[HN Gopher] 2D Rubik's Cube solution visualization
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2D Rubik's Cube solution visualization
Author : iamben
Score : 245 points
Date : 2022-11-23 09:03 UTC (13 hours ago)
(HTM) web link (twitter.com)
(TXT) w3m dump (twitter.com)
| yamrzou wrote:
| Someone linked [1] an interesting tool in the replies: _MagicTile
| - Geometrical and Topological Analogues of Rubik 's Cube_ -
| http://roice3.org/magictile/
|
| "If you want to try solving the Rubik's Cube this way, you should
| try @roice713's MagicTile. You can choose the Rubik's cube among
| hundreds of puzzles. The stereographic projection makes it look
| like the animation in this post."
|
| [1] https://twitter.com/mananself/status/1595132523264167936
| thaumasiotes wrote:
| > The stereographic projection makes it look like the animation
| in this post.
|
| Couldn't be further from the truth. The image in the tweet is a
| huge improvement over the stereographic projection.
| klyrs wrote:
| It is the same thing, with two tiny changes:
|
| 1. different-size projected squares are replaced with same-
| size circles
|
| 2. the tweet's image puts the north pole on a corner; the
| projection on the upthread link puts the north pole on the
| face.
|
| Keeping the corner at the north pole does make it easier to
| understand, but it's still a stereographic projection.
| lupire wrote:
| Mathologer video going in depth on MagicTile and Rubik's cube
| variants like Kleij Bottle.
|
| https://www.youtube.com/watch?app=desktop&v=DvZnh7-nslo
| kirjavascript wrote:
| another 2D visualisation of the rubiks cube that is popularly
| used for computer simulation speedsolving is qcube[1]
|
| despite not being able to see all sides of the cube, it's
| surprisingly easy to solve on, as you essentially see the same
| stickers that you would in real life.
|
| there is even an IRC based version!
|
| [1] https://mzrg.com/js/qcube-v2.html
| yamrzou wrote:
| How does it work? I couldn't understand keyboard controls.
| kirjavascript wrote:
| here's an image of the keymap: https://cube.garron.us/keyboar
| d_layout/files/heise_simulator...
|
| and an explanation of the notation:
| https://jperm.net/3x3/moves
| rwnspace wrote:
| As someone who as held national records in the sport of
| speedcubing, I don't feel this makes it easier to understand, at
| least if you are going for an instrumental understanding of how
| to solve it. I think the community are pretty good at teaching
| that now! But it does look extremely cool.
|
| My favourite one-liner for improving understanding is something
| roughly like 'solve areas made of pieces, not faces made of
| stickers'. Very much clearer when you have a cube to take apart
| and put together in the order you would solve them.
| phkahler wrote:
| My feeble record is just under one minute. But I spent a lot of
| time thinking about how to represent the cube in a computer.
| Yes think pieces, not stickers. But for a long time I thought
| pieces had position and orientation. More recently I noticed
| that if we imagine each piece of a solved cube being connected
| to the cube center (an imaginary extension of the piece) it
| becomes clear that rotation is the only real freedom, and if a
| piece is in the correct orientation it is automatically in the
| right position! The reverse is not true of course.
|
| I don't think this is helpful for humans solving, but for
| computers it largely takes position out of it. Position does
| determine which pieces are rotated by any given move though.
| iamben wrote:
| Agree with you completely - I can't see how this would help me,
| but it's very cool to watch!
|
| And congrats on the records! I've managed to get just below the
| minute mark a handful of times and remain in complete awe of
| anyone sub 60 seconds!
| rwnspace wrote:
| Thank you, very kind. I myself am in awe of the current best
| solvers, the difference between my previously world-class
| average and the records now is massive.
| jbj wrote:
| on a similar note, you can get yourself a 4D rubiks cube
| (projected into 3D)
|
| It is not a 3x3x3x3 but 2x2x2x2.
|
| It looks like Melinda (the inventor) have made them easier to
| obtain. back when I got one, 3D printed parts, magnets, and
| coating all came from different sources, but absolutely worth it,
| they are very unique and work well.
|
| link: https://superliminal.com/cube/2x2x2x2/
| [deleted]
| bitslayer wrote:
| The corners appear as triangles in the figure. I counted all the
| triangles I could find and was confused because I only saw 7. But
| then I realized the 8th is around the outside of the whole
| figure!
| kazinator wrote:
| I saw this on Mastodon three hours before the $8Chan link was
| posted here.
