We prove that if a set X ⊆ Z weakly self-assembles at temperature 1 in a deterministic (Winfree) tile assembly system satisfying a natural condition known as pumpability, then X is a finite union of semi-doubly periodic sets. This shows that only the most simple of infinite shapes and patterns can be constructed using pumpable temperature 1 tile assembly systems, and gives evidence for the thes...

This report was written by Dr. Donald Fraser of the Department of Paediatrics, Universit!/ of Toronto and The Hospital for Sick Children, Toronto, Ontario, Canada, in consultation with tile Conirnittee Ofl Nutrition of the American Academy of Pediatrics. The /)OSltiOhb taken on the issue examined reflects the current opinion of tile Committee and i)rovi(les tile .ccie iti/ic background for the ...

A tile is a bounded subset of the plane, copies of which may be used to cover the whole plane without gaps or overlap. There are many sources (such as [1]) of beautiful images involving tiling, from medieval Islamic art, through Escher, to more modern work. Perhaps the simplest example of a tile, though, is a solid square, which may tile the plane in a familiar checkerboard pattern. The square ...

We prove that if a set X ⊆ Z weakly self-assembles at temperature 1 in a deterministic (Winfree) tile assembly system satisfying a natural condition known as pumpability, then X is a finite union of semidoubly periodic sets. This shows that only the most simple of infinite shapes and patterns can be constructed using pumpable temperature 1 tile assembly systems, and gives evidence for the thesi...

Self-assembly, the process by which objects autonomously come together to form complex structures, is omnipresent in the physical world. A systematic study of self-assembly as a mathematical process has been initiated. The individual components are modelled as square tiles on the infinite two-dimensional plane. Each side of a tile is covered by a specific “glue”, and two adjacent tiles will sti...

Riparian buffers are a proven practice for removing NO from overland flow and shallow groundwater. However, in landscapes with artificial subsurface (tile) drainage, most of the subsurface flow leaving fields is passed through the buffers in drainage pipes, leaving little opportunity for NO removal. We investigated the feasibility of re-routing a fraction of field tile drainage as subsurface fl...

It is shown that an equilateral convex pentagon tiles the plane if and only if it has two angles adding to 180 o or it is the unique equilateral convex pentagon with Although the area of mathematical tilings has been of interest for a long time there is still much to be discovered. We do not even know which convex polygons tile the plane. Furthermore, for those polygons which do tile, new tilin...

Tile logic extends rewriting logic, taking into account rewriting with side-eeects and rewriting synchronization. Since rewriting logic is the semantic basis of several language implementation eeorts, it is interesting to map tile logic back into rewriting logic in a conservative way, to obtain executable speciications of tile systems. The resulting implementation requires a meta-layer to contr...