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2008
Springer

Self-assembly of Discrete Self-similar Fractals

8 years 4 months ago
Self-assembly of Discrete Self-similar Fractals
In this paper, we search for theoretical limitations of the Tile Assembly Model (TAM), along with techniques to work around such limitations. Specifically, we investigate the self-assembly of fractal shapes in the TAM. We prove that no self-similar fractal weakly self-assembles at temperature 1 in a locally deterministic tile assembly system, and that certain kinds of discrete self-similar fractals do not strictly self-assemble at any temperature. Additionally, we extend the fiber construction of Lathrop, Lutz and Summers (2007) to show that any discrete self-similar fractal belonging to a particular class of "nice" discrete self-similar fractals has a fibered version that strictly self-assembles in the TAM.
Matthew J. Patitz, Scott M. Summers
Added 19 Oct 2010
Updated 19 Oct 2010
Type Conference
Year 2008
Where DNA
Authors Matthew J. Patitz, Scott M. Summers
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