Spatial variability is a basic component of all natural systems. The system being studied here is the topography of an evolving drainage basin. Spatially heterogeneous erosivity within the drainage basin influences the structure of the drainage network, the roughness of small-scale features, and the overall appearance of the simulated topography. The presence of heterogeneities does not simply blur and smear analytical relationships. The heterogeneities themselves introduce new structure to the organization of the drainage basin. Three measures, the slope-area relationship, the cumulative area relationship, and the hypsometric distribution, are all systematically affected by spatial heterogeneity. We will demonstrate how and why these relationships are affected and also how different structures in the heterogeneities themselves are manifested in the resulting simulated topography. ¿ American Geophysical Union 1995.