A method is described for determining the fractal dimension of an ice sheet or other snow-covered surface from a Landsat-type image. The method relies on the well known strong correlation between surface slope and image brightness and it has been applied to a Landsat image of the ice cap on Nordaustlandet, Svalbard. Two transects approximately 100 km in length were studied, and they were found to give consistent results. The surface shows strong evidene of fractal behaviour on scales bclween 0’3 km and at least 10 km, with a fractal dimension of 1-120 for transects of one (topological) dimension This fractal behaviour was compared with that of the underlying bedrock, which also displays fractal behaviour over the same range of linear scales but with a significantly larger fractal dimension of 1 38. This difference accords with glaciologjcal theory.