Message #2241

From: Melinda Green <melinda@superliminal.com>
Subject: Re: [MC4D] Re: color graphs of MagicTiles
Date: Sun, 03 Jun 2012 12:40:02 -0700

Ah ha! I should have thought about that for a few more seconds before
asking because the whole point was because this was another screwy
topology and I forgot to look for the screwiness.

I did briefly look at the sorts of paths that the petals can take and
they are quite interesting. Alternating LLRRLL, etc. can create a
straightish ziz-zag path that miraculously involves all faces except
those two odd ones, whereas if you start with one of those odd faces you
hit a dead-end at the other one! Fascinating.

And yes, they do look a lot like streams of bubbles filling the air. I
like it!
-Melinda

On 6/3/2012 10:07 AM, Roice Nelson wrote:
>
>
>
> On Sat, Jun 2, 2012 at 6:29 PM, Melinda Green wrote:
>
>
> And Roice, how about a pure edge-turning 8-color {3,5} so that I
> can compare against the similar {8,4}s?
>
>
> An edge-only puzzle for that tiling turns out to be impossible. To
> see why, pull up the FE version and highlight the edge cuts on the
> cyan face (or the purple one). Now imagine increasing the size of
> these cuts. If we configure an edge-only version, we can’t make the
> cuts big enough to lead to non-trivial scrambling without also causing
> identified cuts to intersect themselves.
>
> On the positive side, the FE puzzle is quite similar in feel to other
> edge-only puzzles, and I bet it could be solved with only [1,1]
> commutators. I went ahead and configured similar FE versions for the
> {8,4}s, in case that would be helpful for comparisons. These FE
> puzzles make me think of bubbles, which might be a nice name for them :)
>
> seeya,
> Roice
>
>
>