DESCRIPTION OF WELLCOME TILE* The tile is an elongated octagon in shape. It has a blue tinted glaze, and bright blue decoration with the motto in maroon. The sides of the tile are chamfered, and the glaze on the back is in irregular patches. The design of the Society of Apothecaries' Arms-with ribbon-like scrollwork to the sides of Apollo, who has an unusual 'Red Indian' headdress-is quite dist...

Self-assembly is fundamental to both biological processes and nanoscience. Key features of self-assembly are its probabilistic nature and local programmability. These features can be leveraged to design better self-assembled systems. The conventional Tile Assembly Model (TAM) developed by Winfree using Wang tiles is a powerful, Turing-universal theoretical framework which models varied self-ass...

We present here an elementary construction of an aperiodic tile set. Although there already exist dozens of examples of aperiodic tile sets we believe this construction introduces an approach that is different enough to be interesting and that the whole construction and the proof of aperiodicity are hopefully simpler than most existing techniques. Aperiodic tile sets have been widely studied si...

Molecular self-assembly appears to be a promising route to bottom-up fabrication of complex objects. Two major obstacles are how to create structures with more interesting organization than periodic or finite arrays, and how to reduce the fraction of side products and erroneous assemblies. Algorithmic self-assembly provides a theoretical model for investigating these questions: the growth of ar...

We know that tilesets that can tile the plane always admit a quasiperiodic tiling [4, 8], yet they hold many uncomputable properties [3, 11, 21, 25]. The quasi-periodicity function is one way to measure the regularity of a quasiperiodic tiling. We prove that the tilings by a tileset that admits only quasiperiodic tilings have a recursively (and uniformly) bounded quasi-periodicity function. Thi...