my speed cubing page at
http://ssie.binghamton.edu/~jirif. The complete collection of
pretty patterns will be there soon.

F'R2D'RsF RsF D'R2D F'L2F D'R2D2B LsU'F'      28,23,20  DLV
U'R B'R'U R'D2F U F U'F'D'U2BsLsD F           22,20,18  U4V
R2F'D'F2L F'R F R'aF'D B LsDsF'U2             22,19,17  U5V
F'R2D'RsF RsF D'R2D F'L2F D'R2D2F UsL'U'      28,23,20  LV
D B'L'B2L B D2B'L'B2L B D'L2B2D2              22,16     L'2
D2B2D2B2U2F2U R2U F2U2R2D R2D                 26,15     L'8
FaR2F'aD'aR2U'F2D R2D2F2U F2U                 24,17     L'9
D2F2L2U2D B R B2R'B'D2R'B'R2B R D             24,17     L'10
LsF2R2D'FsU'F2sDFsDR2F2Rs                     24,18,13  [SS']
U L D R2U R U'R B'D B'D'B2D'L'U'              18,16     [VH]
R'D2R B'U2B R'D2R B'U2B . U B2L BsL2R'FsU2D L'B2U'      [VHH']
R U'R B'D B'D'B L B'U R'U R U2B2R2L'U         22,19     [VSS']  
LsF2R2D'FsU'F2sDFsDR2F'L'FsU F'U'BsR                    [SS'H]
U'R F'R'F L F'DsBsL U'R'D R D'F               18,18,16  [DOO']
U L D R2U R U'L DsBsR'B L'B'L2B'D'F'          22,20,18  [DVH]
LsF2R2D'FsU'F2sDFsDR2F'R'DsBR'F'LsU                     [DSS'H]
B'L'D L'U'BsLsU'R DsR'D R U R'D L             20,20,17  [DHOO']
B'L F'L2FsR'B R F'LsB'R B2L F L'              20,18,16  [VO]
LsU FsD F2sU'FsU'F L'FsU F'U'BsR              24,22,16  [SHH']
R'F2L'D'L F2B D B'D'FsL B L2D L F'R           22,19,18  [SS'O]
D'L F R U2L U2R2U2L'U R2U R'F'L'D             22,17     [VHO]
R'F'L BsD'F'D B'L'B L F R'DsBsR U             20,20,17  [DSO']
LsU FsD F2sU'FsU'F R'DsB R'F'LsU              24,22,16  [DSHH']
R'D B D R'DsB L B'U'aR B'D'R2B'D'R            20,19,18  [DVSO]
D F'UsL'DsF UsL2F'L DsF'LsD BsR'D B'R'        26,25,19  [DU3U4]
U L F'L DsF'LsD BsR'D LsU'L'U'F'aU'BsL F2U    28,27,22  [DU2U3]
R2sF2R2F2sR2F2.FD'L'DLD'L'DLD'L'DLF'
FD'L'DLD'L'DLD'L'DLF'. F2sR2sD F2sU2R2sD
D'F'D F DsB L'D L UsB'D'B R'F'D'F'D           20,20,18  [WORKS(14)]
U'B2RaU2R'B'U L'B UsR'B U'R B'DsB2R2U         26,22,20  [WS(14)S'(23)]
R D'F2D F'R F UsF DsF'R2D F D'R D F'D'        23,21,19  [ORKK'S(14)(23)]
R U'F R'B'D2R'U'BsLsD B L U'R'U'F U'Ls        23,22,19  [DK]
D'R'BULsB'UB'U'BL'BLB'UB'U'BRsDB'DsF'UsLB     30,30,26  giant meson 1
L D R2D'L2U B'D'B D'R'D R DsL D'B2D           22,19,18  giant meson 2
R2L'DBR'D'BLBL'D'B'D2LDL'U'FD'F'RFL'FLF2R'D2U           
DFRsU'B'D'R'aD'LsBDFD2F2DF'R'B'L'DLBF2RD'R2D        

Notation:

Ra = antislice RL, Fa = FB, etc.
Fs = slice move FB', Rs = RL', etc.
F2s = 180 deg. slice move, etc.

The three-tuple in the second column means the number of quarter,
face, and slice moves. You can Ignore the cryptic notation in square
brackets.

**********************************************************************
|  Jiri FRIDRICH, Research Associate, Dept. of Systems Science and   |
|  Industrial Engineering, Center for Intelligent Systems, SUNY      |
|  Binghamton, Binghamton, NY 13902-6000, Tel.: (607) 797-4660,      |
|  Fax: (607) 777-2577, E-mail: fridrich@binghamton.edu              |
|  http://ssie.binghamton.edu/~jirif/jiri.html                       |
**********************************************************************

......................................................................

