  We show that in the hierarchical tile assembly model, if there is a
producible assembly that overlaps a nontrivial translation of itself
consistently (i.e., the pattern of tile types in the overlap region is
identical in both translations), then arbitrarily large assemblies are
producible. The significance of this result is that tile systems intended to
controllably produce finite structures must avoid pattern repetition in their
producible assemblies that would lead to such overlap. This answers an open
question of Chen and Doty (SODA 2012), who showed that so-called
"partial-order" systems producing a unique finite assembly *and" avoiding such
overlaps must require time linear in the assembly diameter. An application of
our main result is that any system producing a unique finite assembly is
automatically guaranteed to avoid such overlaps, simplifying the hypothesis of
Chen and Doty's main theorem.
