We have carried out an experiment in which a flat copper plate has a fractal roughness that increases from its centre to its edge. When this surface is made hydrophobic, the surface has a gradient from hydrophobic in the centre to superhydrophobic at the edge. This results in droplets deposited at the edge rolling to the centre. Some droplets shoot past the centre but then turn around and come back.
Note that if the surface chemistry makes a surface more hydrophilic at the centre than the edge, droplets will also tend to accumulate in the centre. However, this is a different situation to that here; in our case, the surface chemistry is the same everywhere and it is only the roughness that changes.
Superhydrophobicity: Localized parameters and gradient surfaces
G. McHale, S.J. Elliot, M.I. Newton and N.J. Shirtcliffe, in Mittal, K.L., ed, ‘Contact Angle, Wettability and Adhesion, Koninklijke Brill NV, Vol. 6 219-233 (2009)
Postprint is available here.