We discuss theoretical aspects of the self-assembly of triangular tiles, in particular, right triangular tiles and equilateral triangular tiles, and the self-assembly of hexagonal tiles. We show that triangular tile assembly systems and square tile assembly systems cannot be simulated by each other in a non-trivial way. More precisely, there exists a deterministic square (hexagonal) tile assemb...

Tile logic extends rewriting logic by taking into account side-eeects and rewriting synchronization. These aspects are very important when we model process calculi, because they allow us to express the dynamic interaction between processes and \the rest of the world". Since rewriting logic is the semantic basis of several language implementation eeorts, we can deene an executable speciication o...

Abstract The tile rectification process, also called squaring, consists of machining the edges to make them straight, parallel two by and perpendicular other in addition controlling size (calibrating). current industrial lines are based on multiple heads (abrasive wheels) where characterization process terms product quality power consumption is hard be conducted. In this work we present a labor...

In the classical model of tile self-assembly, unit square tiles translate in the plane and attach edgewise to form large crystalline structures. This model of self-assembly has been shown to be capable of asymptotically optimal assembly of arbitrary shapes and, via information-theoretic arguments, increasingly complex shapes necessarily require increasing numbers of distinct types of tiles. We ...

macroeconomic stabilitv is a major prerequisite fo r real economic growth. in th is study in order to allalyse tile empirical relation ship between macroeconomic instability and per capita real growth, a regression model has been specifi ed for tile iranian economy . in this equation , lour variables including hudget deficit as a ratio to gdp. intlation rate , percenltlge change in tile rea! ex...

In this survey paper, I describe three applications of tilings to music theory: the representation of tuning systems and chord relationships by lattices, modeling voice leading by tilings of n-dimensional space, and the classification of rhythmic tiling canons, which are essentially one-dimensional tilings.

Let T be a tile made up of finitely many rectangles whose corners have rational coordinates and whose sides are parallel to the coordinate axes. This paper gives necessary and sufficient conditions for a square to be tilable by finitely many Qweighted tiles with the same shape as T , and necessary and sufficient conditions for a square to be tilable by finitely many Z-weighted tiles with the sa...

Wang tiles are square tiles with colored edges. We construct an aperiodic set of Wang tiles that is strongly deterministic in the sense that any two adjacent edges of a tile determine the tile uniquely. Consequently, the tiling group of this set is not hyperbolic and it acts discretely and co-compactly on a CAT(0) space.

Aperiodic tilings with a small number of prototiles are of particular interest, both theoretically and for applications in crystallography. In this direction, many people have tried to construct aperiodic tilings that are built from a single prototile with nearest neighbour matching rules, which is then called a monotile. One strand of the search for a planar monotile has focussed on hexagonal ...

The aim of this paper is to collect definitions and results on the main classes of 2D languages introduced with the attempt of generalizing regular and context-free string languages and in same time preserving some of their nice properties. Almost all the models here described are based on tiles. So we also summarize some results on Wang tiles and its applications.