23 citations · 120 across the 28 of their papers we have counts for
5 papers · 1 filter
Canonical projection tilings defined by patterns
Nicolas Bédaride, Thomas Fernique
We give a necessary and sufficient condition on a -dimensional affine subspace of to be characterized by a finite set of patterns which are forbidden to appear in…
Weak colored local rules for planar tilings
Thomas Fernique, Mathieu Sablik
A linear subspace of has colored local rules if there exists a finite set of decorated tiles whose tilings are digitizations of . The local rules are weak if…
Weak local rules for planar octagonal tilings
Nicolas Bédaride, Thomas Fernique
We provide an effective characterization of the planar octagonal tilings which admit weak local rules. As a corollary, we show that they are all based on quadratic irrationalities,…
No Weak Local Rules for the 4p-Fold Tilings
Nicolas Bédaride, Thomas Fernique
On the one hand, Socolar showed in 1990 that the n-fold planar tilings admit weak local rules when n is not divisible by 4 (the n=10 case corresponds to the Penrose tilings and is…
When periodicities enforce aperiodicity
Nicolas Bédaride, Thomas Fernique
Aperiodic tilings are non-periodic tilings defined by local rules. They are widely used to model quasicrystals, and a central question is to understand which of the non-periodic ti…