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math.DS2024
On the long-range order of the Spectre tilings
Michael Baake, Franz Gähler, Jan MazÃ¡Ä +1
The Spectre is an aperiodic monotile for the Euclidean plane that is truly chiral in the sense that it tiles the plane without any need for a reflected tile. The topological and dy…
math.DS2024
A naturally appearing family of Cantorvals
Michael Baake, Anton Gorodetski, Jan MazáÄ
The aim of this note is to show the existence of a large family of Cantorvals arising in the projection description of primitive two-letter substitutions. This provides a common an…
math.MG2024
On the Fibonacci tiling and its modern ramifications
Michael Baake, Franz Gähler, Jan MazáÄ
In the last 30 years, the mathematical theory of aperiodic order has developed enormously. Many new tilings and properties have been discovered, few of which are covered or anticip…