FRACTAL CHARACTERIZATION OF AGGREGATE-SIZE DISTRIBUTION - THE QUESTION OF SCALE-INVARIANCE

Aggregate-size distributions are often described as fractal based on t he power law relationship between cumulative aggregate number and aggr egate size. The slope of the natural log of cumulative number of aggre gates as a function of natural log of diameter is the fractal dimensio n. If aggregate density, shape, and relative diameter (diameter as a f raction of the smallest diameter of the size-class) are scale invarian t, then aggregate number can be calculated from mass. These three fact ors can be combined into a single unknown factor, G(i). The objectives of this study were to test the assumption of a scale invariant G(i) a nd to compare the fractal dimension from calculated cumulative number of aggregates with the fractal dimension from counted cumulative numbe r of aggregates. Numbers of aggregates were counted for each size clas s of two data sets. Calculations for the 48 samples of Data Set 1 span ned six classes ranging from sizes 1 to 32 mm, and calculations for 12 samples of Data Set 2 spanned four classes ranging from sizes 0.5 to 8 mm. The fractal dimension from counted cumulative number of aggregat es was significantly smaller than the fractal dimension determined fro m calculated cumulative number of aggregates for Data Set 1 (2.44 vs. 2.51) but significantly larger for Data Set 2 (2.41 vs. 2.03). The G(i ) factor was significantly different across many of the size classes f or both data sets. Since G(i) consisted of subcomponents (density, sha pe, relative diameter), we cannot be certain which subcomponent(s) was (were) scale variant. Scale variant G(i) complicates the use of fract al mathematics to describe dry soil aggregate distributions.