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, ...

Substitutions generate hierarchical colorings of the plane. Despite the non-locality of substitution rules, one can extend them by adding compatible local matching rules to obtain locally checkable colorings as the set of tilings of finite tileset. We show that the resulting tileset can furthermore be chosen strongly deterministic, a tile being uniquely determined by any two adjacent edges. A t...

We present a method for generating well-distributed point according to a given density. Our method is based on a single precomputed tile. The tile is both self-similar and hierarchical. A selfsimilar tile allows to increase the density of points in large steps by recursively subdividing the tile. A hierarchical tile allows to smoothly adjust the density of points. We present an interesting meth...

Tile-based self-assembly is a model of “algorithmic crystal growth” in which square “tiles” represent molecules that bind to each other via specific and variable-strength bonds on their four sides, driven by random mixing in solution but constrained by the local binding rules of the tile bonds. In the late 1990s, Erik Winfree introduced a discrete mathematical model of DNA tile assembly called ...

OIl August 4, 1906, I resected tile left tibial diaphysis of a girl aged fourteen years for sarcoma diagnosed clinically and radiologically (Figs. I and 2). Tile segment excised was replaced by a graft of equal length from tile fibula, the soft tissue attacilments of which were disturbed as little as possible durillg mobilisation in order to preserve tile blood supply. My reason for undertaking...

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...