Good luck to the kids doing GCSEs in the future

This is interesting - could it be used for procedural generation of tiles?

Specifically, they found a special more simple type of aperiodic tiling, i think

But mathematicians absolutely had tiled the plane in a way that doesn’t repeat before, just not quite like this one. There’s even a veritasium video about it

Not really oniony though

That thumbnail has a whole lot of repeating going on in it.

I suspect that it doesn't if you look closely at it (either that or they just stupidly used a stock photo of a random pattern).

We are super good at noticing patterns though so even if they aren't 100% identical our brains will interpret it as a pattern. I'm pretty sure this mathematical breakthrough isn't going to be super useful for decorational purposes.

I think it's the stock photo thing, since the one in the article definitely repeats: https://i.imgur.com/yx07VN5.png

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That's not what an aperiodic tiling means.
The analogy is:
3.141414141414141414141414 with 14 repeating infinitely would kinda be like periodic.

The first few digits of pi are:
3.141592653589793238462643383279502884197... but it continues on forever.
That's closer to aperiodic.

What you've done is point at the two instances of 97 and said, "see it repeats".

Just like you will never find a finite series of digits that if repeated will give you pi exactly. You will never find a group that if repeated infinitely, would tile infinitely.

You are wrong though. Think again what it means if the pattern would repeat itself. If you go infinite way that direction, does it ever start from the beginning and repeat itself? The answer is no.

I guess I don't know enough about mathematics? To me it seems like I don't even have to go "infinitely far" when it seems to be doing so just a slight bit over?

You see these small parts that look alike, but they do not repeat in the same order.

I believe that it might be possible, but of course this is not yet peer reviewed so it could be false as well.

Those few similar looking things aren't really repetition of the pattern if you think about it. If their surroundings and placement change every time... And if it never starts again from the beginning it never really repeats.

Ah gotcha, basically I was thinking too granularly.

I think I sorta understand?

Eh, perhaps you are right to some extent about not being oniony enough (it’s my first post to the sub). But this is the first time a plane can be tiled aperiodically with a SINGLE tile. I’ve seen Veritasium’s video a while ago.

I think the researchers used some computer programs to produce patches of tiles procedurally in the paper. Research paper is here free if you want to investigate: https://arxiv.org/abs/2303.10798

Exactly. The research paper goes into this concept actually with larger tiles made with the original tile: https://arxiv.org/abs/2303.10798

Can't use it as wrapping paper, useless.

All the previous tilings needed more than one shape. This is the first that is a single shape repeated.