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Fractal Dimensions of Soil Aggregate‐size Distributions Calculated by Number and Mass
Author(s) -
Perfect E.,
Rasiah V.,
Kay B. D.
Publication year - 1992
Publication title -
soil science society of america journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.836
H-Index - 168
eISSN - 1435-0661
pISSN - 0361-5995
DOI - 10.2136/sssaj1992.03615995005600050012x
Subject(s) - fractal dimension , mathematics , fractal , range (aeronautics) , scale invariance , statistics , aggregate (composite) , scale (ratio) , geometry , mathematical analysis , physics , materials science , composite material , quantum mechanics
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.