  Transport processes underpin a multitude of phenomena, ranging from the
propagation of atoms on lattices, to the mobility patterns of microorganisms
and earthquakes, to name a few. The dynamics of these processes is very rich
and key to understanding the complex nature of the underlying physics, but the
way in which we classify them is often too simplistic to fully reflect this
complexity. Here, we report on the experimental observation of a breakdown of
self-similar propagation for light inside a scattering medium - a transport
regime exhibiting different scaling rates for each spatial moment of the
associated probability distribution. Notably, we show that this phenomenon
arises for light waves even in the simple case of isotropic and homogeneous
disorder, and can be controlled by tuning the turbidity of the system. These
results support the idea that the traditional dichotomy between normal and
anomalous diffusion is reductive and that a richer framework should be
constructed based on the concept of self-similarity as this class of transport
regimes may be far more common that it is currently believed. In addition, this
insight can help understand scenarios where transport is dominated by rare
propagation events, as in non-linear and active media, or more generally in
other fields of research.
