  Self-similar structures occur naturally and have been employed to engineer
exotic physical properties. Here we show that acoustic modes of a fractal-like
system of tensioned strings can display increased mechanical quality factors
due to the enhancement of dissipation dilution. We describe a realistic
resonator design in which the quality factor of the fundamental mode is
enhanced by as much as two orders of magnitude compared to a simple string with
the same size and tension. Our findings can open new avenues in force sensing,
cavity quantum optomechanics and experiments with suspended test masses.
