Tiling models are classical statistical models in which different geometric shapes, the tiles, are packed together such that they cover space completely. In this paper we discuss a class of two-dimensional tiling models in which the tiles are rectangles and isosceles triangles. Some of these models have been solved recently by means of Bethe Ansatz. We discuss the question why only these models...

Reo is an exogenous coordination model for software components. The informal semantics of Reo has been matched by several proposals of formalization, exploiting co-algebraic techniques, constraint-automata, and coloring tables. We aim to show that the Tile Model offers a flexible and adequate semantic setting for Reo, such that: (i) it is able to capture context-aware behavior; (ii) it is equip...

We exhibit a subset of a finite Abelian group, which tiles the group by translation, and such that its tiling complements do not have a common spectrum (orthogonal basis for their L space consisting of group characters). This disproves the Universal Spectrum Conjecture of Lagarias and Wang [7]. Further, we construct a set in some finite Abelian group, which tiles the group but has no spectrum. ...

A tiling of a subset A of R is a countable set T of tiles in R such that: (1) ∪T = A, (2) whenever S, T belong to T and are distinct we have intS ∩ intT = ∅. Part of a pentagonal tiling is shown in Figure 2. A patch is a tiling by finitely many tiles of a connected, simply connected subset of R which cannot be disconnected by removing one point. To say that a patch A belongs to a tiling T means...

We introduce and study the number of tilings of unit height rectangles with irrational tiles. We prove that the class of sequences of these numbers coincides with the class of diagonals of N-rational generating functions and a class of certain binomial multisums. We then give asymptotic applications and establish connections to hypergeometric functions and Catalan numbers.

For n ≥ 1, let an count the number of ways one can tile a 1 × n chessboard using 1× 1 square tiles, which come in w colors, and 1× 2 rectangular tiles, which come in t colors. The results for an generalize the Fibonacci numbers and provide generalizations of many of the properties satisfied by the Fibonacci and Lucas numbers. We count the total number of 1× 1 square tiles and 1× 2 rectangular t...

Original scientific paper Intelligent system for automated visual quality control of ceramic tiles based on machine vision is presented in this paper. The ceramic tiles production process is almost fully and well automated in almost all production stages with exception of quality control stage at the end. The ceramic tiles quality is checked by using visual quality control principles where main...

We propose the concept of self-assembly of smart tiles, i.e., tiles which possess a local computational device in addition to having edge glues that can be activated or deactivated by signals. We demonstrate the potential of self-assembly with smart tiles to efficiently perform robotic tasks such as the replication of convex shapes. The smart tile assembly system we construct does not make any ...

We consider staged self-assembly, in which squareshaped Wang tiles can be added to bins in several stages. Within these bins the tiles may connect to each other, depending on the glue types of their edges. In general, self-assembly constructs complex (polyomino-shaped) structures from a limited set of square tiles. Previous work by Demaine et al. considered a setting in which assembly proceeds ...

In self-assembly research, reducing the number of distinct tiles necessary to compute functions can make it feasible to implement tile systems to solve complex problems. Existing methods for solving 3-SAT , a well-known NP-complete problem, in the tile assembly model involve either using Θ(n) distinct tiles to nondeterministically decide whether an n-variable Boolean formula is satisfiable or s...