Fractal Dimensions of Soil Aggregate‐size Distributions Calculated by Number and Mass

Abstract

Abstract The fractal dimension, D , has been used to characterize soil aggregate‐size distributions. However, D is based on the number‐size relationship. In most soils applications, it is the mass‐size relationship that is determined. A number‐size distribution can be generated from the mass‐size distribution, assuming scale‐invariant shape and density. Variation in shape and density as a function of size may introduce errors in the calculation of D . We compared the fractal dimensions of soil aggregates estimated from mass‐size distribution data ( D m ), with those computed from actual number‐size distribution data determined by counting ( D n ). The fractal dimension ranged from 0.67 to 3.92 for D n , and from 0.79 to 4.06 for D m . A significant linear relation was found between D m and D n , with R 2 = 0.935. The resulting intercept and slope were not significantly different from zero and one, respectively, indicating a 1:1 relationship. This implies that the assumption of scale‐invariant shape and density was valid across the range of aggregate sizes studied (5.0 × 10 −1 to 3.2 × 10 1 mm). Thus, the fractal dimension can be estimated from mass‐distribution data within this range.