  In this paper, we present high-level overviews of tile-based self-assembling
systems capable of producing complex, infinite, aperiodic structures known as
discrete self-similar fractals. Fractals have a variety of interesting
mathematical and structural properties, and by utilizing the bottom-up growth
paradigm of self-assembly to create them we not only learn important techniques
for building such complex structures, we also gain insight into how similar
structural complexity arises in natural self-assembling systems. Our results
fundamentally leverage hierarchical assembly processes, and use as our building
blocks square "tile" components which are capable of activating and
deactivating their binding "glues" a constant number of times each, based only
on local interactions. We provide the first constructions capable of building
arbitrary discrete self-similar fractals at scale factor 1, and many at
temperature 1 (i.e. "non-cooperatively"), including the Sierpinski triangle.
