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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...
The Phase Transition for Dyadic Tilings
dyadic rectangle tiling phase transition percolation generating function
2011/9/5
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...
The Art of Space Filling in Penrose Tilings and Fractals
Art Space Penrose Tilings and Fractals
2011/9/14
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...
Computing (or not) Quasi-Periodicity Functions of Tilings
Computing (or not) Quasi-Periodicity Functions Tilings
2011/3/2
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...
Computing (or not) Quasi-Periodicity Functions of Tilings
Computing Quasi-Periodicity Functions of Tilings
2010/12/28
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...
Flippable tilings of constant curvature surfaces
Flippable tilings constant curvature surfaces
2011/1/19
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...
On Some fundamental aspects of Polyominoes on Random Voronoi Tilings
fundamental aspects Polyominoes Random Voronoi Tilings
2010/12/9
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...
About some Riemann surfaces and plane tilings
Riemann surfaces orbifold plane tiling geometry of discrete type generalized metric
2009/3/2
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...
About some Riemann surfaces and plane tilings
Riemann surfaces orbifold plane tiling geometry of discrete type generalized metric
2009/1/7
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...