Scaled pier fractals do not strictly self-assemble
Computational Geometry
2014-06-18 v1
Abstract
A \emph{pier fractal} is a discrete self-similar fractal whose generator contains at least one \emph{pier}, that is, a member of the generator with exactly one adjacent point. Tree fractals and pinch-point fractals are special cases of pier fractals. In this paper, we study \emph{scaled pier fractals}, where a \emph{scaled fractal} is the shape obtained by replacing each point in the original fractal by a block of points, for some . We prove that no scaled discrete self-similar pier fractal strictly self-assembles, at any temperature, in Winfree's abstract Tile Assembly Model.
Cite
@article{arxiv.1406.4197,
title = {Scaled pier fractals do not strictly self-assemble},
author = {David Furcy and Scott M. Summers},
journal= {arXiv preprint arXiv:1406.4197},
year = {2014}
}