Fractal and multifractal analysis of cassava root system grown by the root-box method

The root system development and its localized distribution were examined using cassava plants grown in narrow root boxes of appropriate sizes which were adjusted to the root growth. Analyses based on fractal geometry were applied in addition to measurements of the weight and length of the root systems to evaluate the root distribution quantitatively. The root system distribution was converted to a digitized image, and the fractal dimension was calculated by the box-counting method (D-box) for the whole root system and different positions in the soil. Furthermore, 1000 random measurements for local fractal dimension by the mass-radius method (D-local) were conducted per root system, and the multifractal spectrum was analyzed. The total root weight increased until 90 days after planting (DAP), whereas the total length ceased to increase at 60 DAP. Neither apparent bulking of storage root nor decrease in root length was observed during the experimental period. The potential rooting habit of cassava was two-dimensionally exhibited under a uniform soil environment in the boxes. The complexity in root distribution as a whole root system shown by the global D (D-box) was almost constant. However, both the trends in positional D-box difference and multifractal analysis showed that the root distribution was localized and heterogeneity in the localization changed with root system development. The root system of cassava grown in the boxes can be characterized as an abundant but uneven root distribution with a highly advanced branching pattern by large global D and kurtosis of the multifractal spectra.