  The relation between wetting properties and geometric parameters of fractal
surfaces are widely discussed on the literature and, however, there are still
divergences on this topic. Here we propose a simple theoretical model to
describe the wetting properties of a droplet of water placed on a hierarchical
structured surface and test the predictions of the model and the dependence of
the droplet wetting state on the initial conditions using simulation of the
3-spin Potts model. We show that increasing the auto-similarity level of the
hierarchy -- called $n$ -- does not affect considerably the stable wetting
state of the droplet but increases its contact angle. Simulations also explicit
the existence of metastable states on this type of surfaces and shows that,
when $n$ increases, the metastability becomes more pronounced. Finally we show
that the fractal dimension of the surface is not a good predictor of the
contact angle of the droplet.
