23 citations · 120 across the 28 of their papers we have counts for
10 papers · 1 filter
Square-Triangle Tilings: Lift & Flip to Sample?
Thomas Fernique, Olga Mikhailovna Sizova
We introduce an elementary transformation called flips on tilings by squares and triangles and conjecture that it connects any two tilings of the same region of the Euclidean plane…
Geometrical Penrose Tilings are characterized by their 1-atlas
Thomas Fernique, Victor Lutfalla
Rhombus Penrose tilings are tilings of the plane by two decorated rhombi such that the decoration match at the junction between two tiles (like in a jigsaw puzzle). In dynamical te…
Ammann Bars for Octagonal Tilings
Thomas Fernique, Carole Porrier
Ammann bars are formed by segments (decorations) on the tiles of a tiling such that forming straight lines with them while tiling forces non-periodicity. Only a few cases are known…
Purely local growth of a quasicrystal
Thomas Fernique, Ilya Galanov
Self-assembly is the process in which the components of a system, whether molecules, polymers, or macroscopic particles, are organized into ordered structures as a result of local…
Density of Binary Disc Packings: Playing with Stoichiometry
Thomas Fernique
We consider hard-disc mixtures with disc sizes within ratio , that is, the small disc exactly fits in the hole between four large discs. For each prescribed stoichiomet…
Density of Binary Disc Packings: The 9 Compact Packings
Nicolas Bédaride, Thomas Fernique
A disc packing in the plane is compact if its contact graph is a triangulation. There are values of such that a compact packing by discs of radii and exists. We pro…