"Systolic" KQ puzzles

[Roice Nelson]

Hey y'all,

I'll post this on discord too, but decided to share it here first. I must admit I am wondering if maybe the email list should be retired at this point. Anyway...

I'm preparing for an "illustrating math" talk in May, and that prep led me to realize there was another (arguably better!) way to do "Earthquake" puzzles in MagicTile... "better" in the sense that it doesn't require detaching stickers from the surface during a twist like the earthquake does. I'm calling these "systolic" puzzles, and like the earthquake they are also based on the "systolic pants decomposition" of a hyperbolic surface.

On the sphere, all loops can be shrunk to a point. But on surfaces with higher genus, there are systoles that can not be completely shrunk. The new puzzles use these systolic loops for the twist cuts, whereas the classical puzzles use shrinkable loops. 

Systolic puzzles are possible for other hyperbolic surfaces too, but I haven't made the implementation general yet. The new ones are in the puzzle tree at "Hyperbolic -> Klein Quartic -> {7,3} 24-Color -> Systolic". As usual, download at roice3.org/magictile

The twists repeat after 4 rotations, like a classic Rubik's cube. You might find the clicking a little strange to get used to, but a hint is to think of them being defined by vertices (a hyperbolic "pair of pants" is defined by 2 hexagons, each centered on a KQ vertex. If you have done the earthquake before, it is very related).

I don't know how hard these are to solve, but some of them are deeper cut, and that generally increases difficulty. I suspect the shallow-cut ones are pretty easy, and hope the deeper cuts have surprises.

Apologies, the puzzle building is a bit slow. I've optimized it some, but it could use some more attention. I'm taking a break for now though - these were kind of difficult to get working!

Here's the original post about the earthquake puzzle btw: Archived Thread ...and pic below of what feels like the most "classic" cut. 

I hope you enjoy!

Roice

[Andrew Farkas]

Hey all,

Thank you so much for the new puzzles, Roice! Luna Harran and I each solved the "systolic classic" puzzle yesterday, and I highly recommend it. Since all the twists use geodesic motion, it really forces you to figure out how to use holonomy to get pieces in the right orientations. It's a bit long, but definitely worth it.

— Andrew

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[Aaron V.]

Please don't discontinue email not everyone uses discord.

To view this discussion visit https://groups.google.com/d/msgid/hypercubing/CALmdYqrt768EeCSxcKJpOx5TtU0bFjmD5DpB7phF6HLVPDD-eQ%40mail.gmail.com.

[Roice Nelson]

Thanks for the input Aaron. I chatted with Melinda on this yesterday too, and we had concluded to not do anything here. I kinda wish I didn't muddy the waters with the suggestion, but it is still good to know email is still wanted!

Roice

[Roice Nelson]

It was so cool to see Andrew and Luna solve the classic so quickly :) The deep-cut versions are still uncharted territory! I also don't know if folks have solved the shallow ones yet either, which may be fun.

I did want to mention... Discord folks found the twisting confusing and had good ideas for improving it. I added highlighting (and a setting to allow turning it on/off) yesterday to help with intuition, but do plan to try to make the improvement ideas happen. That will take a little time though, and the reason I'm mentioning here is that the change will end up affecting log files. Please consider any solutions you make in the meantime as incompatible with future MagicTile versions!

Cheers,

Roice

[Aaron V.]

No worries Roice.

To view this discussion visit https://groups.google.com/d/msgid/hypercubing/CAEMuGXpe4-WT4XDv97j10zb2pJvrPadCqrPyb7rMn5tkWZJsuA%40mail.gmail.com.