# Message #2381

From: Roice Nelson <roice3@gmail.com>

Subject: Re: [MC4D] Re: Escher-style puzzle on Hyperbolic plane

Date: Sat, 08 Sep 2012 22:10:02 -0500

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 <mananself@gmail.com> 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 <roice3@…> 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.

>

>