  Fractals are fascinating structures, not only for their aesthetic appeal, but
also because they allow for the investigation of physical properties in
non-integer dimensions. In these unconventional systems, a myriad of intrinsic
features might come into play, such as the fractal dimension, the spectral
dimension, or the fractal geometry. Despite abundant theoretical and numerical
studies, experiments in fractal networks remain elusive. Here, we
experimentally investigate quantum transport in fractal networks by performing
continuous-time quantum walks in fractal photonic lattices with incremental
propagation lengths. Photons act as the walkers and evolve in the lattices
after being injected into one initial site. We unveil the transport properties
through the photon evolution pattern at different propagation lengths and the
analysis of the variance and the P'olya number, which are calculated based on
the probability distribution of the patterns. Contrarily to classical fractals,
we observe anomalous transport governed solely by the fractal dimension. In
addition, the critical point at which there is a transition from normal to
anomalous transport is highly dependent on the fractal geometry. Our experiment
allows the verification of physical laws in a quantitative manner and reveals
the transport dynamics with unprecedented detail, thus opening a path to the
understanding of more complex quantum phenomena governed by fractality.
