  Structural hierarchy is found in myriad biological systems and has improved
man-made structures ranging from the Eiffel tower to optical cavities.
Hierarchical metamaterials utilize structure at multiple size scales to realize
new and highly desirable properties which can be strikingly different from
those of the constituent materials. In mechanical resonators whose rigidity is
provided by static tension, structural hierarchy can reduce the dissipation of
the fundamental mode to ultralow levels due to an unconventional form of soft
clamping. Here, we apply hierarchical design to silicon nitride nanomechanical
resonators and realize binary tree-shaped resonators with quality factors as
high as $10^9$ at 107 kHz frequency, reaching the parameter regime of levitated
particles. The resonators' thermal-noise-limited force sensitivities reach
$740\ \mathrm{zN/\sqrt{Hz}}$ at room temperature and $\mathrm{90\
zN/\sqrt{Hz}}$ at 6 K, surpassing state-of-the-art cantilevers currently used
for force microscopy. We also find that the self-similar structure of binary
tree resonators results in fractional spectral dimensions, which is
characteristic of fractal geometries. Moreover, we show that the hierarchical
design principles can be extended to 2D trampoline membranes, and we fabricate
ultralow dissipation membranes suitable for interferometric position
measurements in Fabry-P\'erot cavities. Hierarchical nanomechanical resonators
open new avenues in force sensing, signal transduction and quantum
optomechanics, where low dissipation is paramount and operation with the
fundamental mode is often advantageous.
