Escher tiling is well known as a tiling that consists of one or a few recognizable figures, such as animals. The Escherization problem involves finding the most similar shape to a given goal figure that can tile the plane. However, it is easy to imagine ...

Current work presents a new approach to quantum color codes on compact surfaces with genus g ≥ 2 using the identification of these surfaces with hyperbolic polygons and hyperbolic tessellations. We show that this method may give rise to color codes with ...

In this paper we present some classes of topological quantum codes on surfaces with genus g ≥ 2 derived from hyperbolic tessellations with a specific property. We find classes of codes with distance d = 3 and encoding rates asymptotically going to 1, 1/...

We prove that a surprisingly simple algorithm folds the surface of every convex polyhedron, in any dimension, into a flat folding by a continuous motion, while preserving intrinsic distances and avoiding crossings. The flattening respects the straight-...

In 1998 and in 2001, the author introduced a Fibonacci technique in order to study two tessellations of the hyperbolic plane, the pentagrid and the heptagrid, the tilings {5, 4} and {7, 3} respectively. In this paper, we revisit the application of the ...

In this paper we present six classes of topological quantum codes (TQC) on compactsurfaces with genus g ≥ 2. These codes are derived from self-dual, quasi self-dual anddenser tessellations associated with embeddings of self-dual complete graphs and com-...

In this paper, we look at the following question. We consider cellular automata in the hyperbolic plane, see [6, 22, 9, 12] and we consider the global function defined on all possible configurations. Is the injectivity of this function undecidable? The ...

In this paper, we look at the following question. We consider cellular automata in the hyperbolic plane, see [6, 22, 9, 12] and we consider the global function defined on all possible configurations. Is the injectivity of this function undecidable? The ...

In this paper, we construct the first weakly universal cellular automaton on the ternary heptagrid. It requires six states only. It provides a universal automaton with less states than in the case of the pentagrid where the best result is nine states, a ...

This paper addresses the methodological issues of developing and visualising added value geo-enabled content for mobile information systems. The research was carried out under the framework of WebPark, an EC-IST R&D project that developed a location ...

"Escherization" [9] is a process that finds an Escher-like tiling of the plane from tiles that resemble a user-supplied goal shape. We show how the original Escherization algorithm can be adapted to the dihedral case, producing tilings with two distinct ...

We present Najm, a set of tools built on the axioms of absolute geometry for exploring the design space of Islamic star patterns. Our approach makes use of a novel family of tilings, called "inflation tilings," which are particularly well suited as ...

Screen space rendering statistics are gathered from 150 3D objects, each modeled by between 2-K and 40-K triangles. While there is wide variance by individual object, the overall trend is that the distribution of triangles by screen size is roughly ...

A blind noise variance algorithm that recovers the variance of noise in two steps is proposed. The sample variances are computed for square cells tessellating the noise image. Several tessellations are applied with the size of the cells increasing ...

This paper presents the solution of the following optimization problem that appears in the design of double-loop structures for local networks and also in data memory, allocation and data alignment in SIMD processors.