|
| https://piaille.fr/@Mnaudin/109389968985022395
|
| It's a really poor representation, for specific reasons:
|
| - it doesn't convey how the corner and edge colors are
| constrained into moving together, due to being mounted on the
| same cube piece.
|
| - doesn't convey how the center face pieces stay in place
| relative to each other.
|
| - certain rotations "cheat": the dots dance around, not staying
| on their orbit tracks.
| cvoss wrote:
| But the actual 3D Rubik's Cube is also a really poor
| representation, because at all times you can only see at most
| half of the cube. I guess the point of making a 2D
| representation is to correct that problem. I can much more
| easily superimpose the missing connections you have mentioned
| in my mind's eye onto this 2D representation than I can
| remember the 3D layout of the half of the cube I can't see. Not
| everyone's brain works that way, but mine does.
| 988747 wrote:
| If I understand it correctly, this visualization does not take
| into account the constraints of some faces being physically tied
| to each other, by being on the same cube. So, while it can show
| the process of solving cube, it is not a replacement for the cube
| (i.e. you can't use it as a simulation to try to figure out new
| algorithms)
| nsilvestri wrote:
| It does, but not elegantly: when a non-slice move is made, you
| have to rotate the 3x3 group at the center. You see it in the
| animation.
| benniomars wrote:
| How is this easier to understand? And is the Rubik's Cuber hard
| to understand at all?
|
| You got 26 cubes in 3D space that need to go to their correct
| locations. They can move in 3 axis. They are color coded for
| recognition.
|
| I think anyone is able to solve the first 2 layers intuitively.
| Just start by following one of those 26 little cubes and see how
| it moves about.
| swores wrote:
| I'm sure it was just a typo but in case it confuses somebody
| reading your comment: 27 cubes, not 26 :)
| leviathan wrote:
| The cube in the center doesn't exist
| swores wrote:
| Then it was me who was confused, thanks for the correction
| :)
| withinboredom wrote:
| The cube in the center would beg to differ.
| thaumasiotes wrote:
| It exists. (Well, as a matter of the mechanics of the
| physical object, there is no center cube, but the other
| parts aren't cubes either.)
|
| But it is not one of the cubes that need to go to their
| correct locations. The center cube is not moved by any
| operation on the cube; it is always in its correct
| location.
| 988747 wrote:
| Center cube is not moved, but it is rotated. However,
| since it does not have any colored faces then it's
| rotations are meaningless.
| thaumasiotes wrote:
| If the cubes have correct locations, none of them need to
| have colored faces. The location is enough.
|
| (At least, that's true of the 26 outer cubes. You can't
| get them all into place without simultaneously aligning
| them correctly. I don't actually know if correct
| alignment of the center cube is also required, but it'd
| be my first guess.)
| 988747 wrote:
| That's provably false - I witnessed it many times when
| solving the cube myself. Colored faces determine
| orientation, in addition to location. In the Rubik
| solving method that I know (a simple method for amateurs,
| not remotely close to professional speed cubing methods)
| there's actually a late stage where ALL the cubes are in
| their correct locations, except some of the third layer
| corners might have a wrong orientation - there's a
| dedicated sequence of turns that allows to solve that.
| lupire wrote:
| By the same logic, there are 6 more invisible cubes, 1
| above each face. Where does it end?
| thaumasiotes wrote:
| The center cube is obviously part of the mental model of
| the cube, the Platonic object that the physical object is
| supposed to represent.
|
| Nobody believes there are invisible cubes outside the
| Rubik's cube. That's not the same logic; that's you
| trying and failing to imagine a problem with the idea
| that cutting a cube into three parts along each of its
| three axes will generate a hidden central subcube.
| [deleted]
| jb1991 wrote:
| Exactly this. It's not just rubik's cubes, it's also very easy
| to, for example, use just a few lines of bash to implement a
| stable, featureful sync tool like dropbox. Everyone's always
| making things seem more complicated than they really are.
| umanwizard wrote:
| Er... what? I don't understand how this is related at all.
| And yes, I know about the famous Dropbox HN comment.
|
| I agree with the other commenter that a normal 3D cube feels
| much more intuitive and simple. I guess it's just personal
| preference/thinking style.
| detritus wrote:
| I genuinely can't tell if you're being sardonic here. This
| being HN, I guess I have to assume you're being earnest.
| bombcar wrote:
| Mentioning Dropbox is the key to it being sarcastic.
|
| Like someone saying "less space than a nomad. Lame."
