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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.