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I don't understand what's so magical about the hat. It's a non-square shape that repeats.
by flangola7 4y ago
I don't understand what's so magical about the hat. It's a non-square shape that repeats.
- brickers 4y agoit’s a non-square shape that does not and cannot repeat
- klyrs 4y agoTechnically the shape itself repeats like a mug, infinitely tiling the plane. However, that tiling is not overly repetitive -- if it's like the Penrose tiling, it can be self-similar in a handful of rotations about a single origin, but unlike a square tiling, does not admit infinitely many self-similarities.
- flangola7 4y agoHow can you cover infinite surface without infinite number of objects?
- contravariant 4y agoI mean the obvious answer is to use infinitely large objects, but I think you're just being asinine at this point.
- flangola7 4y agoNo I really don't understand. I look at the image and clearly see the same shape repeated again and again
- brickers 4y agoYou’re right that the shape is used again and again, but the pattern of how it is laid does not repeat. So the new thing here is that there is a single shape that can cover the plane AND that it does this without the pattern repeating (and as an aside it cannot be made to do it with repeats)
- uoaei 4y ago"Aperiodic" is the opposite of "periodic"
- mcphage 4y agoWhen people talk about patterns that repeat, they usually mean one of the 17 wallpaper groups (https://en.wikipedia.org/wiki/Wallpaper_group https://en.wikipedia.org/wiki/Wallpaper_group). And people are interested in patterns that do tile the grid completely, but don't match one of those patterns. Originally it took thousands, but people had gotten it down to 2 shapes that together tiled the grid completely, but not in one of those 17 groups. Now, people have gotten it down to a single shape that—by itself—tiles the pattern infinitely, but not in one of those 17 groups.