Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

A chiral aperiodic monotile

arxiv.org

Post reply on HN
Print view View original

41–50 of 83 posts

Re: A chiral aperiodic monotile

#41

Post by pfd1986 »

ColinWright wrote: post #33

There was a rumour that if they found a chiral aperiodic monotile then they might call it a Vampire Tile, because it doesn't have a reflection. Seems like they didn't go with that. I also see that the old discussion has come up: "But what can it be used for?" These sorts of things are pursued because they are fun, and there's a community of people who find it interesting. Is Rachmaninoff's second piano concerto usefu…

I agree with you that application is not necessarily the point (one of my mentors would always answer this questions with "what's a baby for?")

But in materials science / physics this has been a long standing puzzle: we know that hard polygons vibrating thermally should have a global entropy maximum (ground state) equal to their closest packing configuration. Can this ground state configuration be aperiodic?

So far, all quasicrystals discovered are either not in stable equilibrium or are in equilibrium at that pressure and temperature, but are not the ground state of the material (i.e. at infinite pressure, that QC would be unstable). The discovery of an aperiodic single tile shape means that, in equilibrium, this polygon should have a ground truth that is aperiodic. That basically settles this long-standing question.

Re: A chiral aperiodic monotile

#42

Post by dpflan »

tobr wrote: post #40
dpflan wrote: post #34

Earlier quoted context omitted.

You've reminded me of an older Quora post about: What do grad students in math do all day? Do they just sit at their desk and think? [1] Here are excerpts: """ The main issue is that, by the time you get to the frontiers of math, the words to describe the concepts don't really exist yet. Communicating these ideas is a bit like trying to explain a vacuum cleaner to someone who has never seen one, except you're only al…

Hm, challenge accepted: It uses a fan and a hose to suck up dust. You use it to get rid of dirt in your home. The dirt ends up in a bag. Now and then you must get a new bag, when the old one is full. If you have some tiny item or two that lies in the way of the dust, you will want to put that away, or else it can get lost in the bag.

Nice, I think you’re close to making it have a rhyme scheme… next challenge?

Re: A chiral aperiodic monotile

#43

Post by Thomashuet »

BlueTemplar wrote: post #39
codeflo wrote: post #26

This excites me much more than the original result, which I considered to use two tiles[1]. The fact that it’s a such tiny modification of the original result is crazy. Even if you don’t intend to read the paper, look at the illustrations of the hierarchical substitution algorithm at the top of pages 6 and 7, those are just beautiful. [1] The authors discuss various historic definitions of tilings and whether reflect…

And yet again, it's only available as PDF (rather than the standard HTML), which is super annoying when you have no desire to print it out, especially to view on a small screen. Nor that is seems like this document benefits in any way to be pre-separated into discrete pages (unlike for say, slides).

You can display it in HTML too: https://academ.us/article/2305.17743/

Re: A chiral aperiodic monotile

#44

Post by Thomashuet »

scotty79 wrote: post #35

Is that finally the single tile you can use to cover whole space aperiodically without flipping it upside down?

Yes. Actually if you just want to cover the whole space aperiodically, you can already do it with a simple rectangle, it's just that rectangles also allow you to do it periodically and this new tile only allows aperiodically.

Re: A chiral aperiodic monotile

#45

Post by jhncls »

BlueTemplar wrote: post #39
codeflo wrote: post #26

This excites me much more than the original result, which I considered to use two tiles[1]. The fact that it’s a such tiny modification of the original result is crazy. Even if you don’t intend to read the paper, look at the illustrations of the hierarchical substitution algorithm at the top of pages 6 and 7, those are just beautiful. [1] The authors discuss various historic definitions of tilings and whether reflect…

And yet again, it's only available as PDF (rather than the standard HTML), which is super annoying when you have no desire to print it out, especially to view on a small screen. Nor that is seems like this document benefits in any way to be pre-separated into discrete pages (unlike for say, slides).

Well, this is just a first version, enabling to quickly prove they are the first. The coming days, the internets will be filled with many more webpages than can be possibly read. In the old days, you had to wait many months before something went from found to officially published.

Re: A chiral aperiodic monotile

#46

Post by gilleain »

joshu wrote: post #21

Only slightly related: anyone know how to make porcelain or other normal tiles? If I wanted to redo the bathroom in these or whatever, can they be made?

I recently bought this book : "Arts & Crafts of the Islamic Lands: Principles • Materials • Practice" (Thames and Hudson Ltd, edited by Khaled Azzam).

It has a section on making similar (ish) geometric tiles, although the description is really for square tiles with the geometric design on the face.

From recent experience of drawing and reproducing tiles (including trying to draw the 'hat' monotile) I think the tolerances on your physical tiles would have to be quite small. Either that or make them as a more regular shape and cut out the correct tile from that larger one.

Re: A chiral aperiodic monotile

#47

Post by plagiarist »

sapling-ginger wrote: post #11
onos wrote: post #3

Can anyone explain why people are interested in tilings?

Game graphics. Aperiodic tiling allows us to render a natural-looking surface using a minimal texture graphic file.

I think it is computationally easier and more effective to blend two relatively prime periodic rectangular tilings?

Re: A chiral aperiodic monotile

#50

Post by tiler2915072 »

joshu wrote: post #21

Only slightly related: anyone know how to make porcelain or other normal tiles? If I wanted to redo the bathroom in these or whatever, can they be made?

I’ve spent a decent amount of time figuring out to make porcelain tile. The most reliable way to do so and avoid cracking is to use a plaster mold and push slabs of clay into it. Cookie cutter and other slab methods produce too much cracking without heavy duty equipment or maybe a different clay formulation (I’m using standard porcelain which isn’t the easiest material)
Post reply on HN