Self-Assembly of Discrete Self-Similar Fractals

Matthew J. Patitz; Scott M. Summers

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arXiv · 0803.1672

Self-Assembly of Discrete Self-Similar Fractals

Matthew J. Patitz·Scott M. Summers

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Abstract

In 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.

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Matthew J. Patitz, Scott M. Summers. 2008-04-26. Self-Assembly of Discrete Self-Similar Fractals. https://arxiv.org/abs/0803.1672

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