Thread: "Escher-style puzzle on Hyperbolic plane"

On 9/5/2012 12:08 AM, schuma wrote:
> Hi guys,
>
> Today I discovered an app on iOS, called Circull
>
> http://itunes.apple.com/us/app/circull/id392042223?mt=8
>
> For review, see:
>
> http://www.youtube.com/watch?v=sm8QwdslC2U
>
> It's a match-three game. It's quite easy but I really like the illustration. In the back end there are tessellations including {6,4}, {7,3} etc. Different levels have different tessellations.
>
> Is it possible to make a twisty puzzle of this style? That would be a great plus for MagicTile.

I really like all the little artistic touches like the embossed edges
and the sounds. It seems like an interesting idea to add to MT if it
could easily support it. Or perhaps it would be better as its own puzzle
built to share the MT engine. What I wonder even more is whether
Andrey's MagicTile633 or its engine could be easily adapted to support
the 3D version of Circull. And people shouldn't fear it because it's
only a 3D puzzle after all. OK sure, it's hyperbolic but it's still
just 3D. :-)

-Melinda

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Cool, thanks for passing this along Nan.

Strange coincidence. Shortly after seeing your message, a friend made a G+
post about another hyperbolic plane game called HyperRogue III. Looks like
it has Android support.
http://roguetemple.com/z/hyper.php

I tried out Circull, and it is fun to play! I think it could benefit from
the hyperbolic panning that Don came up with (copied in MT), rather than
the purely geodesic panning. The latter causes material near the center to
move very quickly when you drag near the edge of the disk. That's just a
minor comment though, and I think the game is really well done.

You asked about whether MT could support twisty puzzles of this style. By
that, do you mean puzzles where the faces are Escher-style images? It
would take coding since the program currently has no concept of sticker
orientations, but it'd certainly be possible with some effort.

seeya,
Roice


On Wed, Sep 5, 2012 at 2:26 AM, Melinda Green wrote:

>
> On 9/5/2012 12:08 AM, schuma wrote:
> > Hi guys,
> >
> > Today I discovered an app on iOS, called Circull
> >
> > http://itunes.apple.com/us/app/circull/id392042223?mt=8
> >
> > For review, see:
> >
> > http://www.youtube.com/watch?v=sm8QwdslC2U
> >
> > It's a match-three game. It's quite easy but I really like the
> illustration. In the back end there are tessellations including {6,4},
> {7,3} etc. Different levels have different tessellations.
> >
> > Is it possible to make a twisty puzzle of this style? That would be a
> great plus for MagicTile.
>
> I really like all the little artistic touches like the embossed edges
> and the sounds. It seems like an interesting idea to add to MT if it
> could easily support it. Or perhaps it would be better as its own puzzle
> built to share the MT engine. What I wonder even more is whether
> Andrey's MagicTile633 or its engine could be easily adapted to support
> the 3D version of Circull. And people shouldn't fear it because it's
> only a 3D puzzle after all. OK sure, it's hyperbolic but it's still
> just 3D. :-)
>
> -Melinda

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Cool, thanks for passing this along Nan.

Hi Roice,

I don't have a clear vision about how MagicTile supports Escher-style image=
s. I understand it's tons of coding to do. I just think that if you make Es=
cher-style images in MT, it'll attract more people because it's more artist=
ic. Maybe for public (or common geeky people), Escher's paints are more fam=
ous than the term "hyperbolic tessellation".=20

I can imagine two possible ways to introduce the images.=20

One way is that the stickers are painted with the images, and the cuts are =
circles as before. This is like the Rubik's cubes with picture stickers. I =
think this is what you meant.

The other way is to say each bird/rabbit/elephant/etc is a piece with irreg=
ular shape, and mimic the movement of the pieces in Circull. In the first l=
evel of Circull=20

http://a4.mzstatic.com/us/r1000/078/Purple/10/fb/2c/mzl.wibirnew.320x480-75=
.jpg

two adjacent birds can swap. There are two cases: (1) two birds' beaks meet=
at one point. In this case the birds will turn by 45 deg around the beaks.=
(2) two birds' wings and tails meet each other. In this case the birds wil=
l turn by 180 deg around the tails.

