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Fractal geometry of bean root systems: correlations between spatial and fractal dimension

Authors:

Nielsen, K.L.; Lynch, J.P.; Weiss, H.N.

Source:

American Journal of Botany, Volume 84, Issue 1, p.26-33 (1997)

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Abstract:

An obstacle to the study of root architecture is the difficulty of measuring and quantifying the three-dimensional configuration of roots in soil. A study was conducted to determine if fractal geometry might be useful in estimating the three-dimensional complexity of root architecture from more accessible measurements. A set of results called projection theorems predict that the fractal dimension (FD) of a projection of a root system should be identical to the FD of roots in three-dimensional space (three-dimensional FD). To test this prediction, SimRoot, an explicit geometric simulation model of root growth derived from empirical measurements of common bean ( Phaseolus vulgaris ), was used. The three-dimensional FD, FD of horizontal plane intercepts (planar FD), FD of vertical line intercepts (linear FD), and FD of orthogonal projections onto planes (projected FD) were calculated. Three-dimensional FD was found to differ from corresponding projected FD, suggesting that the analysis of roots grown in a narrow space or excavated and flattened prior to analysis is problematic. A log-linear relationship was found between FD of roots and spatial dimension. This log-linear relationship suggests that the three-dimensional FD of root systems may be accurately estimated from excavations and tracing of root intersections on exposed planes.