Self-Assembly of Discrete Self-Similar Fractals
Computational Complexity
2008-04-26 v2 Discrete Mathematics
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.
Keywords
Cite
@article{arxiv.0803.1672,
title = {Self-Assembly of Discrete Self-Similar Fractals},
author = {Matthew J. Patitz and Scott M. Summers},
journal= {arXiv preprint arXiv:0803.1672},
year = {2008}
}