In this paper we analyze the magnitude and spatial organization of small-scale surface features (the surface texture) of the Greenland and Antarctic ice sheets. The texture is revealed in shaded relief maps of digital elevation models because surface slopes emphasize short-wavelength topography. We show that the surface slope components parallel to and perpendicular to the ice flow direction of ice sheets are both qualitatively and quantitatively different from one another. The parallel component variations are larger in magnitude than the perpendicular component variations, and features in maps of the parallel component are elongated perpendicular to the ice flow direction, while features in maps of the perpendicular component are elongated at a diagonal to the ice flow direction. These properties may be explained by a simple model of glacier dynamics in which a linearly viscous slab of ice flows over a random, isotropic, red noise bed. In this model an anisotropic surface results from an isotropic bed because the surface anisotropy derives from the anisotropic transfer of bed topography to the surface by viscous flow dynamics. The modeling results suggest that analysis of surface texture magnitude and anisotropy can be used to identify areas of sliding ice from surface topography data alone and can be used to roughly estimate sliding rates where bed topography is known.