Abstract
Fractal geometry methods allow to quantitatively describe self-similar or self-affined landscape shapes, allow the complex/holistic study of natural objects in various scales and 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.
If the drainage patterns or valley networks are self-similar fractals in various scales, it is possible to determine the fractal dimension by using the method "fractal dimension of drainage patterns and valley networks according to Turcotte (1997)". Conversely, if the river and valley networks are self-affined fractals, it is appropriate to determine fractal dimension by methods that use regular grids.
When applying a regular grid method to determine the fractal dimension on valley schematic networks according to Howard (1967), it was found that the "fractal dimension of drainage patterns and valley networks according to Mandelbrot (1982)", the "box-counting dimension according to Turcotte (2007a)" and the "capacity dimension according to Tichý (2012)" methods show values in the open interval (1, 2).