4 ms·

Can someone ELI5 why this is different from Penrose tiling?

by mnw21cam 4y ago

timmg 4y ago
As I understand it: they found a single shape. Where existing Penrose tilings were composed of two (or more) shapes.
- phkahler 4y ago
  But in one sense this is actually 2 shapes that are mirror images. It's still really cool, but I don't think it is ultimately what we've been looking for. As proof that it's not, we all know that a paper presenting one that doesn't need its mirror image to tile the plane aperiodically would still be a big dea.
- pohl 4y ago
  ...they found a single shape Kind of, though, right? One could also look at it as they've found two shapes that happen to be reflections of each other.
  - Jarmsy 4y ago
    Rigid transformations of a single shape https://en.wikipedia.org/wiki/Rigid_transformation https://en.wikipedia.org/wiki/Rigid_transformation
- dekhn 4y ago
  It's not really a single shape since the tiling contains the shape's reflection which is normally considered a different shape since its handedness changes.
sojuz151 4y ago
It is just a single tile type, not two
- phkahler 4y ago
  The two Penrose tiles are also an affine transformation of each other.
  - Jarmsy 4y ago
    Whereas in this new tiling there's a single shape and its rigid transformations.
  - OscarCunningham 4y ago
    I don't think they can be if you want to enforce the matching rules using the tile's shape.
    - hgsgm 4y ago
      > matching rules using the tile's shape. That excludes affine transformation.
lsaferite 4y ago
That's covered in the article.
- ggrelet 4y ago
  It has a paywall.
  - jlund-molfese 4y ago
    But almost every HN post to pay-walled content includes an archive.is link to bypass the paywall.
  - lsaferite 4y ago
    They didn't indicate they couldn't read the article due to a paywall. They just asked for an ELI5 on something that's covered in the 4th paragraph of the article. My reaction would be different if you said you couldn't read the article and asked the same question.
  - schiffern 4y ago
    https://archive.is/RW7Wy https://archive.is/RW7Wy
- deleted 4y ago
  [deleted]

Can someone ELI5 why this is different from Penrose tiling?

timmg 4y ago

As I understand it: they found a single shape. Where existing Penrose tilings were composed of two (or more) shapes.

phkahler 4y ago
But in one sense this is actually 2 shapes that are mirror images. It's still really cool, but I don't think it is ultimately what we've been looking for. As proof that it's not, we all know that a paper presenting one that doesn't need its mirror image to tile the plane aperiodically would still be a big dea.
pohl 4y ago
...they found a single shape Kind of, though, right? One could also look at it as they've found two shapes that happen to be reflections of each other.
- Jarmsy 4y ago
  Rigid transformations of a single shape https://en.wikipedia.org/wiki/Rigid_transformation https://en.wikipedia.org/wiki/Rigid_transformation
dekhn 4y ago
It's not really a single shape since the tiling contains the shape's reflection which is normally considered a different shape since its handedness changes.

sojuz151 4y ago

It is just a single tile type, not two

phkahler 4y ago
The two Penrose tiles are also an affine transformation of each other.
- Jarmsy 4y ago
  Whereas in this new tiling there's a single shape and its rigid transformations.
- OscarCunningham 4y ago
  I don't think they can be if you want to enforce the matching rules using the tile's shape.
  - hgsgm 4y ago
    > matching rules using the tile's shape. That excludes affine transformation.

lsaferite 4y ago

That's covered in the article.

ggrelet 4y ago
It has a paywall.
- jlund-molfese 4y ago
  But almost every HN post to pay-walled content includes an archive.is link to bypass the paywall.
- lsaferite 4y ago
  They didn't indicate they couldn't read the article due to a paywall. They just asked for an ELI5 on something that's covered in the 4th paragraph of the article. My reaction would be different if you said you couldn't read the article and asked the same question.
- schiffern 4y ago
  https://archive.is/RW7Wy https://archive.is/RW7Wy
deleted 4y ago
[deleted]