FRACTALS, FRACTAL DIMENSIONS AND LANDSCAPES - A REVIEW

Mandelbrot's fractal geometry is a revolution in topological space the ory and, for the first time, provides the possibility of simulating an d describing landscapes precisely by using a mathematical model. Fract al analysis appears to capture some ''new'' information that tradition al parameters do not contain. A landscape should be (or is at most) st atistically self-similar or statistically self-affine if it possesses a fractal nature. Mandelbrot's fractional Brownian motion (fBm) is the most useful mathematical model for simulating landscape surfaces. The fractal dimensions for different landscapes and calculated by differe nt methods are difficult to compare. The limited size of the regions s urveyed and the spatial resolution of the digital elevation models (DE Ms) limit the precision and stability of the computed fractal dimensio n. Interpolation artifacts of DEMs and anisotropy create additional di fficulties in the computation of fractal dimensions. Fractal dimension s appear to be spatially variable over landscapes. The region-dependen t spatial variation of the dimension has more practical significance t han the scale-dependent spatial variation. However, it is very difficu lt to use the fractal dimension as a distributed geomorphic parameter with high ''spatial resolution''. The application of fractals to lands cape analysis is a developing and immature field and much of the theor etical rigour of fractal geometry has not yet been exploited. The phys ical significance of landscape fractal characteristics remains to be e xplained. Research in geographical information theory and fractal theo ry needs to be strengthened in order to improve the application of fra ctal geometry to the geosciences.