A new aperiodic tile set containing only 13 tiles over 5 colors is presented. Its construction is based on a technique recently developed by J. Kari. The tilings simulate behavior of sequential machines that multiply real numbers in balanced representations by real constants.

The tile assembly model has allowed the study of the nature’s process of self-assembly and the development of self-assembling systems for solving complex computational problems. Research into this model has led to progress in two distinct classes of computational systems: Internet-sized distributed computation, such as software architectures for computational grids, and molecular computation, s...

We study the times to grow structures within the tile self-assembly model proposed by Winfree, and the possible shapes that can be achieved. Our earlier work was confined to the growth of rectangular structures, in which the rates of attachment of border tiles and rule tiles were the same. By varying the relative rates one can engineer interesting new shapes, which have been observed in the lab...

DNA tile self-assembly has emerged as a rich and promising primitive for nano-technology. This paper studies the problems of minimizing assembly time and error rate by changing the tile concentrations because changing the tile concentrations is easy to implement in actual lab experiments. We prove that setting the concentration of tile Ti proportional to the square root of Ni where Ni is the nu...

A new approach to automatic generation of tile mosaic images containing square tiles suitable for the information hiding purpose is proposed. The generated tile mosaic image contains no overlapping tiles, and the orientations of the tiles are deterministic. The properties of the generated image allow simple tile feature detection, and result in efficient data embedding and extraction. The orien...

In this appendix, we prove the undecidability of the following problems: the constrained domino problem (proved undecidable by Wang): give a tile set and a tile as input, ask whether it is possible to form a tiling of the plane containing the given tile; the unconstrained domino problem (Berger's Theorem): the input is a tile set and the question is whether one can tile the plane with it; the p...

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, ...

The CERES-Maize model was developed to investigate how variations in environmental conditions, management decisions, and genetics interact to a€ect crop development and growth. A tile drainage subroutine was incorporated into CERES-Maize to improve soil-water and nitrogen leaching under subsurface tile drainage conditions. The purpose of this work was to evaluate the soil-water, soil-nitrogen, ...

In this work we propose a generalization of Winfree’s abstract Tile Assembly Model (aTAM) in which tile types are assigned rigid shapes, or geometries, along each tile face. We examine the number of distinct tile types needed to assemble shapes within this model, the temperature required for efficient assembly, and the problem of designing compact geometric faces to meet given compatibility spe...

Tile-based many-core architectures are extensively used in modern system-on-chip designs to achieve scalable computing performance with adequate energy efficiency. Heterogeneity is the key element boost and keep consumption under certain limits for several application domains. However, steady increase of using many custom heterogeneous tiles leads an expansion design integration cost limited re...