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math.MG2023
Planar aperiodic tile sets: from Wang tiles to the Hat and Spectre monotiles
Tinka Bruneau, Michael F. Whittaker
A brief history of planar aperiodic tile sets is presented, starting from the Domino Problem proposed by Hao Wang in 1961. We provide highlights that led to the discovery of the Ta…
math.MG2019
An aperiodic monotile that forces nonperiodicity through dendrites
Michael Mampusti, Michael F. Whittaker
We introduce a new type of aperiodic hexagonal monotile; a prototile that admits infinitely many tilings of the plane, but any such tiling lacks any translational symmetry. Adding…