Application of fractal geometry to modelling nature

An overview and some experimental results are presented on the use of fractal geometry to describe geographical topography and for the synthesis of new topographic surfaces. An informal introduction to the basic concepts of fractal geometry is first given to illustrate the principles, followed by a more formal description. Since topography models are based on Brown surfaces, Brown functions, also called Weiner functions, are considered in some detail. A method is proposed for determining the fractal dimension of a surface on a regular square grid. Experiments with surfaces created by midpoint displacement and methods indicate that, for finite data sets, the relationship for the fractal dimension does not hold for H approaching unity or zero, where the parameter H defines the fractional degree of integration or differentiation of the Brown function. A 400 km/sup 2/ area near Pretoria is analyzed to find its surface fractal dimensions. An approach to synthetic generation of topographic surfaces is also described.<>