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 Post subject: RefleCube: a reflection on the Rubik's Cube
PostPosted: Mon Dec 17, 2012 1:44 am 
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Hi guys,

Recently I made a puzzle simulator called RefleCube:

http://nanma80.github.com/

The idea is, instead of twisting a layer by 90 degrees like on the Rubik's Cube, we can mirror a layer. For example, the top layer (U) can be mirrored with respect to the plane bisecting the cube into left and right halves. The result of the reflection is swapping UFR with UFL, UBR with UBL, UR with UL. You can mirror the top layer with respect to the plane bisecting the cube into front and back halves, too.

We can also think of reflecting a layer with respect to a diagonal plane so that UFR<->UBL, UF<->UL, UR<->UB.

I call the first transform "mirror +", and the second transform "mirror X".

You can choose to play a puzzle with only one type of mirroring moves, or both of them (which implies the Rubik's Cube's twisting moves).

I also included the common Rubik's cube and a half-turn cube (only allows 180 degree turns) because they are related.

This puzzle is inspired by Magic Cube 2D and the discussion about it in the Yahoo group. I also emulated this puzzle using MC4D and MPUlt before implementing it. You know, we can use 4D rotation to emulate 3D reflection.

I'm not going to tell you what can happen or cannot happen on RefleCube. Find out by yourself!

Nan

edit: I just added several sizes: 2x2, 4x4 and 5x5. For each size all the mirroring styles are supported. Use shift+click and alt+click to turn the deeper layers. Have fun!


Last edited by schuma on Sun Dec 30, 2012 6:54 pm, edited 1 time in total.

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 Post subject: Re: RefleCube: a reflection on the Rubik's Cube
PostPosted: Mon Dec 17, 2012 2:13 am 
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So interesting!
Thanks Nan.

Edit: I just solved the Mirror & Twist, I think it would be the easier one, so cool! Maybe Oskar can make it :shock: .
Edit 2: I can't believe it, I just solved the Mirror+ too!! So much fun, once you get used to it visually, actually the Mirrir & Twist was harder.

Cheers,
Burgo.

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1st 3x3 solve Oct 2010 (Even though I lived through the 80s).
PB 3x3 55sec Jan 2011 (When I was a kid 1:30 was speedcubing so I'm stoked).
1st 3x3 Earth (nemesis) solve Jan 2011 My You Tube (Now has ALLCrazy 3X3 Planets with Reduction)


Last edited by Burgo on Mon Dec 17, 2012 3:07 am, edited 1 time in total.

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 Post subject: Re: RefleCube: a reflection on the Rubik's Cube
PostPosted: Mon Dec 17, 2012 3:04 am 
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Very cool Nan. It was a lot of fun figuring these out and solving them. I especially like that corners can be mirrored or a single corner twisted since that has a very similar feel to MC4D and Gelatinbrain's 3.11.1

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 Post subject: Re: RefleCube: a reflection on the Rubik's Cube
PostPosted: Mon Dec 17, 2012 11:50 pm 
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Burgo wrote:
So interesting!
Thanks Nan.

Edit: I just solved the Mirror & Twist, I think it would be the easier one, so cool! Maybe Oskar can make it :shock: .
Edit 2: I can't believe it, I just solved the Mirror+ too!! So much fun, once you get used to it visually, actually the Mirrir & Twist was harder.

Cheers,
Burgo.


I'm glad that you have having fun. You must be able to solve MirrorX, too.

Today that I'm thinking about it. Maybe a physical version is possible: the corner pieces must not keep their shapes otherwise mirroring is impossible. But what if they can change shapes or automatically disassemble and re-assemble... that would be crazy. But some designers here already proved that they can make crazy things.


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 Post subject: Re: RefleCube: a reflection on the Rubik's Cube
PostPosted: Tue Dec 18, 2012 1:05 am 
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schuma wrote:
I'm glad that you have having fun. You must be able to solve MirrorX, too.
Of the variations, the Mirror-X is the most interesting to me, by far. The Mirro-+ is pretty trivial once you figure out the edge parity and the mirror + twist gives you too much freedom.

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 Post subject: Re: RefleCube: a reflection on the Rubik's Cube
PostPosted: Wed Dec 19, 2012 1:54 am 
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Hi Nan and Brandon,

The Mirror X is definately the harder puzzle, I have found some sequences for it, but not everything I need so far, but I'm very close (it's very achieveable too). I will invest more time in the future, because I know I can solve it, but for now I only solved the first 2. I don't know if I've hit all the `333 RC parity cases` yet, because I haven't solved them very many times, or read the spoiler, but I did cover quite a few of them. The most enjoyable solve for me was the Mirror & Twist (which I reduced to a 333 RC).. and I would encourage everyone here to give it a go, it's very accessible, and I'm surprised at the lack of responses!

Cheers,
Burgo.

