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American Journal of Botany, Vol 84, 26, Copyright © 1997 by Botanical Society of America, Inc.

STRUCTURE AND DEVELOPMENT

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

KL Nielsen, JP Lynch and HN Weiss

An obstacle to the study of root architecture is the difficulty of measuring and quantifying the three-dimensional configuration of roots in soil. The objective of this work was 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 we employed SimRoot, an explicit geometric simulation model of root growth derived from empirical measurements of common bean (Phaseolus vulgaris L.). We computed 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). 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.


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T. C. WALK, E. VAN ERP, and J. P. LYNCH
Modelling Applicability of Fractal Analysis to Efficiency of Soil Exploration by Roots
Ann. Bot., July 1, 2004; 94(1): 119 - 128.
[Abstract] [Full Text] [PDF]

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K. Foroutan-pour, P. Dutilleul, and D. L. Smith
Soybean Canopy Development as Affected by Population Density and Intercropping with Corn: Fractal Analysis in Comparison with Other Quantitative Approaches
Crop Sci., November 1, 1999; 39(6): 1784 - 1791.
[Abstract] [Full Text]


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Copyright © 1997 by the Botanical Society of America, Inc.