On times to compute shapes in 2D tile self-assembly

We study the times to grow structures within the tile self-assembly model proposed byWinfree, 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 laboratory. We show that the results from an extension of our earlier stochastic models agree remarkably closely with experimental results. This is an important further demonstration of the validity and usefulness of our stochastic models, which have also been used successfully in studies of error correction in DNA self assembly.