_________________
1st 3x3 solve Oct 2010 (Even though I lived through the 80s).
PB 3x3 55sec Jan 2011 (When I was a kid 1:30 was speedcubing so I'm stoked).
1st 3x3 Earth (nemesis) solve Jan 2011 My You Tube (Now has ALLCrazy 3X3 Planets with Reduction)


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 Post subject: Re: RefleCube: a reflection on the Rubik's Cube
PostPosted: Wed Dec 19, 2012 8:18 am 
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Very cool puzzles. So different from anything I've ever played with. Bravo!

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 Post subject: Re: RefleCube: a reflection on the Rubik's Cube
PostPosted: Wed Dec 19, 2012 12:16 pm 
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Burgo wrote:
Hi Nan and Brandon,

The Mirror X is definately the harder puzzle, I have found some sequences for it, but not everything I need so far, but I'm very close (it's very achieveable too). I will invest more time in the future, because I know I can solve it, but for now I only solved the first 2. I don't know if I've hit all the `333 RC parity cases` yet, because I haven't solved them very many times, or read the spoiler, but I did cover quite a few of them. The most enjoyable solve for me was the Mirror & Twist (which I reduced to a 333 RC).. and I would encourage everyone here to give it a go, it's very accessible[...]

Hey Burgo,

I was really happy that Nan created these since I was not anticipating they'd be as novel as they've turned out to be. I'm somewhat surprised you solved the Mirror + Twist puzzle so easily since to me it seems very closely related to the Mirror-X. Instead of treating that puzzle like a 3x3x3 I instead treated it like the Mirror-X and then used 3x3x3 moves for easy setups and corner orbit fixing.

Also, the Mirror-X (and of course the Mirror + Twist) puzzle has a single corner twisted issue. Did you run into this on the Mirror+Twist puzzle? I don't see how 3x3x3 moves help at all in resolving it. I tackled it exactly like I did on the Mirror-X puzzle. I'd be interested in hearing about your approach to this problem.

Burgo wrote:
and I'm surprised at the lack of responses!
It seems people don't give simulated puzzles a chance because they incorrectly assume that solving on a computer is harder than solving physically. Once you break free of relying on muscle memory for solving, computer simulations become a great complimentary supplement to physical solving.

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 Post subject: Re: RefleCube: a reflection on the Rubik's Cube
PostPosted: Wed Dec 19, 2012 6:30 pm 
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bmenrigh wrote:
Burgo wrote:
and I'm surprised at the lack of responses!
It seems people don't give simulated puzzles a chance because they incorrectly assume that solving on a computer is harder than solving physically. Once you break free of relying on muscle memory for solving, computer simulations become a great complimentary supplement to physical solving.

It may be much simpler than that. Some people just have other things going on and can't jump into every new puzzle 8-)

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 Post subject: Re: RefleCube: a reflection on the Rubik's Cube
PostPosted: Wed Dec 19, 2012 7:08 pm 
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rline wrote:
bmenrigh wrote:
Burgo wrote:
and I'm surprised at the lack of responses!
[...]because they incorrectly assume that solving on a computer is harder than solving physically
It may be much simpler than that. Some people just have other things going on and can't jump into every new puzzle 8-)

Yeah my statement is too broad. I'm sure there are many reasons. One only has to look at the thread(s) for a single physical puzzle such as the Rex Dodecahedron to see that interest for costly physical puzzles is many orders of magnitude greater than interest in free virtual ones.

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 Post subject: Re: RefleCube: a reflection on the Rubik's Cube
PostPosted: Wed Dec 19, 2012 7:11 pm 
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For the Mirror-X puzzle, can anyone find a way to twist a corner in fewer than 16 mirror operations? My routine is 16 moves and I've tried a lot but haven't been able to find a shorter one.

And Nan, if you add anything, a move counter would be nice. Don't worry about undoing moves decreasing the counter. It's okay if the counter monotonically increases for every move.

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 Post subject: Re: RefleCube: a reflection on the Rubik's Cube
PostPosted: Wed Dec 19, 2012 8:06 pm 
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Very cool schuma! The puzzles have some new and interesting properties for solving, and the simulator functions flawlessly for me. I will have fun working out the solutions =)

bmenrigh wrote:
For the Mirror-X puzzle, can anyone find a way to twist a corner in fewer than 16 mirror operations? My routine is 16 moves and I've tried a lot but haven't been able to find a shorter one.


Ful Lfd Ful Ruf Ful Lfd Ful Ruf (8 moves) rotates the FRD corner CCW

For the notation, each move is represented with 3 letters, the first letter is the face and the 2nd/3rd letters describe which corner of that face to click near.


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 Post subject: Re: RefleCube: a reflection on the Rubik's Cube
PostPosted: Wed Dec 19, 2012 8:25 pm 
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DKwan wrote:
Very cool schuma! The puzzles have some new and interesting properties for solving, and the simulator functions flawlessly for me. I will have fun working out the solutions =)

bmenrigh wrote:
For the Mirror-X puzzle, can anyone find a way to twist a corner in fewer than 16 mirror operations? My routine is 16 moves and I've tried a lot but haven't been able to find a shorter one.


