4 research outputs found
An alternative proof for an aperiodic monotile
We give an alternative simple proof that the monotile introduced by Smith,
Myers, Kaplan and Goodman-Strass is aperiodic.Comment: 19 pages, 19 figure
On the structure of Ammann A2 tilings
We establish a structure theorem for the family of Ammann A2 tilings of the
plane. Using that theorem we show that every Ammann A2 tiling is self-similar
in the sense of [B. Solomyak, Nonperiodicity implies unique composition for
self-similar translationally finite tilings, Discrete and Computational
Geometry 20 (1998) 265-279]. By the same techniques we show that Ammann A2
tilings are not robust in the sense of [B. Durand, A. Romashchenko, A. Shen.
Fixed-point tile sets and their applications, Journal of Computer and System
Sciences, 78:3 (2012) 731--764]