Message #2770
From: Andrey <andreyastrelin@yahoo.com>
Subject: {10,3}, 6 colors? Re: [MC4D] The exotic {4,4,4}
Date: Mon, 26 Aug 2013 08:15:05 -0000
Hello, Roice,
I’ve tried to add new puzzle to Magic Tiles, but without success. The puzzle I’ve selected is non-oriented {10,3}, 6 colors (another version of hemidodecahedron), colors should be like this: http://groups.yahoo.com/group/4D_Cubing/photos/album/772706687/pic/2032129608/view . But all that I could get is a carpet with white spots (but they all are in proper places). What should I write in xml and why?
Andrey
— In 4D_Cubing@yahoogroups.com, Roice Nelson <roice3@…> wrote:
>
> I want to recall that Andrey pointed out all the 3C puzzles are
> topologically the same, and behave like the {4,3} 3C (hemicube). The state
> space does feel too small to really be enjoyable…even as an appetizer :)
>
> Thanks so much for the suggestions Melinda. I especially like the idea to
> cache the puzzle build data. Don’t know why I never thought of that
> before! I added your thoughts to my running trello list.
>
> Cheers,
> Roice
>
>
>
> On Mon, Aug 12, 2013 at 8:30 PM, Melinda Green <melinda@…>wrote:
>
> >
> >
> > Very nice, Roice!
> >
> > I was pretty sure the {inf,3} wouldn’t be very difficult but I didn’t
> > expect it to be this easy It seems like god’s number for it can be counted
> > on one hand! One nit: Scrambling it with 1000 twists rings the "solved"
> > bell a whole bunch of times as it accidentally solves it self many times.
> > Silencing the solved sound during scrambling will be helpful, but then you
> > should probably also discard all the twists that led to it since it just
> > becomes unneeded log file baggage.
> >
> > The experience of scrolling around in the {32,3} is better than I
> > imagined. Somehow I expected to see only the fundamental polygons. With N
> > >= 100 you can probably just mask off the outermost few pixels of the limit
> > making it indistinguishable from the inf version. You might also not center
> > a face in the disk to disguise its finiteness. Users can still scroll a
> > face to the center but they’d almost need to be trying to do that, and the
> > larger the N, the harder that will be.
> >
> > The ragged borders are indeed unsightly. Normally that’s not a problem for
> > solvers but it does go against the wonderful amount of polish you’ve
> > applied to MT in general. At the very least it shows us what the experience
> > can be which will be important in finding out how interesting these puzzles
> > are compared with other potential puzzles.
> >
> > As for the time needed to initialize these puzzles, perhaps you can cache
> > all the build data for all puzzles so that you never pay more than once for
> > each? It might also be nice to ship with the build data for whichever
> > puzzle you make the default. One last minor suggestion: If it’s not tricky,
> > would you please see if you can make the expanding circles animation spawn
> > new circles centered on the mouse pointer when it’s in the frame? That
> > would provide a nice distraction while waiting.
> >
> > Really nice work, Roice. Thanks a lot!
> > -Melinda
> >
> >
> > On 8/12/2013 5:37 PM, Roice Nelson wrote:
> >
> > Hi Melinda,
> >
> > I liked your idea to do large N puzzles, so I configured some biggish
> > ones and added them to the download :) They are in the tree at "Hyperbolic
> > -> Large Polygons". They take a bit longer to build and the textures get a
> > little pixelated, but things work reasonably well. Solving the {32,3} 3C
> > will effectively be the same experience as an {inf,3} 3C, though I would
> > still like to see the infinite puzzle someday too. One strange thing about
> > {inf,3} will be that no matter how much you hyperbolic pan, you won’t be
> > able to separate tiles from the disk boundary, whereas in these puzzles you
> > can drag a tile across the disk center and to the other side.
