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
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!
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.
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
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).
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…
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