  Spherically symmetric transonic accretion of a fractal medium has been
studied in both the stationary and the dynamic regimes. The stationary
transonic solution is greatly sensitive to infinitesimal deviations in the
outer boundary condition, but the flow becomes transonic and stable, when its
evolution is followed through time. The evolution towards transonicity is more
pronounced for a fractal medium than what is it for a continuum. The dynamic
approach also shows that there is a remarkable closeness between an equation of
motion for a perturbation in the flow, and the metric of an analogue acoustic
black hole. The stationary inflow solutions of a fractal medium are as much
stable under the influence of linearised perturbations, as they are for the
fluid continuum.