> >
> > Download link:
> > http://www.gravitation3d.com/magictile/downloads/MagicTile_v2.zip
> >
> > And some pictures:
> >
> > http://groups.yahoo.com/group/4D_Cubing/photos/album/1694853720/pic/435475920/view
> >
> > http://groups.yahoo.com/group/4D_Cubing/photos/album/1694853720/pic/810718037/view
> >
> > http://groups.yahoo.com/group/4D_Cubing/photos/album/1694853720/pic/600497813/view
> >
> > seeya,
> > Roice
> >
> >
> >
> > On Sun, Aug 11, 2013 at 10:32 PM, Melinda Green <melinda@…>wrote:
> >
> >>
> >>
> >> Hello Roice,
> >>
> >> I’m glad that you think that this puzzle makes sense. Also, I like your
> >> idea of using fundamental domain triangles. As for other colorings (and
> >> topologies), I would first hope to see the simplest one(s) first. This
> >> 3-coloring seems about as simple as possible though perhaps one could
> >> remove an edge or two by torturing the topology a bit. As for incorporating
> >> into MT versus creating a stand-alone puzzle, I have a feeling that there
> >> might be some clever ways to incorporate it. One way might be to implement
> >> it as a {N,3} for some large N. If a user were to pan far enough to see
> >> the ragged edge, so be it. If it must be a stand-alone puzzle, it might
> >> allow for your alternate colorings and perhaps other interesting variants
> >> that would otherwise be too difficult.
> >>
> >> -Melinda
> >>
> >>
> >> On 8/11/2013 8:06 PM, Roice Nelson wrote:
> >>
> >> The puzzle in your pictures *needs* to be made!
> >>
> >> It feels like the current MagicTile engine will fall woefully short for
> >> this task, though maybe I am overestimating the difficulty. Off the cuff,
> >> an approach could be to try to allow building up puzzles using fundamental
> >> domain triangles rather than entire tiles, because it will be necessary to
> >> only show portions of these infinite-faceted tiles. (In the past, I’ve
> >> wondered if that enhancement is going to be necessary for uniform tilings.)
> >> It does seem like a big piece of work, and it might even be easier to
> >> write some special-case code for this puzzle rather than attempting to fit
> >> it into the engine.
> >>
> >> I bet there is an infinite set of coloring possibilities for this
> >> tiling too.
> >>
> >>
> >>
> >> On Sun, Aug 11, 2013 at 7:19 PM, Melinda Green <melinda@…>wrote:
> >>
> >>>
> >>>
> >>> Here’s a slightly less awful sketch:
> >>>
> >>> http://groups.yahoo.com/group/4D_Cubing/photos/album/1962624577/pic/40875152/view/
> >>>
> >>>
> >>> On 8/11/2013 4:34 PM, Melinda Green wrote:
> >>>
> >>> Lovely, Roice!
> >>>
> >>> This makes me wonder whether it might be possible to add a 3-color
> >>> {inf,3}<http://groups.yahoo.com/group/4D_Cubing/photos/album/1962624577/pic/908182938/view/>to MagicTile something like this:
> >>>
> >>> groups.yahoo.com/group/4D_Cubing/photos/album/1962624577/pic/908182938/view/
> >>>
> >>> -Melinda
> >>>
> >>> On 8/10/2013 2:10 PM, Roice Nelson wrote:
> >>>
> >>> Hi all,
> >>>
> >>> Check out a new physical model of the exotic {4,4,4} H³ honeycomb!
> >>>
> >>> http://shpws.me/oFpu
> >>>
> >>>
> >>> Each cell is a tiling of squares with an infinite number of facets.
> >>> All vertices are ideal (meaning they live at infinity, on the Poincare ball
> >>> boundary). Four cells meet at every edge, and an infinite number of cells
> >>> meet at every vertex (the vertex figure is a tiling of squares too). This
> >>> honeycomb is self-dual.
> >>>
> >>> I printed only half of the Poincare ball in this model, which has
> >>> multiple advantages: you can see inside better, and it saves on printing
> >>> costs. The view is face-centered, meaning the projection places the center
> >>> of one (ideal) 2D polygon at the center of the ball. An edge-centered view
> >>> is also possible. Vertex-centered views are impossible since every vertex
> >>> is ideal. A view centered on the interior of a cell is possible, but (I
> >>> think, given my current understanding) a cell-centered view is also
> >>> impossible.