Case (1) can be made in the twisty puzzle: maybe all eight birds whose beak=
s meet at a point can rotate as a 8-cycle. Because the cut is not a perfect=
circle but a zig-zag "circle", the tails of moving birds may sweep over th=
e other birds' wings. But I'll think it's OK.=20

Case (2) is more complicated. I don't see a good way to make a 8-cycle vers=
ion of it. If we don't allow this kind of move, the twisty puzzle would be =
trivial. But we can make our own rules any way.

Any thoughts?

Nan

--- In 4D_Cubing@yahoogroups.com, Roice Nelson wrote:
> You asked about whether MT could support twisty puzzles of this style. B=
y
> that, do you mean puzzles where the faces are Escher-style images? It
> would take coding since the program currently has no concept of sticker
> orientations, but it'd certainly be possible with some effort.

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Hi Nan,

I like your idea to permute entire tiles around. (Avoiding slicing all
together would likely make things easier to program too.)

On your case (2), since the wings/tails meet at an edge of the underlying
{3,8} tiling, a natural way to do it would be as a 2-cycle rotation. Seems
like that could make the resulting puzzle too easy, but maybe not (say, if
you don't allow 2-cycles around the bird bellies and backs). I don't see a
way to do an 8-cycle here either, since the {3,8} doesn't have 8-fold
symmetry around an edge.

Another idea would be to have a permutation which took a strip of birds on
an h-line and translated them. In combination with your 8-cycle rotation
around a vertex, this could make an interesting and challenging puzzle.

Also, I think the "no slicing" approach to puzzles you're describing could
have application to a {3,3,8} puzzle :D

seeya,
Roice


On Thu, Sep 6, 2012 at 12:59 AM, schuma wrote:

> Hi Roice,
>
> I don't have a clear vision about how MagicTile supports Escher-style
> images. I understand it's tons of coding to do. I just think that if you
> make Escher-style images in MT, it'll attract more people because it's more
> artistic. Maybe for public (or common geeky people), Escher's paints are
> more famous than the term "hyperbolic tessellation".
>
> I can imagine two possible ways to introduce the images.
>
> One way is that the stickers are painted with the images, and the cuts are
> circles as before. This is like the Rubik's cubes with picture stickers. I
> think this is what you meant.
>
> The other way is to say each bird/rabbit/elephant/etc is a piece with
> irregular shape, and mimic the movement of the pieces in Circull. In the
> first level of Circull
>
>
> http://a4.mzstatic.com/us/r1000/078/Purple/10/fb/2c/mzl.wibirnew.320x480-75.jpg
>
> two adjacent birds can swap. There are two cases: (1) two birds' beaks
> meet at one point. In this case the birds will turn by 45 deg around the
> beaks. (2) two birds' wings and tails meet each other. In this case the
> birds will turn by 180 deg around the tails.
>
> Case (1) can be made in the twisty puzzle: maybe all eight birds whose
> beaks meet at a point can rotate as a 8-cycle. Because the cut is not a
> perfect circle but a zig-zag "circle", the tails of moving birds may sweep
> over the other birds' wings. But I'll think it's OK.
>
> Case (2) is more complicated. I don't see a good way to make a 8-cycle
> version of it. If we don't allow this kind of move, the twisty puzzle would
> be trivial. But we can make our own rules any way.
>
> Any thoughts?
>
> Nan
>
> --- In 4D_Cubing@yahoogroups.com, Roice Nelson wrote:
> > You asked about whether MT could support twisty puzzles of this style.
> By
> > that, do you mean puzzles where the faces are Escher-style images? It
> > would take coding since the program currently has no concept of sticker
> > orientations, but it'd certainly be possible with some effort.
>
>

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Hi Nan,