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math.DS2022★ 3 cited
Patch frequencies in Penrose rhombic tilings
Jan Mazáč
This short exposition presents an algorithm for an exact calculation of patch frequencies for the rhombic Penrose tiling. We recall a construction of Penrose tilings via dualisatio…
math.DS2022
Correlation functions of the Rudin-Shapiro sequence
Jan Mazáč
In this paper, we show that all odd-point correlation functions of the balanced Rudin--Shapiro sequence vanish and that all even-point correlation functions depend only on a single…
math.DS2022★ 3 cited
Fibonacci direct product variation tilings
Michael Baake, Franz Gähler, Jan Mazáč
The direct product of two Fibonacci tilings can be described as a genuine stone inflation rule with four prototiles. This rule admits various modifications, which lead to 48 differ…