Fractal dimensions of a green broccoli and a white cauliflower

Abstract

The fractal structures of a green broccoli and a white cauliflower are investigated by box-counting method of their cross-sections. The capacity dimensions of the cross-sections are $1.78 \pm 0.02$ for a green broccoli and $1.88 \pm 0.02$ for a white cauliflower, and both are independent of their directions. From the results we predict that the capacity dimensions of the bulks are about 2.7 for a green broccoli and $2.8.$ for a white cauliflower. The vertical cross-sections of the two plants are modeled into self-similar sets of triangular and rectangular trees. We discuss the conditions of the fractal objects in the model trees.