FRACTAL MODELING AND SPATIAL VARIABILITY OF NATURAL PHENOMENA

Fractal ideas have generated a lot of interest recently in natural sci ences. Mandelbrot's theory is particularly relevant to physical geogra phers since it deals in part with the spatial variability of natural p henomena, scales of observation, and resultant geometric properties. T he first part of this review consists in a description of the fractal model and the methods that can be used to determine the fractal (Hausd orff) dimension, as well as a description of the immediate interests o f fractals in natural sciences. The second part deals with the applica tion of fractals to the spatial variability of different phenomena (e. g. pedology, drainage networks, turbulence, etc.). Nested levels of va riation are generally observed and one basic interest of fractals is r elated to the fact that the fractal dimension varies with the range of scales considered. A third section is concerned with the analysis of topographic surfaces, from the microscale (e.g. a few millimetres) to the scale of drainage basins. Different ways of using fractal concepts for the analysis of topographic surfaces are presented. More specific ally, these are the use of fractal surfaces as a null hypothesis and i nitial surface for the study of geomorphic processes, and the use of t he fractal dimension for the characterization of surface roughness (fo r hydraulic and hydrologic studies). Finally, this review considers br iefly the significance of chaos theory in physical geography and geomo rphology. Fractal concepts are clearly predominant in the study of dyn amic systems behaviour.