Metallic mean Wang tiles and their Rauzy fractals

Sebastien Labbé (U Bordeaux)

Apr 23. 2025, 09:00 — 09:30

We will recall the new family of metallic mean Wang tiles. This is a family of sets of aperiodic Wang tiles (unit squares with labeled edges) whose dynamics involves the positive root of the polynomial $x^2-nx-1$. This root is sometimes called the $n$-th metallic mean, and in particular, the golden ratio when $n=1$ and the silver ratio when $n=2$. The metallic mean Wang shifts are self-similar. The Rauzy fractal defined from the self-similarity is polygonal and forms a partition of the canonical window of a 4-to-2 cut and project scheme.

 

Further Information
Venue:
ESI Boltzmann Lecture Hall
Recordings:
Recording
Files:
Slides
Associated Event:
Uniform Distribution of Sequences (Workshop)
Organizer(s):
Henk Bruin (U of Vienna)
Robbert Fokkink (TU Delft)
Jörg Thuswaldner (Montanuniversität Leoben)