From fractal analysis along a line to fractals on the plane

Self-similar fractals are useful models for soil solid and pore sets. The scaling properties of these fractals along a line and across an area can be described by the fractal dimensions. One method, for estimating the soil areal fractal dimension from the solid and pore set distributions along the lines, was proposed and tested with real macro- and micromorphological data on three soils of Mexico. The soil areal fractal dimension (D_a) was compared with the soil mass fractal dimension (D_m) estimated by two-dimensional binary image analysis, separately for solids and pores. Both methods are based on the box-counting technique and are suitable for determining the soil ‘box' or ‘capacity' fractal dimension, that seems to be apt to estimate the alternative filling of an area by a fractal set of solids and pores. This paper examines the relations between the fractal dimensions obtained along a line, across an area and directly from the image. Analysis of D_a and D_m data seems to suggest that both soil genesis and management practice can contribute to areal fractal dimension dynamics. It was shown that fractal dimensions are useful parameters able to monitor tillage influence on soil properties and to estimate the degree of soil compaction.