Extended fractal analysis method and its application for linear rivers

Abstract

Extended fractal analysis method can analyze the fractal character (i.e. self-similarity) objectively, especially the difference and change of the shape and the structure in different observation scale intervals. As one of the common fractal objects, river on the map can be surveyed its length and quantified the complexity of its shape and structure as well as its partial details with Extended Fractal Dimension Analysis method (abbreviated as EFDA). Compared to the traditional method, EFDA has unparalleled advantages. Considering the extended fractal character with scaling variance, and based on its simulating function adopting the Inverse Logistic Model, the paper gained the extended fractal function for quantifying the length of the river depending on the different observing scales. Furthermore, based on the mathematical derivation of its simulating function and fractal analysis, the paper obtained the relevant parameter for establishing Meta Fractal Dimension (abbreviated as MFD) Model to quantify the local complexity of the river on the map. Several experiments based on the China's seven major rivers done indicate that this method is easy to operate and has a relatively high calculation precision and a logical result of spatial analysis.