A simple experiment for the examination of dendritic river systems

Every year, rivers carry away a volume of 3.7.1013 m 3 of water [1]. Furthermore, the erosion they induce has great influence on the shape of the landscape. It is quite understandable that many people are doing research on problems connected with rivers, but most of them are interested in special geomorphological, hydrological, or engineering problems as, for example, the stability of an embarkment consolidation of river X or the effects of a dam placed in river K Quite to the contrary, the river system's general features, especially their dendritic pattern, are exactly what we are interested in. To this purpose, a simple model system was built. In recent years, Mandelbrot [2] and others discovered that the fractal dimension is a measurement quantity by which a great variety of wrinkled and twisted patterns is described very well. In the meantime, many systems, such as Lichtenberg figures [3], dendritic structures of electrodeposited copper [4], or transects across vegetation [5] were examined using this concept of fractal dimensionality. A great number of other applications can be found in [2] and [61. So there is good reason to expect that river systems can also be characterized in this way. Especially, the log-log plots published by Leopold and Miller [8] already point in this direction. Furthermore, Haken [7, 91 has given a theoretical understanding of the fact that many systems with complicated dynamics and/or spatial structure exist which nevertheless can be well described by a small number of parameters. Another fruitful development was initiated by Witten and Sander [101 with