> >>>
> >>> I rendered one tile and all the tiles around it, so only one level of
> >>> recursion. I also experimented with deeper recursion, but felt the
> >>> resulting density inhibited understanding. Probably best would be to have
> >>> two models at different recursion depths side by side to study together. I
> >>> had to artificially increase edge widths near the boundary to make things
> >>> printable.
> >>>
> >>> These things are totally cool to handle in person, so consider
> >>> ordering one or two of the honeycomb models :) As I’ve heard Henry
> >>> Segerman comment, the "bandwidth" of information is really high. You
> >>> definitely notice things you wouldn’t if only viewing them on the computer
> >>> screen. The {3,6,3} and {6,3,6} are very similar to the {4,4,4}, just
> >>> based on different Euclidean tilings, so models of those are surely coming
> >>> as well.
> >>>
> >>> So… whose going to make a puzzle based on this exotic honeycomb? :D
> >>>
> >>> Cheers,
> >>> Roice
> >>>
> >>>
> >>> As a postscript, here are a few thoughts I had about the {4,4,4} while
> >>> working on the model…
> >>>
> >>> In a previous thread on the {4,4,4}<http://games.groups.yahoo.com/group/4D_Cubing/message/1226>,
> >>> Nan made an insightful comment. He said:
> >>>
> >>> I believe the first step to understand {4,4,4} is to understand
> >>>> {infinity,
> >>>> infinity} in the hyperbolic plane.
> >>>
> >>>
> >>> I can see now they are indeed quite analogous. Wikipedia has some great
> >>> pictures of the {â,â} tiling and {p,q} tilings that approach it by
> >>> increasing p or q. Check out the progression that starts with an {â,3}
> >>> tiling and increases q, which is the bottom row of the table here:
> >>>
> >>>
> >>> http://en.wikipedia.org/wiki/Uniform_tilings_in_hyperbolic_plane#Regular_hyperbolic_tilings
> >>>
> >>>
> >>> The {â} polygons are inscribed in horocycles<http://en.wikipedia.org/wiki/Horocycle> (a
> >>> circle of infinite radius with a unique center point on the disk boundary).
> >>> The horocycles increase in size with this progression until, in the limit,
> >>> the inscribing circle is* the boundary of the disk itself.* Something
> >>> strange about that is an {â,â} tile loses its center. A horocycle has a
> >>> single center on the boundary, so the inscribed {â,q} tiles have a clear
> >>> center, but because an {â,â} tile is inscribed in the entire boundary,
> >>> there is no longer a unique center. Tile centers are at infinity for the
> >>> whole progression, so you’d think they would also live at infinity in the
> >>> limit. At the same time, all vertices have also become ideal in the limit,
> >>> and these are the only points of a tile living at infinity. So every
> >>> vertex seems equally valid as a tile center. Weird.
> >>>
> >>> This is good warm-up to jumping up a dimension. The {4,4,3} is kind of
> >>> like an {â,q} with finite q. It’s cells are inscribed in horospheres, and
> >>> have finite vertices and a unique center. The {4,4,4} is like the {â,â}
> >>> because cells are inscribed in the boundary of hyperbolic space. They
> >>> don’t really have a unique center, and every vertex is ideal. Again, each
> >>> vertex sort of acts like a center point.
> >>>
> >>> (Perhaps there is a better way to think about this… Maybe when all
> >>> the vertices go to infinity, the cell center should be considered to have
> >>> snapped back to being finite? Maybe the center is at some average of all
> >>> the ideal vertices or at a center of mass? That makes sense for an ideal
> >>> tetrahedron, but can it for a cell that is an ideal {4,4} tiling? I don’t
> >>> know!)
> >>>
> >>>
> >>>
> >>>
> >>>
> >>>
> >>
> >>
> >>
> >>
> >
> >
> >
> >
> >
>