Remember, the less insight into a problem, the simpler it seems to be!
----------------------------------------------------------------------

bmenrigh · **Posted:** Fri Nov 30, 2012 8:10 pm

wwwmwww wrote:

So a meson really is a quark antiquark pair. And we have Douglas R. Hofstadter to thank for this term. Odd that the key to finding this was "pons asinorum"...

So I guess this means everyone should stop using the incorrect spelling.

Carl

Fantastic find! I love the reference to a pair of quarks (corners) that can never be isolated (twisted in isolation).

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

Hi Brandon and all other,

I found this in a book , I bougt it 1981.
The pattern is developed from David Singmaster
Perhaps this is earlier than the sequences from Jessica Fridrich.
(I lost my Scientific American prints ( Hofstadter) from this years

But I found some Books ) Book from Tom Werneck

Attachment:

CubeInCube0001.png [ 129.38 KiB | Viewed 3202 times ]

I use this sequence yet.

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

Hi guys!!

I developed sequences for big and small mezon pattern on 3x3x3 cube in the mid 80's.

My sequence for Small Mezons is surely optimal, 12 turns.

My sequence for Big Mezons (Cube in Cube) is not, but i developed it without computer aids. It consists of 2 block 3-cycles, Each 10 moves so total 20 turns.

PS! The last one is the same Andrea posted, but i guess it would be nice to see the patterns interactively :wink:

Per

wwwmwww · **Posted:** Sat Dec 01, 2012 11:12 am

bmenrigh wrote:

Fantastic find! I love the reference to a pair of quarks (corners) that can never be isolated (twisted in isolation).

Yes... I have a much deeper appreciation of the name now. I really like that too. However that illustration is sort of funny. Can you tell the difference between the Christian Cross and the Plummer Cross from that illustration? He does go on to explain it in text and also explains the name "pons asinorum" which I'd been wondering about as well.

Attachment:

PonsAsinorum.png [ 42.54 KiB | Viewed 3181 times ]

Carl

wwwmwww · **Posted:** Sat Dec 01, 2012 11:32 am

Andrea wrote:

Hi Brandon and all other,

I found this in a book , I bougt it 1981.
The pattern is developed from David Singmaster
Perhaps this is earlier than the sequences from Jessica Fridrich.
(I lost my Scientific American prints ( Hofstadter) from this years

But I found some Books ) Book from Tom Werneck

So its clear this pattern was developed even earlier. However do any of these sources call it a meson? It appears to me they were named "meson" by Hofstadter but in the text I just posted above he does credit the "MIT cube-hacking community" for some of these names so its certainly possible the name "meson" for this state goes back even further but this is the first source I've found that nicely details WHY this state is named "meson". Which was the main thing I was after.

perfredlund wrote:

My sequence for Small Mezons is surely optimal, 12 turns.

My sequence for Big Mezons (Cube in Cube) is not, but i developed it without computer aids. It consists of 2 block 3-cycles, Each 10 moves so total 20 turns.

Nice sequences... BUT I wish we'd now stop the proliferation of this misspelling of meson. I believe bmenrigh hit the nail on the head. It appears pytlivyj_1 had originally mistranslated Мезон to "mezon" instead of "meson" back in 2010 and everyone on this site has been misspelling it since. I'd really prefer to correct this before it gets so ingrained that people get stuck with this misspelling and become unwilling to change. Meson fits PERFECTLY once its understood exactly what it means and its clear this has been forgotten in the last ~30 years.

Carl

wwwmwww · **Posted:** Sat Dec 01, 2012 12:02 pm

So know knowing the meaning of meson we can now go back and check to see which of Doug's examples used the name meson correctly.

A Helicopter Dodecahedron in a FTD meson
Correct. This big face quark requires the anti-quark on the opposite face

A Helicopter Cube in a VTC meson
Correct. This big vertex quark requires the anti-quark on the opposite vertex

A Helicopter Cube in a different type of VTC meson
Correct. This big vertex quark requires the anti-quark on the opposite vertex

A Helicopter Cube in a FTC meson
Incorrect. This is NOT a meson. There is no anti-quark.

A Bermuda Cube in a VTC meson
I'm on the fence about this one. The anti-quark looks different then the quark. However its close enough that if any state on this Bermuda Cube was going to be called a meson this would be it.

A AI 4x4x4 Cube in a VTC meson
Correct. I believe this state would requite the opposite corner to be in the anti-quark state. Not 100% sure of that but close.

