  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.
