Message #3498

From: Melinda Green <melinda@superliminal.com>
Subject: Re: [MC4D] Earthquake Puzzle
Date: Mon, 15 Aug 2016 19:35:31 -0700

On 8/15/2016 8:45 AM, Roice Nelson roice3@gmail.com [4D_Cubing] wrote:
>
> Thanks for your response Melinda. Your email really adds to the
> description of the twisting! I have some inlines below…
>
> I stared a bit at this image
> <http://math.ucr.edu/home/baez/pentacontihexahedron2.jpg> to try
> to understand what’s going on. From your description it sounds
> like each twist cuts one off the three struts of a red hub, turns
> one of those arms around its cut, flipping the hub over and
> swapping the other two struts. Is that correct?
>
>
> Yes, exactly!
>
> That seems to suggest that the scrambling twists plus solving
> twists is always even. It also suggests there are other types of
> possible twists. One of them seems like the most natural one to me
> which twists a selected strut by 180 degrees, swapping the hubs at
> each end. That one seems to be a "true" Big Chop-like deep cut
> since it’s symmetric on both sides. Actually, it looks like there
> are more than one way to do that too though the simple geometric
> rotation seems the most natural.
>
>
> Very cool, I hadn’t considered this. I think the twist you envision
> will swap two sets of systoles, with four cuts total, and all of them
> will detach during the twist.

Exactly.

>
> Your idea made me think of something else as well… I had thought
> about systolic twists on a torus puzzles, which could be done without
> detaching the surface at all. But I hadn’t thought about doing twists
> with two "around the horn" cuts on a single strut of the genus-3
> surface. I’m guessing the cuts wouldn’t be geodesics or shortest
> length in this case, but it still does seem like it should be
> possible. I’ll have to think on that more.

That’s sort of what I was expecting from your initial description. It
reminds me of the Dual Circle
<https://www.youtube.com/watch?v=uOAwjIebYDA> puzzle which has an
intriguing resemblance to the MC4D duoprisms puzzles.

>
> Lots of possibilities!
>
> The really neat thing about your new feature is that it works at a
> kind of meta level by operating on the hubs and struts of high
> genus surfaces similarly to how we’ve been twisting vertices and
> edges within them. Heck, it looks like you could even create
> puzzles within puzzles where you manipulate the structure like you
> are doing now while also allowing users to twist the elements
> within the texture with a modifier key or something. Does that
> make any sense?
>
>
> Yeah! One thing about the earthquake twists is that they are
> "centered" on vertices, so a natural "twist within a twist" would be
> the normal vertex-centered twist MagicTile already supports.
>
> In fact, you can do an earthquake twist where all 3 systoles break
> from the surface instead of just two of them, which makes it a little
> easier to see why earthquakes are vertex-centered. This is like a
> 3-cycle rotation about a hub. I didn’t include that twisting because
> I thought it might make the puzzle easier if more permutation options
> were allowed.

It’s definitely trippy to see one systole twisting in place while the
others detach and reattach but I don’t understand how that makes
anything more clear. The pure vertex earthquake twist is more symmetric
and I’d expect it would be easier to understand, no? Maybe you’re even
making it more difficult on yourself to support those non-detaching
earthquake twists. Was that a big part of what made the implementation
difficult? In the current case of one rotating systole and the rest
moving, I’m often reminded of the Grand Staircase
<https://www.youtube.com/watch?v=uFvizAQHJz8> in the Harry Potter movies
in which the ends of particular staircases detach and reattach to
different landings.

Now here’s a truly crazy idea. In trying to imagine both the 2D and 3D
aspects together, I imagined the current 2D view as a plane in 3-space,
intersected by 3D arches. One could initiate earthquake twists on the 3D
structure, and 2D twists in the plane. Looked at this way it bares a
striking resemblance to that amazing rendering you did called Hyperbolic
Catacombs
<http://gallery.bridgesmathart.org/exhibitions/2015-joint-mathematics-meetings/roice3>.
I never did follow what that thing was so I have no idea if shares any
connection with this puzzle, but if it does, then it suggests the
possibility of a wonderfully immersive VR puzzle.

> Plus the controls were already difficult to try to make intuitive.
>
> I think the twist you described earlier would be an edge-centered
> earthquake.

Exactly. The only missing analog would be an earthquake face twist. On
this puzzle, that’s equivalent to a twist of the opposite vertex but in
larger puzzles may be interesting though the UI challenges makes me
think it’s probably not worth attempting.

> Assuming I haven’t gone completely off into the weeds, I’d love to
> see the {7,3} or other IRPs supported in this way. None of this is
> to pressure you to implement anything but rather to try to
> understand what this new puzzle means and where it could go.
>
>
> Totally, I want to see this too, and I have some surprises in this
> direction I’ve been working on with Burkard. I’m nowhere near there
> yet with the earthquake puzzle, and not even there with the classic
> KQ, but we will have some cool stuff to show. Hopefully what you are
> picturing will come eventually too!
>
> Best,
> Roice
>
> P.S. I’ve been checking all changes into GitHub, and anyone who is
> interested in participating in the development is welcome. Hopefully
> looking at recent code diffs could help others find their way around
> the code base.

Here’s the link for reference: https://github.com/roice3/MagicTile

Great stuff, Roice!
-Melinda