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Fractal Theory and Its Application in Studying the Feature of Landforms

It had been proved that the trends of the mountains, the shapes of the rivers, even the distribution of the various plants had the characteristics of fractal. Fractal and multi-fractal can be used to describe complex geometric shapes such as regular Cantor sets with non-uniform mass distributions. Investigation indicated that fractal and multi-fractal theory had been used widely in scientific field. In the past few years, fractal and multi-fractal had also been found to have important applications to characterize the terrains with the feature of complicity and irregularity. In this paper, the meaning of parameters of multi-fractal spectrum was discussed in detail at first, then simple dimension and merits of the multi-fractal characterization were defined respectively. Finally, taking the mountain landslide as example, we compared indices of simple fractal dimension and multi-fractal spectra of the area before landslide with those of the same area after the mountain slide; also we tried to explain the difference between these two groups of indices.