| jb1991 wrote:
| yep sorry, the Dropbox reference is a long-standing HN
| inside joke about comments like these. You can probably
| search to find the whole history of this reference, it's
| rather amusing.
| pvg wrote:
| _long-standing HN inside joke_
|
| It's more of a worn-out trope by this point and better
| skipped. Just sneerfully flag lame comments.
| detritus wrote:
| detritus wrote:
| I know the meme, which is why I was wondering, haha :)
| It's also the sort of thing that could've been meant
| entirely sincerely, in line with the comment of the
| person you were responding, being particularly painful to
| me as I've always had a massive mental block with Rubiks
| Cubes!
|
| Dark [Rubik's] Magic that they are.
| [deleted]
| joshspankit wrote:
| Kind of reminds me of playing the 4D Rubik's cube
| slim wrote:
| I never wanted to learn how to solve it, because finiding my way
| to solve it _is the game_. who 's like me?
|
| I bought a rubik's cube when my son was born, because I wanted
| something to play that was not my phone while he was on my lap. 3
| years later I'm able to complete one face in like 5 min
| consistently. still a long way to solve it, new techniques to
| discover and hours of play in sight. yay!
| gregfjohnson wrote:
| Given that you can solve the top layer, there is a really nice
| hack that lets you work out the rest of the puzzle. Say your
| top layer is completely solved, except that one of the top side
| pieces is flipped 180 degrees. You know a sequence of moves
| that will fix that piece, to solve the top layer. If you do
| that sequence and then run the same sequence backwards, you
| will get the cube back to the same place, first with that side
| piece fixed, and then rotated 180 degrees again. But here is
| the trick: Before you run the sequence backwards, rotate the
| top! You will restore the cube exactly to where it was, except
| that now TWO of the top side pieces will have been flipped 180
| degrees! This is referred to as a commutator operation, and is
| what Ryan Heise explains. Variants of this trick will let you
| rotate two corners in opposite directions, and re-position two
| top pieces and one bottom piece. One last thing: when solving
| the bottom layer, you may find yourself unable to re-position
| cubies into place using 3-way moves. Just rotate the top layer
| 90 degrees and you will then be able to proceed to completion.
| lupire wrote:
| It's a huge leap to get past the first layer. Your curt rate of
| progress suggests that your strategy will not solve the cube in
| your lifetime.
|
| And it's almost impossible to do it without taking notes on
| paper or computer. (If that were doable, their wouldn't be so
| many walkthroughs). Solving the cube is a hard applied group
| theory "homework" problem.
|
| This video explains the principles of solving a Rubik's cube on
| your own.
|
| https://www.youtube.com/watch?app=desktop&v=-NL76uQOpI0
| robot_no_421 wrote:
| It's still fun once you learn how to solve it. But fun in a
| different way.
|
| You're treating it as a puzzle to solve. But once you learn how
| to solve it, it ceases to be a puzzle and it becomes a really
| fun fidget toy. Seeing how fast you can solve it is enjoyable
| and gives your fingers some great dexterity exercise. I have
| one on my desk and when I want to take a break from coding I'll
| scramble it up and fidget around with it for a bit.
| _nalply wrote:
| I found my way to solve the Rubik cube thirty years ago. I
| still can solve the cube in between 5 and 10 minutes. My way of
| solving is not the fastest. Sometimes I have to repeat the last
| sequence six times and this takes a long time. But I know that
| my way is mine and only mine, and this makes me happy.
| SAI_Peregrinus wrote:
| The [Heise
| method](https://www.ryanheise.com/cube/heise_method.html) is
| essentially that, but formalized. No algorithms to memorize,
| just understanding how the cube works and using that to solve
| it.
| hota_mazi wrote:
| Actually, solving the cube is just the beginning of the game.
|
| If you are interested in optimizing, there are an infinite
| numbers of axes you can work on to solve faster.
|
| First, there are several general approaches, although
| realistically, only two (CFOP, Roux).
|
| Each of these methods have phases which you can practice and
| improve on separately, A lot of them require simple
| memorization (muscle memory for the most part) but all of them
| at some point contain a certain level of intuition and pattern
| recognition (e.g. lookahead), and for that, the only limit is
| your brain.
|
| It's a fascinating puzzle with neverending interest, at least
| for me (I solve in average around 25 seconds).
| greenbit wrote:
| Was trying to make sense of that solve, but couldn't see any
| algorithmic thing happening. Either that's the craziest method I
| ever saw, or it's just a reversal of a random scramble.
|
| Regardless, none of that takes away from the nifty 2D projection
| technique!
