%0 Journal Article
%T Self-Assembly of Discrete Self-Similar Fractals
%A Matthew J. Patitz
%A Scott M. Summers
%J Computer Science
%D 2008
%I arXiv
%X 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.
%U http://arxiv.org/abs/0803.1672v2