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 $c \times c$ block of points, for some $c \in \mathbb{ Z}^+$. We prove that no scaled discrete self-similar pier fractal strictly self-assembles, at any temperature, in Winfree's abstract Tile Assembly Model.
Categories: cs.CG