相关论文: A protocol for a message system for the tiles of t…
This paper introduces a method of navigation in a large family of tilings of the hyperbolic plane and looks at the question of possible applications in the light of the few ones which were already obtained.
In this paper we present new results regarding the periodicity of outer billiards in the hyperbolic plane around polygonal tables which are tiles in regular two-piece tilings of the hyperbolic plane.
Tilings of the hyperbolic plane are of significant interest among many branches of mathematics, physics and computer science. Yet, their construction remains a non-trivial task. Current approaches primarily use tree-based recursive…
A semi-regular tiling of the hyperbolic plane is a tessellation by regular geodesic polygons with the property that each vertex has the same vertex-type, which is a cyclic tuple of integers that determine the number of sides of the polygons…
In this paper, we remind previous results about the tilings $\{p,q\}$ of the hyperbolic plane. We introduce two new ways to split the hyperbolic plane in order to algorithmically construct the tilings $\{p,q\}$ when $q$ is odd.
In this work, we describe the first modular, and programmable platform capable of transmitting a text message using chemical signalling -- a method also known as molecular communication. This form of communication is attractive for…
Symmetry sharing facilitates coherent interfaces which can transition from periodic to aperiodic structures. Motivated by the design and construction of such systems, we present hexagonal aperiodic tilings with a single edge-length which…
We describe a method to classify crystallographic tilings of the Euclidean and hyperbolic planes by tiles whose stabiliser group contains translation isometries or whose topology is not that of a closed disk. We tackle this problem from two…
Suppose that wirelessly communicating sensors are placed in a regular fashion on the points of a lattice. Common communication protocols allow the sensors to broadcast messages at arbitrary times, which can lead to problems should two…
In this paper we define an infinite family of triangular tilings of the hyperbolic plane defined by two parameters ranging in the natural nummbers and we give a uniform way to define coordinates for locating the triangles of the tiling.
In this paper, we develop the mathematical tools needed to explore isotopy classes of tilings on hyperbolic surfaces of finite genus, possibly nonorientable, with boundary, and punctured. More specifically, we generalize results on…
We study tilings of the plane composed of two repeating tiles of different assigned areas relative to an arbitrary periodic lattice. We classify isoperimetric configurations (i.e., configurations with minimal length of the interfaces) both…
In this paper, we look at the improvement of our knowledge on a family of tilings of the hyperbolic plane which is brought in by the use of Sergeyev's numeral system based on grossone. It appears that the information we can get by using…
Tilings of a surface of negative Euler characteristic by n-gons with n\ge 7 is a finite problem. We develop the algorithm for finding all the tilings for fixed number of tiles and present the calculation for tilings of surfaces of small…
The top of the attractor $A$ of a hyperbolic iterated function system $\left\{ f_{i}:\mathbb{R}^{n}\rightarrow\mathbb{R}^{n}|i=1,2,\dots,M\right\} $ is defined and used to extend self-similar tilings to overlapping systems. The theory…
This paper shows that a multiple translative tile in the plane must be a multiple lattice tile.
Several articles deal with tilings with squares and dominoes of the well-known regular square mosaic in Euclidean plane, but not any with the hyperbolic regular square mosaics. In this article, we examine the tiling problem with colored…
Recently, hyperbolic lattices that tile the negatively curved hyperbolic plane emerged as a new paradigm of synthetic matter, and their energy levels were characterized by a band structure in a four- (or higher-)dimensional momentum space.…
In this paper I will unite two games, symplectic billiards and tiling billiards. The new game is called symplectic tiling billiards. I will prove a result about periodic orbits of symplectic tiling billiards in a very special case and then…
We introduce a new tiling algorithm for hyperbolic 3-manifolds. We use it to compute the maximal cusp area matrix; this completely characterizes the space of all embedded and disjoint cusp neighborhoods. As another application of our work,…