aperiodic monotile
from Diary 2023-03-22
aperiodic monotile
cs_kaplan In a new paper, David Smith, Joseph Myers, Chaim Goodman-Strauss and I prove that a polykite that we call "the hat" is an aperiodic monotile, AKA an einstein. We finally got down to 1! https://arxiv.org/abs/2303.10798 4/6
https://pbs.twimg.com/media/FrtQ6M_WIAE5ns8?format=jpg&name=medium#.png
cs_kaplan Please visit https://cs.uwaterloo.ca/~csk/hat/ for more information. There you'll find an interactive, browser-based application for constructing your own patches o
alytile Big news came in this morning. At last, the Einstein problem in mathematics has been solved. The first discoverer, Dave Smith, is a comrade in artistically exploring tessellations. He drew the fractal tile diagram below in an attempt to understand the mysterious tiles that can only be laid aperiodically!
https://pbs.twimg.com/media/Frur0--agAETCeq?format=jpg&name=medium#.png
alytile Einsteins can be transformed for two dimensions, so there are countless of them. Since this Einstein was discovered artistically by Dave, it is a dream that you might be the one to find other types of Einsteins.
https://pbs.twimg.com/profile_images/3063135117/a699f2d33c38f2b6ee52be1b685cb150_normal.jpeg#.png
alytile .
@cs_kaplan
Thank you for your verification on the substitution rule! I hope this fractal tile could contribute to better understanding of Figure 2.8 of the original paper.
https://arxiv.org/abs/2303.10798
https://pbs.twimg.com/media/FrvvRIgaIAUXpKa?format=jpg&name=medium#.png
alytile This time the Smith Hat tile has two dimensions of deformation freedom and .
@cs_kaplan
provides the animation. Just note that the tiles at the end of the parameter can be periodic tiling (Tile(0,1), Tile(1,1), Tile(1,0) are applicable).
https://pbs.twimg.com/media/Frxi4EmacAAN2mx?format=jpg&name=medium#.png https://pbs.twimg.com/profile_images/1485052872886603778/XIKENQso_normal.jpg#.png
alytile Someone made an application to line them up as soon as possible!
In the beginning, you can do it! and then it collapses in the middle.
I guess any method other than the replacement rule will always fail...
https://pbs.twimg.com/media/FrxjWHjacAAJZF6?format=jpg&name=medium#.png
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