  In this work, we explore the features of gluonic cascades in static and
Bjorken expanding media by numerically solving the full BDIM evolution
equations in longitudinal momentum fraction $x$ and transverse momentum
$\boldsymbol{k}$ using the Monte Carlo event generator MINCAS. Confirming the
scaling of the energy spectra at low-$x$, discovered in earlier works, we use
this insight to compare the amount of broadening in static and expanding media.
We compare angular distributions for the in-cone radiation for different medium
profiles with the effective scaling laws and conclude that the out-of-cone
energy loss proceeds via the radiative break-up of hard fragments, followed by
an angular broadening of soft fragments. While the dilution of the medium due
to expansion significantly affects the broadening of the leading fragments, we
provide evidence that in the low-$x$ regime, which is responsible for most of
the gluon multiplicity in the cascade, the angular distributions are very
similar when comparing different medium profiles at an equivalent, effective
in-medium path length. This is mainly due to the fact that in this regime, the
broadening is dominated by multiple splittings. Finally, we discuss the impact
of our results on the phenomenological description of the out-of-cone radiation
and jet quenching.