Ful Lfd Ful Ruf Ful Lfd Ful Ruf (8 moves) rotates the FRD corner CCW

For the notation, each move is represented with 3 letters, the first letter is the face and the 2nd/3rd letters describe which corner of that face to click near.

Ah brilliant! You managed to twist a corner in place with the Ful Lfd Ful conjugate.

Mine was based on Ruf Ufr Ruf which isolates a corner in RDB which I would mirror in place with Drf. As a commutator this mirrors two corners. I then used a setup move and applied the mirror sequence which unmirrored one of the corners and put a second mirror in one of them.

Your construction is so much more direct and elegant.

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 Post subject: Re: RefleCube: a reflection on the Rubik's Cube
PostPosted: Wed Dec 19, 2012 11:52 pm 
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DKwan wrote:
Ful Lfd Ful Ruf Ful Lfd Ful Ruf (8 moves) rotates the FRD corner CCW


Oh it's so simple, AFTER seeing your algorithm: Ful brings FRD to FUL, Lfd mirrors it in place, and Ful puts it back. Then the sequence commutate with Ruf. Great job!

I'm also quite satisfied with this simulator. It's not tedious. it's a small puzzle. But it's also rich in that there are many parity cases. Even experienced solvers find it pretty interesting. The look is familiar, so that many people would jump in rather than being intimidated. I think this puzzle changes how I think what a good new puzzle is.

Brandon: move count is added. Thanks.


bmenrigh wrote:
Once you break free of relying on muscle memory for solving, computer simulations become a great complimentary supplement to physical solving.


For 3x3x3, I actually rely on muscle memory. For example, on a good physical puzzle, I do full PLL, 21 algorithms in total. But on computer, I can only do three PLLs: one three cycle of corners, one three cycle of edges and its inverse. And in the worst case I have to use four algorithms on a computer to do what I can do by one algorithm on a physical puzzle. But you know, it doesn't stop me from solving simulated puzzles.


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 Post subject: Re: RefleCube: a reflection on the Rubik's Cube
PostPosted: Thu Dec 20, 2012 7:28 am 
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bmenrigh wrote:
Also, the Mirror-X (and of course the Mirror + Twist) puzzle has a single corner twisted issue. Did you run into this on the Mirror+Twist puzzle? I don't see how 3x3x3 moves help at all in resolving it. I tackled it exactly like I did on the Mirror-X puzzle. I'd be interested in hearing about your approach to this problem.
For the F2L I used the U layer to mirror anything that needed altering (so I used the mirroring to reduce to a 333). In the LL I'm pretty sure I had 2 `333 parity` problems: 2 LL edges swapped, and a single corner twisted. For the 2 LL edges swapped (which can be seen as 2 corners also) I could use mirroring directly in the LL, but the single corner rotated required me to disassemble one F2L edge corner pair (although it was more of an exploritory moment than a serious unpacking): Just now, I went back and tried a few things to immitate what I did, and this seems close: RUR' [mirror FUL<>BUR] F'UF [mirror FUR<>BUL] RUR' [mirror FUL<>BUR] F'UF (and U FRUR'U'F' reveals it). This method can be used to mirror corners too, but please be merciful, it was just a bit of off the cuff solving and I haven't had the time to look into it more thoroughly.

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1st 3x3 solve Oct 2010 (Even though I lived through the 80s).
PB 3x3 55sec Jan 2011 (When I was a kid 1:30 was speedcubing so I'm stoked).
1st 3x3 Earth (nemesis) solve Jan 2011 My You Tube (Now has ALLCrazy 3X3 Planets with Reduction)


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 Post subject: Re: RefleCube: a reflection on the Rubik's Cube
PostPosted: Sun Dec 30, 2012 6:56 pm 
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Hi RefleCube players. Thank you all for your support. Since you guys find these puzzles interesting and have solved them quickly, I just added several sizes: 2x2, 4x4 and 5x5. For each size all the mirroring styles are supported. Use shift+click and alt+click to turn the deeper layers.

Imagine what kind of weird parities you'll see in the 4x4. Have fun!


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 Post subject: Re: RefleCube: a reflection on the Rubik's Cube
PostPosted: Fri Jan 04, 2013 2:13 am 
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I finally finished all the variations. It took me longer than expected. The 4x4x4 Mirror-X was the only subtlety difficult one. You can't naively reduce to a 3x3x3 Mirror-X and expect it to always be solvable.

Very fun, thanks :D

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 Post subject: Re: RefleCube: a reflection on the Rubik's Cube
PostPosted: Fri Jan 04, 2013 3:00 am 
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Brandon, what kind of parity did you have? Is it flipping a paired up edge?

I didn't use reduction method, so my view could be different from yours.


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 Post subject: Re: RefleCube: a reflection on the Rubik's Cube
PostPosted: Fri Jan 04, 2013 3:07 am 
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I reduced centers and then found a pair of swapped edge wings. After fixing those I found that the centers were reduced 90 degrees from the orbits of the corners. It was not possible to solve the corners in a way that would match the centers.

Flipping a pair of edge wings is quite easy.

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