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In his doctoral thesis [3] and subsequent papers [4, 5], Todd Drumm developed a theory of fundamental domains for discrete groups of isometries of Minkowski (2 + 1)-space E, using polyhedra called c...
Abstract: The existence question for tiling of the $n$-dimensional Euclidian space by crosses is well known. A few existence and nonexistence results are known in the literature. Of special interest a...
Abstract: A dyadic tile of order n is any rectangle obtained from the unit square by n successive bisections by horizontal or vertical cuts. Let each dyadic tile of order n be available with probabili...
Incorporating designs into the tiles that form tessellations presents an interesting challenge for artists. Creating a viable MC Escher like image that works esthetically as well as functionally requi...
We know that tilesets that can tile the plane always admit a quasiperiodic tiling [4, 8], yet they hold many uncomputable properties [3, 11, 21, 25].The quasi-periodicity function is one way to measur...
We know that tilesets that can tile the plane always admit a quasiperiodic tiling [4, 8], yet they hold many uncomputable properties [3, 11, 21, 25].The quasi-periodicity function is one way to measur...
We call “flippable tilings” of a constant curvature surface a tiling by “black” and “white” faces, so that each edge is adjacent to two black and two white faces (one of each on each side), the black ...
A combinatorial substitution is a map over tilings which allows to define sets of tilings with a strong hierarchical structure. In this paper, we show that such sets of tilings are sofic, that is, can...
Consider a Voronoi tiling of Rd based on a realization of a inhomogeneous Poisson random set. A Voronoi polyomino is a finite and connected union of Voronoi tiles.In this paper we provide tail bounds ...
Tilings by translation      Tilings  translation        2010/12/9
To tile means to cover a given part of space, without overlaps, using a small number,often just one, of different types of objects. When we are covering the floor of a room using identical rectangular...
In this paper, after a short introduction, we focus on some properties of Riemann surfaces that are connected with aspects from classical and modern crystallography. The third part of the paper cont...
In this paper, after a short introduction, we focus on some properties of Riemann surfaces that are connected with aspects from classical and modern crystallography. The third part of the paper cont...

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