[en] Single fracture measurements are difficult to obtain, but they are the only means we have to observe and study natural fracture morphology. The character of the fracture openings (apertures) is often one of the primary factors controlling fluid flow in the fracture. In particular, the shape, distribution, and connectivity of contact areas and flow channels can affect the relative permeability of wetting and non-wetting fluid phases in unsaturated systems. In this paper we use three methods of fractal analysis (the slit-island, the divider, and the variogram) as well as statistical and geostatistical analysis to characterize the geometry of measured fracture apertures obtained from two different fractured rock specimens from the field. One of these is a granitic fracture (crack) of homogeneous lithology and no displacement, the other is a fracture (fault) obtained from a highly altered fault zone, containing striations and slickensides. We discuss the fractal and geostatistical analysis of these two fractures in the context of what information is most helpful for making predictions about fluid flow in single fractures