An FTO in a VTO meson
Correct. The opposite vertex is in the anti-quark state.

A mosaic cube in a different type of VTC meson
I don't think this is a meson. I believe the Mosaic cube offers enough freedom that you could get only a single vertex into this state. Please correct me if I'm wrong. If so I guess you could put the opposite corner into the anti-quark state but some of the meaning is lost if one can exist without the other.

Even this could be considered a Rex Cube in a FTC meson
I don't know enough about the Rex Cube. Does this apparent face turn force the opposite face to be in this state? I suspect not but I'm really not certain. The reason I think that is because if the two faces were linked that way I think I would have expected them to be 180 degrees out of phase with each other and they are not. If my suspicions is correct I would NOT call this a meson.

Carl

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

Let me just add some background information on how i came up with that small MESON sequence. Actually i was looking for short sequences for twisting corners on the top layer.

The sune/antisune combination is well known ( i did not know those names back then ...) I was still looking for corner 2-twist on 2 non-adjacent corners. First i came up with this

However i felt this was still not optimal. But commuting a single twist was already optimised so then what to try next? Yes, correct - swap 2 corners in 2 "different" ways. Giving the desired effect, What i found was this

A simple conjugation (cyclical shift yields THIS.

From this a 13-turn adjacent 2-twist can be deduced. I will not show this here ...

Per

glazik · **Joined:** Wed Oct 12, 2011 12:54 pm

Back to basic physics again...

A very small improvement:
4 Whirled Rings (6x) (29 btm)

A few more patterns:

6 Connected Rings with 2 Crossings (6x)
Edges:
SR2 SF2 ND2 SR2 SF2 NU2
Grids:
NU2 NF2 NR2 NL2 NB2 ND2
6 Connected Rings with 2 Crossings (6x) (10 btm)

The following are improved versions of grids already published on Walter's website:

6 Grids (Order 3) (5x)
Rings:
MR MF' MR' NB NF' SR' WU' SR
Edges:
SR' [SF', D' NF2 NB2 D U NB2 NF2 U'] SR
6 Grids (Order 3) (5x) (26 btm)

6 Grids (Order 3) (6x)
Rings:
M2R M2F' M2R' NB NF' SR' WU' SR
Edges:
SR' [SF', D' NF2 NB2 D U NB2 NF2 U'] SR
6 Grids (Order 3) (6x) (26 btm)

6 Grids (Order 3) (7x)
Corners:
L2 R U' B2 L U SR' SU' L' U' F2 L D' U2
Edges:
SF [D N3L2 N3R2 D' U' N3R2 N3L2 U, SR] SF'
Centers:
[N3L N3R', N3U N3D']
6 Grids (Order 3) (7x) (39 btm)

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

A small improvement:

6 Grids (Order 3) (7x) (37 btm).

Achieved from same parts by simple insertion :wink:

This can be further improved to:

6 Grids (Order 3) (7x) (34 btm).

I'd bet it's pretty darn close to optimal :roll:

Per

Waran · **Posted:** Sun Dec 09, 2012 4:30 pm

Hi there,

I improved a few of previously posted patterns:

4x: Zig-Zag
TU' TL2 F2 TD2 TF2 D2 TR2 TU2 ML2 TF2 TU' (11 btm)

4x: Y Loops
F B D2 R2 (MD' ML MU MR' WD WR) R2 D2 B2
R2 F2 SR D MR2 D' SR' D MR2 D' F2 R2 SF' (26 btm)

6x: 6 Y Boomerangs
WR SF WD' F2
U2 L2 (V3R' V3D' V3R V3D) L2 U2 F B (14 btm)

6x: 6 Triangle Boomerangs
WR SF WD' B2
D2 R2 (V3R' V3D' V3R V3D) R2 D2 B' F' (14 btm)

6x: 2 Y Loops
F B D2 R2 (ND' V3L V3U NR' WD WR) R2 D2 B2
R2 F2 SR D NR2 D' SR' D NR2 D' F2 R2 SF' (26 btm)

Waran · **Posted:** Sun Dec 09, 2012 4:41 pm

... and these are some new ones:

5x: 6 Grids
U WR D2 B2 D2 WR' U2 B2 U2
NU MR TD2 TB2 TD2 MR' TU2 TB2 U
NR2 NF2 NB2 NR2 NU ND NF2 NB2 ND2
VB2 NL2 MF2 VR2 NB2 NU ND WR2 NU'
MF WR MF' SR' MF WR' MF' SR (44 btm)

5x: 4 Snowflakes
NR2 NL2 NF2 NB2 NU2 NR2 NL2 NF2 NB2 TD2 WF2 WR2 D2 WF2 WR2 (15 btm)

