Difference between revisions of "Self-Assembly of Discrete Self-Similar Fractals"
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discrete self-similar fractals has a fibered version that strictly self-assembles in the TAM. | discrete self-similar fractals has a fibered version that strictly self-assembles in the TAM. | ||
|authors=Matthew J. Patitz and Scott M. Summers | |authors=Matthew J. Patitz and Scott M. Summers | ||
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Revision as of 14:35, 4 December 2011
Published on:
Abstract
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.
Authors
Matthew J. Patitz and Scott M. Summers