| noroot wrote:
| I also wondered the same and could not recognize any of the
| normal speed cubing methods.
| exitb wrote:
| There are algorithms that are more efficient than the typical
| speed cubing methods, but are based on large amounts of
| computation, rather than pattern matching, thus unfit for
| humans.
| karmakaze wrote:
| If it depends on large amounts of computation, how can it be
| considered more efficient? If it's precomputed, then it's
| again pattern matching. If by algorithm you mean the sequence
| of rotations, then yes there is a small upper bound that
| speedcubers typically exceed in solving any specific
| randomization. _[I never liked that some call a fixed
| sequence of moves an algorithm.]_
|
| Rubik's Cube solution unlocked by memorising 3915 final move
| sequences[0].
|
| > For the first time, a speedcuber has demonstrated a
| solution to the Rubik's cube that combines the two final
| steps of the puzzle's solution into one
|
| [0] https://www.newscientist.com/article/2334632-rubiks-cube-
| sol...
| krisoft wrote:
| > If it depends on large amounts of computation, how can it
| be considered more efficient?
|
| More efficient in terms of rotations necessary to solve the
| cube.
| koide wrote:
| I guess you mean efficient in that they produce a shorter (or
| even the shortest) sequence of moves to solve a given
| scramble. But if it takes 5 minutes of computation to produce
| the solve, then in practice they are not yet very efficient.
| exitb wrote:
| By computation in this case I mean evaluating the state of
| the cube after a series of moves. It's extremely difficult
| for a human, but a computer can simulate millions of moves
| in a fraction of a second. So realistically, any modern
| computer can find a low rotation count solution to any
| scramble almost instantaneously.
| MayeulC wrote:
| it depends how much you value a move, vs a computer
| instruction.
|
| Get a faster computer and a larger cube, the trade-off is
| likely worth it. A rubik's cube isn't such an intractable
| problem, I doubt a computer can't solve it faster than a
| human: in the worst case, they can rely on the same
| algorithm. Then, they can try to find shortcuts or just
| shorter paths.
|
| I always thought minimizing the number of moves was the
| goal, hence "more efficient" made sense to me too.
| raintrees wrote:
| https://nitter.net/jagarikin/status/1593771091738374144
| andirk wrote:
| This is so beautiful. Changing dimensions is often mind boggling
| even though it makes sense.
| fouronnes3 wrote:
| 4DToys is a VR game where you can "physically" play with 4D
| objects - as a 3D being of course, so you only get so see and
| touch one 3D slice, but the object is free to move in 4D
| (there's an actual 4D physics engine). There's something out of
| this world to hold a 4D cube in your hand and rotate it. You
| also get a software cursor to move yourself along the fourth
| spatial dimension.
| infamousclyde wrote:
| It's a spectacular visualization, kudos to the author. However,
| I'm not sure it made it particularly easier to understand,
| although I know that is subjective.
|
| Something that helped me was [1]. It took me from being someone
| who could not solve at all, to actually being quite good-- in the
| 13-20 second range. The beginner method listed on the site can
| easily put you in the sub-minute territory.
|
| [1]: http://badmephisto.com/
| gilleain wrote:
| I like this guy:
|
| > Q: I Added you as a friend but you didn't accept. WHY DO YOU
| HATE ME?
|
| > A: I dont accept any friend invites. But maybe I still hate
| you, who knows?
| rwnspace wrote:
| You'll like him even more if you know who Andrej Karpathy is,
| as they're the same person.
| [deleted]
| wantsanagent wrote:
| Cube solving is a path finding problem.
|
| The way to learn path finding problem is to understand how your
| actions move you through the space you're navigating.
|
| One of the most effective ways to learn these relationships is to
| work backwards.
|
| Starting from the goal, take a step away, then step back. Then
| take two steps away, then those steps back. Then take different
| steps away and steps back.
|
| As you move farther and farther from the goal you get an
| explosion of options that quickly requires deduction of
| strategies over memorization of all paths back to the goal.
|
| This can help ground learning the well known techniques for cube
| solving.
|
| This visualization _might_ help with that process, but just
| playing solutions from start to finish (IMO) doesn 't.
| taeric wrote:
| I found it somewhat fun to think of it in terms of
| permutations. https://taeric.github.io/cube-permutations-1.html
| is where I started with the idea. Never went too far with it,
| sadly.
|
| I do have my own 2d view of the rubics cube there. Was fun to
| watch the squares jump around. :D
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(page generated 2022-11-23 23:01 UTC)