  The formation of iterated structures, such as satellite and sub-satellite
drops, filaments and bubbles, is a common feature in interfacial hydrodynamics.
Here we undertake a computational and theoretical study of their origin in the
case of thin films of viscous fluids that are destabilized by long-range
molecular or other forces. We demonstrate that iterated structures appear as a
consequence of discrete self-similarity, where certain patterns repeat
themselves, subject to rescaling, periodically in a logarithmic time scale. The
result is an infinite sequence of ridges and filaments with similarity
properties. The character of these discretely self-similar solutions as the
result of a Hopf bifurcation from ordinarily self-similar solutions is also
described.