5x: 4 Chalices
MR2 MF2 U2 (WR2 WD WF2 WD') T3D2 MR2 MF2 WR2 WF2 (12 btm)

5x: 4 Cups
SD2 MR2 MF2 VD2 MR2 MF2 WR2 WF2
U2 (WR2 WD WF2 WD') (13 btm)

7x: 4 Left Looking Pac-Man Monsters
TU V3F2 VR2 M2U2 VR2 VF2 M2U2 NR2 MF2 TR2 SF2 L2 ND R2 SF2 NL2 S2F2 TR2 D TL2 S2F2 N3R2
NF2 MF2 NB2 T3R2 D T3L2 NF2 MF2 NB2 T3L2 D'
(F' MR' NB N3F' MR F2 MR' NB' N3F MR F' CU)3 CU (66 btm)

I know, we had these fellows before. Last time they looked cross-eyed, now they look to the left.

7x: 8 Propellers (3x3x3)
F SR2 B2 SD2 B SD F SD2 F2 SR2 B
T3U T3D' N3R' N3L N3U' N3D NL N3L' N3R NR' NU' ND NR NL' (25 btm)

7x: 6 Double Boomerangs
F B R2 D2 (M2U ND' V4R' N3U' V3R MD ND N3L' N3R' NU MD' V3L N3D' V4L' NU' M2D) D2 R2 B' F' (24 btm)

7x: 6 Pumpkins
B2 D' U' L R
(M2R' VU MR N3U' N3R NU'
V4D' N3R' N3L N3U' MR' ND NR' NL M2D WR)
R' L' U D B2 (26 btm)

7x: 4 Peaks, 6 Diagonals
U' B R (VD' NR' MD' N3R' ND N3U MR' N3D NU N3L MD NL VU' WR) R' B' D R D' NR' D R' D' NR
F NL2 F' R' F NL2 F' R B2 NU' L B SR NU L NU' R' B' NU L' B2 U (49 btm)

glazik · **Joined:** Wed Oct 12, 2011 12:54 pm

Hi Walter,

A few algorithms have been improved (could still be further optimized with more work):

4x: Y Loops
SF
R2 F2 (SR D MR2 D' SR' D MR2 D') F2 R2
R2 B2 D2 (MD' ML MU MR' WU' WR) D2 B2 R2
SF'
4x: Y Loops (23 btm)

6x: Y Loops
SF
R2 F2 (SR D NR2 D' SR' D NR2 D') F2 R2
R2 B2 D2 (ND' V3L V3U NR' WU' WR) D2 B2 R2
SF'
6x: Y Loops (23 btm)

7x: 4 Peaks, 6 Diagonals
Centers:
U F' L' (VB' NU' MF N3U' NB N3F MU' N3B NF N3D MF' ND VF' WU) L F U'
Edges:
(U F') (B' L F' NU F NU' L' B NU F' NU' F) (F U')
(D' B) (F R' B NU B' NU' R F' NU B NU' B') (B' D)
7x: 4 Peaks, 6 Diagonals (46 btm)
A shorter solution for edges should certainly exist for this last one :wink:

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

Alternative solution:

5X: 4 Cups (13 btm).

Same btm but otherwise better in 3 of 4 metrics :mrgreen:

Hope to improve some of the other patterns later

Per

glazik · **Joined:** Wed Oct 12, 2011 12:54 pm

Another improved pattern:

5x: 4 Snowflakes
(MF2 MR2 NU2 NB2 NF2 NR2 NL2 ND2)
(D2 WF2 WR2 D2)

5x: 4 Snowflakes (11 btm)

Waran · **Posted:** Thu Dec 13, 2012 3:15 pm

Great algorithms! I was amazed to see that the Snowflake pattern can be achieved with only 11 turn. This might be an optimal solution.

I further optimized the Pumpkins pattern:

7x: 6 Pumpkins
B2 D' U' L R (M2R' VU MR N3U' N3R NU')
V4D' N3R' N3L N3U' S3R NF NR' NL M2F R2 U D B2 (24 btm)

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

@ Glazik.
Maybe 16 turns is not optimal for those edges. But cancelling 4 turns makes it optimal anyway. Possibly some insertion could make the overall solution shorter??

Per

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

An improvement has been made to the Pac-Man faces:

7X: 4 Left Looking Pac-Man Monsters (58 btm).

