Abstract: Fractal theory is a new branch of modern mathematics. It is a new worldview and methodology. The coupling of fractal with geography has accelerated the geography's development. This paper firstly introduces the application and development of fractal theory in hydrological researches, then addresses two computational approaches to the fractal dimension of river network, and expounds the meanings of the two fractal dimensions. By applying Arc/Info and ArcView, we have established the spatial database for Malianhe River Basin. Two approaches, respectively based on the Overlay Method and the Horton's Law, are developed to analyse the fractal dimension of the water system in Malianhe River Basin. This paper puts forward a synthetic approach coupling fractal theory, GIS technology with the physiognomoical model. Compared with the traditional approach, it has the advantages of easy operation and high efficiency, which promotes the application of GIS in river network fractal studies and brings the change of fractal dimension estimation from maps to DEMs. Furthermore, the fractal dimension calculation of river network provides not only a new quantitative method to basin morphology, but also a new quantitative index to the randomicity of river's growth.

Key words: DEM, Watershed Fractal Dimension