There is brief discussion of sediment transport, dune formation, river meanders, and the formation of drainage networks. These are interesting because they are formed by a continuous process, but give a structure which has a fractal characteristic. The Amazon river basin on page 265, also reproduced on the front cover, illustrates this. One continuum model of erosion and sediment transport is given and partially analysed: it is shown that a uniform substrate is unstable to the formation of channels. There is a deeper conceptual modelling problem here, with wide ramifications: how can a continuous model predict a solution with fractal characteristics?
At least in the present case, the structure of the answer may be the following: the continuous model is of singular perturbation type, with the (outer) solution admitting `shocks' which are in fact the channels of the network. The description of the fractal structure relies on a local description of channel density as a function of channel width (or depth) and time, which evolves locally using the `inner' description of the model. This kind of idea (which has not been carried out so far) has large scale implications for modelling heterogeneous processes; the most obvious example is fluid turbulence, but there are plenty of others: dendritic structure in solidification (chapter 17) is just one.