Fractal Reconstruction with Unorganized Geochemical Data

Fractal geometry is receiving increased attention as a model for many natural phenomena. In this paper, we address two issues in dealing with unorganized 3-D measured data using fractal geometry: extraction of fractal characters and fractal surface (geochemical landscapes) reconstruction. We start from a set of randomly measured 3-D data on a plane. After classification and concentration of the input data, we present methods for estimating the fractal dimension and texture deviation as fractal characters, and then an improved subdivision scheme is developed to reconstruct fractal surface on the basis of the extracted fractal characters. We demonstrate both characterization and reconstruction with irregularly measured geochemical data from 1767 stream sediment samples in the middle district (450km² in area) of Zhejiang, China.