Einstein tiles..
Mar. 25th, 2023 06:31 pm![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
milktreetl;dr: someone figured out how to do a Penrose-like never-repeating pattern, but with a single tile.
“einstein” means “one stone” in this context, not the physicist.
https://www.sciencenews.org/article/mathematicians-discovered-einstein-tile
“A 13-sided shape known as “the hat” has mathematicians tipping their caps.
It’s the first true example of an “einstein,” a single shape that forms a special tiling of a plane: Like bathroom floor tile, it can cover an entire surface with no gaps or overlaps but only with a pattern that never repeats.
“Everybody is astonished and is delighted, both,” says mathematician Marjorie Senechal of Smith College in Northampton, Mass., who was not involved with the discovery. Mathematicians had been searching for such a shape for half a century. “It wasn’t even clear that such a thing could exist,” Senechal says.”
The thing that I don’t quite get is how it can possibly never repeat. Infinity is rather large, and 13 sides is not. There’s a limited way two tiles can touch, right? So why doesn’t that lead to repeated pattern? Maybe I don’t understand what “aperiodic” means.
Anyway, it’s super cool, and I want to tile my kitchen and bathroom with them now.
“einstein” means “one stone” in this context, not the physicist.
https://www.sciencenews.org/article/mathematicians-discovered-einstein-tile
“A 13-sided shape known as “the hat” has mathematicians tipping their caps.
It’s the first true example of an “einstein,” a single shape that forms a special tiling of a plane: Like bathroom floor tile, it can cover an entire surface with no gaps or overlaps but only with a pattern that never repeats.
“Everybody is astonished and is delighted, both,” says mathematician Marjorie Senechal of Smith College in Northampton, Mass., who was not involved with the discovery. Mathematicians had been searching for such a shape for half a century. “It wasn’t even clear that such a thing could exist,” Senechal says.”
The thing that I don’t quite get is how it can possibly never repeat. Infinity is rather large, and 13 sides is not. There’s a limited way two tiles can touch, right? So why doesn’t that lead to repeated pattern? Maybe I don’t understand what “aperiodic” means.
Anyway, it’s super cool, and I want to tile my kitchen and bathroom with them now.
no subject
Date: 2023-03-25 11:19 pm (UTC)no subject
Date: 2023-03-30 10:18 pm (UTC)I can make a bigger one or one with fewer tiles or whatever.
no subject
Date: 2023-04-01 09:43 pm (UTC)