Message #3500

From: Melinda Green <>
Subject: Re: [MC4D] Earthquake Puzzle
Date: Tue, 16 Aug 2016 22:49:47 -0700

On 8/16/2016 8:34 PM, Roice Nelson [4D_Cubing] wrote:
>> 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 <>
> in the Harry Potter movies in which the ends of particular
> staircases detach and reattach to different landings.
> oh yeah, I agree. The pure vertex earthquake would be easier to
> understand, and would be more easily interpreted as vertex-centered.
> I think my wording was confusing.
> When Arnaud and I were talking about this, we were really hoping for a
> twist that slid along the 3 systoles and didn’t detach anywhere. I’d
> like to be wrong, but that seems to be impossible.

Except for the simple genus 1 (torus) case, I’m not certain but I think
you’re right. For some surfaces I think you can slide two of the
systoles but no more.

> The main difficulty in implementation was performance. These twists
> affect a large number of tiles and stickers at once on the universal
> cover, which is where the engine is doing it’s internal drawing. I
> had to parallelize some parts of puzzle building to deal with the
> fallout of that, and had to profile and make various optimizations to
> get it to run reasonably well. In fact, there are some rendering
> artifacts I haven’t eradicated. It would be easy to switch to the
> symmetric vertex-centered earthquake now, but I probably would have
> had to deal with the same sorts of performance issues if I had started
> there. The v2 engine is so much better than my first MagicTile
> attempt, but this puzzle pushed it’s boundaries. At this point, I
> think I have a sense of how a better v3 engine could be designed, but
> I doubt I’ll ever do it.
> The comparison to the grand staircase does seem very apt!
> 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
> <>.
> 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.
> This got me thinking of MC2D and how the reflection twists are like 3D
> rotation twists out of the plane. Perhaps these earthquake twists are
> also "higher-dimensional" in this sense, and maybe there is some
> natural out-of-plane representation like you are describing which
> would be cool.
>> 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.
> I hadn’t thought through the face-centered earthquake case yet, but
> using Arnaud’s applet
> <> I
> just convinced myself there is no possible earthquake face-twist, at
> least not based on systoles. Click the "systolic pants decomp" option
> there and look at, say, the white "pair of pants" in the center. A
> twist will move material within that pair of pants, but at the end of
> the twist the new location of all the shuffled material will need to
> cover the same original area. If you pan certain heptagon vertices or
> edges to the center of the view, you can see that this works. If you
> move a heptagon center to the center of the view, it doesn’t - there’s
> no way to make a 1/7th turn and get the pants to return to covering
> the original area.

OK, well now I’m having an out-of-pants experience but it made me
realize that I didn’t previously make myself clear. Once I clarify
myself, you may conclude that I indeed have gone off into the weeds
regarding catacombs. When talking about the "meta" puzzle, I was
referring to the topology of the surface itself as opposed to the puzzle
within it though maybe they’re always identical. In the case of KQ, the
genus is 3 making the topology that of a ball-and-stick model of a
tetrahedron. When I talk about vertex twisting at the meta level I’m
talking about cuts through the arms of this tetrahedron
<>. So your
current twists appear to cut three arms, twist one of them in place by
180 degrees while swapping the other two. What I called the pure
"vertex" twist would sever three arms that meet at a meta-vertex, rotate
that whole unit 120 degrees and reattach them all. The "edge" twist cuts
4 arms straight through the center of the tetrahedron and rotates one
half by 180 degrees. By now you probably understand what I mean about
"face" twists, which in the case of KQ is identical to a pure vertex
twist opposite a given systolic triangle.