All reports by Author Scott M. Summers:

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TR08-035
| 18th February 2008
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James I. Lathrop, Jack H. Lutz, Scott M. Summers#### Strict Self-Assembly of Discrete Sierpinski Triangles

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TR08-031
| 14th January 2008
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James I. Lathrop, Jack H. Lutz, Matthew J. Patitz, Scott M. Summers#### Computability and Complexity in Self-Assembly

James I. Lathrop, Jack H. Lutz, Scott M. Summers

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 >>>

James I. Lathrop, Jack H. Lutz, Matthew J. Patitz, Scott M. Summers

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 >>>