Message #1220

From: Melinda Green <>
Subject: Re: [MC4D] MHT633 v0.1 uploaded
Date: Wed, 27 Oct 2010 22:45:16 -0700

On 10/27/2010 7:57 PM, Roice Nelson wrote:
> I can field a few of the questions :)
> @Melinda
> It doesn’t look so large to imagine that someone wouldn’t solve it
> fairly soon after it is feature-complete and debugged. Or maybe
> I’m just just not seeing much of it? How many unique faces does it
> have?
> It’s very much like MagicTile, in that the {6,3,3} tessellation has an
> infinite number of cells. So Andrey used the same approach of
> identifying certain cells with each other. Hence, the number of
> unique faces is simply the number of colors selected from the puzzle
> menu. The 8 color version does seem like it should be quite tractable
> from a number-of-pieces perspective, though perhaps still terribly
> difficult.

Thanks Roice; that’s very helpful. Unique cells = number of colors. Of
course! I don’t know what I was thinking. I guess it’s just a surprising
object that I lost all my familiar landmarks and got lost in the
magnificence of this amazing object that I never even knew existed. BTW,
I saw Don just now and showed this to him and he was delighted. He
definitely wants to work together to create the ultimate slicing engine,
similar to GelatinBrain, possibly even in all dimensions. Just the same
old problem of too many things to do.

> I’ll be interested in ensuing discussion about Melinda’s thoughts on
> movement controls. I have some thoughts floating around as well, but
> they aren’t well formed yet.

I only have clear preferences regarding the left-mouse button. I like
what Andrey did with the right-mouse and would be happy to standardize
on whatever the rest of you think.

> @Matt
> One question I do have, how many hexagons per cell? I’m curious
> but I find it pretty hard to count them manually.
> Not only are there an infinite number of cells in this tessellation,
> but every one of these cells has an infinite number of hexagons! (The
> identification of cells mentioned above also serves to turn this
> aspect of the puzzle into a manageable finite situation.) The cells
> are a {6,3} tiling, the same as you’d see on a bathroom floor, only
> going on forever. This tiling is curved when living in hyperbolic
> space though, and the result is that the view from within hyperbolic
> space is such that only a small number of the hexagonal facets can be
> seen - the rest curve out of view. With sticker shrink, I suppose it
> would be possible to display a much larger number of the facets, since
> that allows one to see somewhat through the cell.

Now that was *not* obvious to me, but very cool. Now I think I get it.
For others struggling with the hyperbolic views and tesselations
including infinite-sided polygons, here is Don’s wonderful page on the
subject in 2D: what
I still don’t have a feeling for is how these multiple "bathroom
tilings" connect to each other. It sure looks like magic to me. I
understand from Andrey that that connectivity is tightly interconnected,
and that’s why he feels this will be very difficult to solve. It really
is quite the object!

> Hope that’s helpful and not too much rambling…

Never. I hope that everyone knows to that it’s just as OK to ramble as
it is to simply delete messages or threads that don’t interest them.

> aside: Andrey, I think some user control over the amount of culling
> could be another nice feature of this puzzle. Also, I think there may
> be a problem in that the culling doesn’t always recalculate after
> drags (seemingly never after left-click ones), nor when a new puzzle
> is opened. It seems to recalculate after the first tiny left-drag on
> a newly opened puzzle, and I’m happy to send detailed repro steps
> offline if needed. I’m questioning if the second image Melinda posted
> on the wiki is a culling state you want to allow the user to get into
> - seems like the user should always see a view more like the first
> image she posted.

I like the second view though I totally agree that a slider to control
the number of repeat units would be killer.