Winfree (1998) showed that discrete Sierpinski triangles can self-assemble in the Tile Assembly Model. A striking molecular realization of this self-assembly, using DNA tiles a few nanometers long and verifying the results by atomic-force microscopy, was achieved by Rothemund, Papadakis, and Winfree (2004). Precisely speaking, the above self-assemblies tile completely ... more >>>

This paper explores the impact of geometry on computability =
and complexity in
Winfree's model of nanoscale self-assembly. We work in the =
two-dimensional
tile assembly model, i.e., in the discrete Euclidean plane Z x Z. Our =
first
main theorem says that there is a roughly quadratic function f ... more >>>