Self-Assembly of Discrete Self-Similar Fractals

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dc.creatorPatitz, Matthew J.
dc.creatorSummers, Scott M.
dc.date2008-03-12
dc.date2008-04-26
dc.date.accessioned2026-07-07T09:35:07Z
dc.date.available2026-07-07T09:35:07Z
dc.descriptionIn this paper, we search for {\it absolute} 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 fully weakly self-assembles at temperature 1, and that certain kinds of self-similar fractals do not strictly self-assemble at any temperature. Additionally, we extend the fiber construction from Lathrop et. al. (2007) to show that any self-similar fractal belonging to a particular class of "nice" self-similar fractals has a fibered version that strictly self-assembles in the TAM.
dc.identifierhttps://arxiv.org/abs/0803.1672
dc.identifierhttp://arxiv.org/abs/0803.1672
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/159727
dc.subjectComputational Complexity
dc.subjectDiscrete Mathematics
dc.titleSelf-Assembly of Discrete Self-Similar Fractals
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