A predicted quasicrystal is based on the 'einstein' tile known as the hat | Hacker News Reader

A predicted quasicrystal is based on the 'einstein' tile known as the hat

sciencenews.org

60 pointsthunderbong25 comments

One of the coolest things about the hat tile is that it was discovered by a hobbyist playing with puzzle software. There's a great Quanta story about this: https://www.quantamagazine.org/hobbyist-finds-maths-elusive-....

There's a great video explanation too with interviews of people behind the scenes:

https://youtu.be/4HHUGnHcDQw?si=APHEQwVxTvcOfC5c&t=382

I find it fascinating. It is inspiring and humbling. Not only he found the hat, he found also a different shape "the turtle". Basically out of thin air and then how they combine those two to find a real monotile. I am writing a bit about this:

https://www.nhatcher.com/post/on-hats-and-sats/

If they found the material properties of that tile, they would be doing 'spectroscopy'.

Jim's blog post about his discovery is also delightful to read: https://hedraweb.wordpress.com/2023/03/23/its-a-shape-jim-bu...

His offhand mention of "Craig's SAT Solver" opened a rabbit hole for me. I put together a blog post on how to draw the tiling without knowing the recursive structure by just feeding the shape into z3: https://www.hgreer.com/HatTile/

> using a SAT solver (in this case, Z3)

isn't z3 SMT solver, not SAT?

Z3 has both, but the tool they are using is the SAT solver.

Hi @QuadmasterXLII, you linked my blog in yours! Thanks, I feel honored! I found your blog halfway going through my own rabbit whole. I think had I seen it before embarking into the project I would have just use yours. That being said it is been a fun ride. It's interesting that we both got triggered by "Craig's SAT solver". Thanks again,

Nicolás

> Although the material is entirely theoretical for now [...] For example, scientists could manually place molecules on a surface in a pattern matching the hat tiling.

Does this even qualify as theoretical? It sounds more like "we did geometry and called it physics."

Crystallography is basically just 3d geometry (with some DE) anyway.

The hat tiling is 2D. There are some 2D crystals like graphene, but those are interesting because they actually exist.

Many bits of physics start out as "did geometry". Will this particular idea pan out? Probably not. Should it be the subject of popular press at this stage? Probably not. But it's worth having scientists explore the possibilities. The paper might be interesting to specialists, once published, https://journals.aps.org/prl/accepted/33074Yb3Ufa1478fd33b04...

Quasicrystals is an excellent example. Penrose tiles were invented in 1974, but quasicrystals were discovered in 1982.

A decade ago I would have agreed with you. But then I discovered the topic of five-symmetries and my absolute favorite non-toxic non-stick pans are coated with that alloy (not long ago deemed impossible) that has the five way symmetry.

So the practical applications are not far behind for these "only 2D" crystals.

Looks like you're referring to https://en.wikipedia.org/wiki/Quasicrystal#Applications, marketed as Cybernox.

But 5 to 13 is a huge jump.

https://www.technologyreview.com/2011/10/12/190784/the-quasi... says "They closed the production line because they had a few problems in the reaction of the coating with salt. If people cook with a lot of salt it will etch the quasicrystalline coating. People didn’t like it, so they did not continue."

I see comments about Cybernox from 2001, so the patents might've expired by now.

It's, in practice, applied gradient-based optimization on a geometrically-defined objective, which means if you squint hard enough it's machine learning.

(I am a crystallographer turned machine learning engineer.)