i'm disappointed to see that filling the plane requires flipping some of the tiles. but it's still magically beautiful.

@artistjohnallen

Жыл бұрын

however, not the chevron

@matejlieskovsky9625

Жыл бұрын

@@artistjohnallen Yeah, but the chevron is not aperiodic.

@ThatOneLadyOverHere

Жыл бұрын

​@@matejlieskovsky9625 why is it here if it's not aperiodic? It looks to me to like is...

@matejlieskovsky9625

Жыл бұрын

@@ThatOneLadyOverHere Ok, sorry, I need to be a bit more precise with my words. The chevron does not *have* to be aperiodic. That is why the chevron is not a solution to the einstein problem. Same thing goes for the other simple shape that kinda looks like a 6. Why they are here? If I understand it correctly, the authors use those two simpler shapes to show some properties of the tiling with their shape, leading up to the proof that their shape is indeed always aperiodic.

@ThatOneLadyOverHere

Жыл бұрын

@Matej Lieskovský ok, so in this case they are still tiling aperiodically they just don't have to. But the goal was to find a shape that could only tile aperiodically then?

Can anyone here speak to the nature of the color coding? The dark blue tiles are reversed, I get that for sure. It seems the light blue ones are touching a significant portion of the blue one. I cannot seem to find any real pattern to the white and grey tiles, I feel like I’m missing something obvious.

For anyone confused as to what's going on, Ayliean posted a video explaining the concept and why this is significant (though as you can see in the comments, it's divisive at best).

The real clue is the first image. This tile is, as far as I see, THE surprise: in this stage, all tiles share the shape, six edges and perfect symetry. If the 13 edge tile can make a non repetitive pattern, then this shape does what? I'm no mathematician, but that's confusingly amazing.

@matejlieskovsky9625

Жыл бұрын

Even 2x1 rectangles *can* tile the plane aperiodically. The complicated tile *must* tile the plane aperiodically. Huge difference (to a mathematician).

Now make a hyperbolic einstein. Should be fairly simple.

@jasondelong83

Жыл бұрын

The original paper shows exactly that, but not much people read deep into the original papers nowadays.

@asheep7797

Жыл бұрын

A pentagon, right?

Quilting pattern anyone? ;)

They also showed that there are an infinite number of unique Einstein tiles.

Is there any constant to be found? Any constant between the lenght of the sides, the O, the A? what? if it was streched out in 3D would its volume be the same? no?

I don't get it. The 7-sided morph ( 0:16 ) also conformably tiles the plane. Or does it do so periodically?

@suncho6502

Жыл бұрын

Or the six sided at the beginning. I don't understand either.

@JohnSchwabacher

Жыл бұрын

That's right: they allow periodic tilings. Not all of the tiles in this "morph" are Einstein tiles, i.e. they don't all force only aperiodic tilings. Only the "hat" does that.

@nonyobisniss7928

Жыл бұрын

@@JohnSchwabacher Not quite. They all force only aperiodic tilings except the two end ones 0:00 and 0:16.

@ThatOneLadyOverHere

Жыл бұрын

​@Nonyo Bisniss so the tape dispenser and chevron are periodic?

@matejlieskovsky9625

Жыл бұрын

@@ThatOneLadyOverHere they can be. Many tiles *can* be aperiodic, we're looking for one that *always* is.

I don´t understand, why it took so long to find this, it seems so easy and obvious

They sey it's not repeating in shapes yet on the left the two dark ablue are always the same

@dannyx1791

Жыл бұрын

I don't suppose you found an answer to this? I've read about it in New Scientist, but it doesn't explain what 'non-repeating' actually means. The individual tile itself is repeated. What constitutes a pattern?

@NILGMTRY

Жыл бұрын

@@dannyx1791 it means there are no translation symetries, if you move any tiling created by this shape in any direction and any distance you are going to see something different than what you started with.

@leodellapietra

Жыл бұрын

@@NILGMTRY roto-translation

@deadseid

Жыл бұрын

@@dannyx1791 similar to how there are repeating sequences within pi, but never a pattern of those sequences.

I think that the royal institute owes him some money

@gdminus1726

9 ай бұрын

it's obvious things that humans are lacking from their knowledge and life. That's why we are still primitive and not a very advanced civilization

so it's a video of tile..? so it's not a single tile but a collection of many tiles... like infinitely many... ok. Cool, I guess. but does is prove anything new, tho? Like don't we live in an infinitely "tiling" universe?

@cm-jr9vt

9 ай бұрын

Aperiodic mono tile

🌌☯️🌌