Review article: methods of fractal geometry used in the study of complex geomorphic networks

Abstract

Fractal geometry methods allow one to quantitatively describe self-similar or self-affined landscape shapes and facilitate the complex/holistic study of natural objects in various scales. They also allow one to compare the values of analyses from different scales (Mandelbrot 1967; Burrough 1981). With respect to the hierarchical scale (Bendix 1994) and fractal self-similarity (Mandelbrot 1982; Stuwe 2007) of the fractal landscape shapes, suitable morphometric characteristics have to be used, and a suitable scale has to be selected, in order to evaluate them in a representative and objective manner. This review article defines and compares: 1) the basic terms in fractal geometry, i.e. fractal dimension, self-similar, self-affined and random fractals, hierarchical scale, fractal self-similarity and the physical limits of a system; 2) selected methods of determining the fractal dimension of complex geomorphic networks. From the fractal landscape shapes forming complex networks, emphasis is placed on drainage patterns and valley networks.

Keywords

• fractal
• drainage patterns
• valley network
• fractal dimension