Not hard to find really, but too many sequences involved. I guess much better could still be found :wink:

Per

glazik · **Joined:** Wed Oct 12, 2011 12:54 pm

@ Walter
This is a pattern similar to the last 6 Pumpkins (same setup and re-use of some parts) :wink:

7x: 6 Mail Boxes
B2 D' U' R L
WR' V3D' WR MR' N3U N3R' NU M2R WU'
L' R' U D B2
7x: 6 Mail Boxes (17 btm)

@ Per
Algorithm (B' D' NB2 NF2 D SF' D' NF2 NB2 D F) is a direct edge 4 3-cycles with good symmetry properties.
The setup is quite long though, but this gives a gain of 3 moves.
I think shorter edge algorithms could still be found...

Centers
U F' L' (VB' NU' MF N3U' NB N3F MU' N3B NF N3D MF' ND VF' WU) L F U'
New Edges
(U2 TF2 NB' R2 NR' ND' F') (B' D' NB2 NF2 D SF' D' NF2 NB2 D F) (F ND NR R2 NB TF2 U2)
7x: 4 Peaks, 6 Diagonals (43 btm)

Waran · **Posted:** Fri Dec 14, 2012 6:54 pm

Here are two similar looking Heart patterns for the 5x5x5 cube.
The second version is much harder to achieve:

5x: 4 Outlined Hearts
MF2 MR2 WR2 (D WF2 D2 WF2 D) WR
ND WR ND2 WR' ND WR MF2 MR2
(VU2 WR' VU WR)2 (25 btm)

5x: 4 Outlined Hearts (v2)
F' L B D2 (L SD2 SR ND SR' SD2 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)4 NU' F2
F2 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 (81 btm or 76 btm actually)

glazik · **Joined:** Wed Oct 12, 2011 12:54 pm

5x: 4 Outlined Hearts
The algorithm can be improved by insertion.

Insert (VU2 WR' VU WR)2 at *:
MF2 MR2 WR2 D WF2 D2 WF2 D WR * ND WR ND2 WR' ND WR MF2 MR2

5x: 4 Outlined Hearts (21 btm)

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

An improvement (yet again):

5X: 4 Outlined Hearts (16 btm).

I'm quite confident it's near optimal

Per

glazik · **Joined:** Wed Oct 12, 2011 12:54 pm

Good work Per!
Your solution is already darn short, but maybe you missed a remaining 1-move cancellation :wink:

Insert SU NB2 NF2 SU' at *:
MF2 * D' WF2 D2 WF2 D' MF2 WR2 MU MR2 MU' NU2 MU2

5x: 4 Outlined Hearts (15 btm)

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

glazik wrote:

Good work Per!
Your solution is already darn short, but maybe you missed a remaining 1-move cancellation :wink:

Insert SU NB2 NF2 SU' at *:
MF2 * D' WF2 D2 WF2 D' MF2 WR2 MU MR2 MU' NU2 MU2

5x: 4 Outlined Hearts (15 btm)

Nice minor improvement Glazik. Actually, i found my solution simply by brute force (solver). Then reversing the turns for the generator (setup).

Per :solved:

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

I made some major improvement to the following:

5X: 6 Grids (28 btm).

I guess still better could be found by insertion ...

EDIT

Optimised version:

5X: 6 Grids (25 btm).

Per :wink:

glazik · **Joined:** Wed Oct 12, 2011 12:54 pm

The algorithm being composed of 3 parts, the (modified) first part can also be inserted into the 2 other already combined parts.

Replace (SF MR' WF MR SF' MR' WF' MR) with (SF' MU' SF MU' SF' MU SF MU) and insert at *:
CU D * MU' T3B2 ND2 MF2 NU2 B2 NF2 NL2 NB2 NF2 NR2 U' D' NL2 NR2 D

5x: 6 Grids (23 btm)

Edit:
You said you used a brute force solver to find near-optimum solutions, in some cases.
Is it a proprietary one or could you give us more information about it (programming language, main features, computing time,...) ?

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

glazik wrote:

The algorithm being composed of 3 parts, the (modified) first part can also be inserted into the 2 other already combined parts.

Replace (SF MR' WF MR SF' MR' WF' MR) with (SF' MU' SF MU' SF' MU SF MU) and insert at *:
CU D * MU' T3B2 ND2 MF2 NU2 B2 NF2 NL2 NB2 NF2 NR2 U' D' NL2 NR2 D

5x: 6 Grids (23 btm)

Edit:
You said you used a brute force solver to find near-optimum solutions, in some cases.
Is it a proprietary one or could you give us more information about it (programming language, main features, computing time,...) ?

Eh... I meant brute force solving. Like my "brain cube vision ... ". There is no such solver that i¨m aware of :cry:

Slight rewrite to eliminate cube rotation:

5X: 6 Grids (23 btm).

Per

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