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A chiral aperiodic monotile

arxiv.org

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Re: A chiral aperiodic monotile

#71

Post by eigenket »

bobbylarrybobby wrote: post #70
eigenket wrote: post #53

Earlier quoted context omitted.

HTLM may be the standard for many things, but it is not the standard for academic papers. PDF is the standard. PDF is the optimal format for this use-case, mostly because of existing tooling which makes it very easy to make academic papers as PDFs. As far as I know no tools exist to make something comparable to an academic paper which would improve view-ability on a small screen.

Ok then, PDF is a bad standard. HTML can do all the same stuff and more.

PDF is not a bad standard, the priorities of the people producing scientific papers as pdfs are just not the same as your priorities.

Re: A chiral aperiodic monotile

#72

Post by jameshart »

mabbo wrote: post #55
rthomas6 wrote: post #51

I wish I could buy ceramic Penrose P3 tiles to put on my floor or wall. They 2 different tiles instead of 1, but they're simple diamond shapes, and they tile aperiodically.

This feels like a niche market someone needs to go after. I would love to have a bathroom floor or a kitchen backsplash tiled in 'hat' in 4 colours (ensuring no two same-colour tiles touched of course).

Which raises the question: how many colors of the inverted hat tile would you need? I don’t believe the inverted hats ever need to touch one another…

I suspect, given the 1:1 correspondence to a hex grid (where some of the hexagons map to an inverted/non inverted pair of hats) that they describe in the original paper that it would be possible to tile with just three colors of noninverted hat, and one color of inverted hat.

Re: A chiral aperiodic monotile

#73

Post by masfuerte »

Doxin wrote: post #63
masfuerte wrote: post #59

Earlier quoted context omitted.

With periodic tilings you can uniformly scale them to make room for grout of any thickness. Intuitively, it seems like aperiodic tiles would have to be manufactured slightly too small to leave room for grout, and the tiling would only work if the grout was exactly the right thickness. I wouldn't want to lay them.

Oh that's an interesting point actually. I hadn't considered the tiles needing to be designed around the grout width. Still, I don't think you'd need to be particularly exact with the tiles or grout. In fact it would probably be best to eyeball it and make sure you work outward from a single spot. Trying to tile by e.g. starting around the outside edges and working inwards is bound to get you in trouble with compound…

On reflection I've realised my point was nonsense. Sorry.

Re: A chiral aperiodic monotile

#74

Post by joshu »

tiler2915072 wrote: post #50
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)

any results? What if I made delrin molds?

Re: A chiral aperiodic monotile

#75

Post by alreadydone »

Thomashuet wrote: post #43
BlueTemplar wrote: post #39

Earlier quoted context omitted.

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/

Thanks! arXiv Vanity fails on this one: https://arxiv-vanity.com/papers/2305.17743

Re: A chiral aperiodic monotile

#76

Post by alreadydone »

mabbo wrote: post #55
rthomas6 wrote: post #51

I wish I could buy ceramic Penrose P3 tiles to put on my floor or wall. They 2 different tiles instead of 1, but they're simple diamond shapes, and they tile aperiodically.

This feels like a niche market someone needs to go after. I would love to have a bathroom floor or a kitchen backsplash tiled in 'hat' in 4 colours (ensuring no two same-colour tiles touched of course).

Could the chromatic number be less than 4 (for some or all hat/turtle/spectre tilings)? Note that for the lattice tilings by squares and equilateral triangles the chromatic number is 2, while for the tiling by regular hexagons it is 3. ZeroRogue has drawn dual graphs of hat tilings https://twitter.com/ZenoRogue/status/1639644061823819777 so you can just try to color them.

Re: A chiral aperiodic monotile

#78

Post by zenorogue »

CGamesPlay wrote: post #25

How could you address each tile, to create an aperiodic tile map? Would be a neat tech demo. Like HyperRogue, for example. https://www.roguetemple.com/z/hyper/

Addressing hierarchically constructed tiling is quite similar to addressing hyperbolic tilings. Both the "hat" tiling and "spectre" tiling already work in HyperRogue. (Spectre is not yet released but pushed to GitHub.)

There is a brief explanation here: https://twitter.com/ZenoRogue/status/1638997769141604360

Re: A chiral aperiodic monotile

#79

Post by tiler2915072 »

joshu wrote: post #74
tiler2915072 wrote: post #50

Earlier quoted context omitted.

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)

any results? What if I made delrin molds?

Plaster is better for ceramics because it helps to evenly dry the clay. Can use delrin to make a plaster mold though!

Re: A chiral aperiodic monotile

#80

Post by sudb »

rthomas6 wrote: post #51

I wish I could buy ceramic Penrose P3 tiles to put on my floor or wall. They 2 different tiles instead of 1, but they're simple diamond shapes, and they tile aperiodically.

The discovery of the aperiodic monotile was what finally pushed me over the line to sign up for a ceramics beginners course funnily enough! Give me about a year...
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