Statistics of channel networks on fractional Brownian surfaces

Many natural forms can be successfully simulated using fractals. We argue that fractals can therefore provide useful models of natural forms in the absence of specific effects and constraints: in effect, null hypotheses for natural forms. The fractional Brownian process is a useful simulation for terrain and offers a method of determining the characteristics of channel networks formed by random processes. We simulate random channel networks and tabulate the statistical distributions of various parameters. The chapter demonstrates that recently observed departures from the random topology model of Shreve are attributable to the geometric constraints imposed by packing networks onto a topographic surface, and not to geologic and geomorphic controls, as previously supposed. -Authors