Discrete tomography deals with reconstructing finite spatial objects from their projections. The objects we study in this paper are called tilings or tile-packings, and they consist of a number of disjoint copies of a fixed tile, where a tile is defined as a connected set of grid points. A row projection specifies how many grid points are covered by tiles in a given row; column projections are ...

A Wang tile [12] is a unit square with each edge colored from a finite set of colors Σ. A set S of Wang tiles is said to tile a planar grid Z if copies of tiles from S can be placed, one at each grid position, such that abutting edges of adjacent tiles have the same color. Multiple copies of any tile may be used, with no restriction on the number. If we allow the tiles to be rotated or reflecte...

Thanks to a careful study of elementary properties of two-bytwo substitution systems, we give a complete self-contained elementary construction of an aperiodic tile set and sketch how to use this tile set to elementary prove the undecidability of the classical Domino Problem.

The two-by-two dot centering model enables predicting the spectral reflectance of color halftones and does not depend on a specific halftoning algorithm. It requires measuring the reflectances of a large number of two-by-two calibration tile patterns. Spectral measurement of hundreds or thousands of tile patterns is cumbersome and time consuming. In order to limit the number of measurements, we...

Centuries ago, European builders developed a reliable means of installing tile for high-traffic, high-use applications which relied on the laying of a sand strata between the structural substrate and the mortar-bed/tile composite top layer. Due to space (height) requirements and other concerns, the sand strata method for tile installation is, for all practical purposes, extinct. Modern theory, ...

Paediatrics [<παῖς (pais=child) + 'ἰάομαι/ἰῶμαι' (iaome/iome=healing)] is the science and the art of treating infants, children and adolescents, supporting their health, growth and development and ensuring their opportunity to achieve full potential in adulthood (1). As a stimulating, diverse and hugely rewarding medical specialty, it manages a wide range of medical conditions, diseases and dis...

Although the design of DNA tiles has been optimised for efficient and specific self-assembly, assembly errors occur so often that applications for molecular computation remain limited. We propose the use of an enveloped tile consisting of a DXbase tile that carries a protector tile to suppress erroneous tile assembly. The design of the enveloped tile promotes the dissociation of the protector t...