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/
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,
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:
> 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."
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.)
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...
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.
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.
Harry probably shouldn't feel so bad about the bug in the published listing.
I typed in plenty of games from computer mags in the 80s and they almost never worked first time. The problems were sometimes my errors (have you ever tried retyping 100s of lines of small-primt code?) and sometimes present in the published listings.
Whichever, the errors meant that reasonable debugging skills were necessary to get any of them working. It was good training.
