Soil Mass, Surface, and Spectral Fractal Dimensions Estimated from Thin Section Photographs

Abstract Aspects of fractal geometry have been used to give quantitative measurements of soil structure. Fractal dimensions measured were the mass fractal dimension ( D m ), surface fractal dimension ( D s ), and the spectral dimension ( d ). We investigated the fractal component of a computer program, STRUCTURA, which measures the fractal dimension of soil from images of soil thin sections. Six thin sections, each showing different structural characteristics, were analyzed in order to obtain a range of fractal dimensions. The dimensions, in particular D m and d , were shown to discriminate the different structures. The values of D m and d ranged from 1.682 to 1.852 and 1.236 to 1.668, respectively. A further objective was to use these results, together with fractal theory, to show the potential fractal geometry has in predicting physical processes such as diffusion within the soil. To assist with the interpretation of fractal dimensions, the dimensions of different soil samples with the same porosity were compared.