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13artzklauser OP t1_jee245u wrote

Reply to comment by togtogtog in ELI5 The New Shape - The Hat by 13artzklauser

Thank you for your explanation. What do you mean by "which bit of the tiling you look at?"

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togtogtog t1_jee33oa wrote

Imagine the tiling is on a wall outside, and goes on for miles.

Now imagine you wanted to take a photo of the tiling.

With squares, or triangles, you could take two different photos of the wall in two different places, but the photos would be identical. You wouldn't be able to tell them apart.

With 'the hat' the two different photos would be different.

In reality, eventually, 'the hat' tiling does repeat, but not anywhere near enough for it to be noticeable.

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Chromotron t1_jeecof1 wrote

> In reality, eventually, 'the hat' tiling does repeat, but not anywhere near enough for it to be noticeable.

To clarrifiy (for OP): that's only because your photo only shows so much of the thing, and there are is only a finite (but very huge) number of possibilities your photo could show. If your photo zooms out more when needed, every part of the wall would be truly unique.

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13artzklauser OP t1_jefb0ld wrote

Wow you explained it so well!! I got it now. Thank you so much!

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whomp1970 t1_jeeypru wrote

#ELI5

See this??

I'd say that's ... three white birds high, and three white birds wide. You agree? There's like, nine complete white birds you can see. Right?

Now I tell you, that's a snapshot of a much bigger mural, painted on the side of a building.

Can you find out where that 3x3 birds section IS on that huge mural?

You probably can't, because no matter which section you focus in on in the mural, all you see are 3x3 birds.

Make sense so far?

The patterns made by the hats ... they don't repeat like that.

Take a look at JUST the darkest blue ones.. They don't really repeat like the white birds do.

And the math people who figured this out, realized that no matter how big the mural is, the dark blue hats in one section, do not resemble the same pattern of dark blue hats in any other section.

That should blow your mind.

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13artzklauser OP t1_jefc529 wrote

Mind=Blown

Your linked illustrations were very helpful. My understanding of the subject has become better. Thank you.

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whomp1970 t1_jefcv8k wrote

Sometimes it baffles me why more people don't use illustrations or pictures to explain things.

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Priceiswrongbitches t1_jefk1zk wrote

I guess I'm not really getting it. I starred a couple of the dark blue hats here. It looks to me like these are the exact same orientation and every other shape around them is the same too. So this pattern has already repeated itself just within a roughly 10x5 block of hats. Am I missing something?

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Sapphire580 t1_jefzmxr wrote

With the birds, if you slid it over even one row of the pattern it would be the same shape, with the hats you’ve got to go over 10 rows and down 2 to get the pattern to even be similar that means how far would you have to go straight over for the pattern to repeat on the same row, and that’s using one shape.

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whomp1970 t1_jeflppv wrote

It's a lot more complicated than that, and I'm not really the best to explain that. I don't really understand the math myself, but I do understand the basic idea they're explaining.

But I think of of the keys is, you have to look at a much larger patch. Like, everything in that image, plus a few more equally sized blocks, together, don't repeat.

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