3 citations · 7 across the 8 of their papers we have counts for
8 papers
Decision problems on geometric tilings
Benjamin Hellouin de Menibus, Victor Lutfalla, Pascal Vanier
We study decision problems on geometric tilings. First, we study a variant of the Domino problem where square tiles are replaced by geometric tiles of arbitrary shape. We show that…
Polygonal corona limit on multigrid dual tilings
Victor Lutfalla, Kévin Perrot
The growth pattern of an invasive cell-to-cell propagation (called the successive coronas) on the square grid is a tilted square. On the triangular and hexagonal grids, it is an he…
The Domino problem is undecidable on every rhombus subshift
Benjamin Hellouin de Menibus, Victor H. Lutfalla, Camille Noûs
We extend the classical Domino problem to any tiling of rhombus-shaped tiles. For any subshift X of edge-to-edge rhombus tilings, such as the Penrose subshift, we prove that the as…
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…
Geometrical tilings : distance, topology, compactness and completeness
Victor Lutfalla
We present the different distances on tilings of Rd that exist in the literature, we prove that (most of) these definitions are correct (i.e. they indeed define metrics on tilings…
Planar Rosa : a family of quasiperiodic substitution discrete plane tilings with -fold rotational symmetry
Jarkko Kari, Victor Lutfalla
We present Planar Rosa, a family of rhombus tilings with a -fold rotational symmetry that are generated by a primitive substitution and that are also discrete plane tilings, me…
Substitution discrete plane tilings with -fold rotational symmetry for odd n
Jarkko Kari, Victor H. Lutfalla
We study substitution tilings that are also discrete plane tilings, that is, satisfy a relaxed version of cut-and-projection. We prove that the Sub Rosa substitution tilings with a…
An effective construction for cut-and-project rhombus tilings with global n-fold rotational symmetry
Victor H. Lutfalla
We give an explicit and effective construction for rhombus cut-and-project tilings with global n-fold rotational symmetry for any n. This construction is based on the dualization o…