Fractal dimensions of a green broccoli and a white cauliflower

Details Fractal dimensions of a green broccoli and a white cauliflower Fractal dimensions of a green broccoli and a white cauliflower

2004-11-24

arxiv.org/abs/cond-mat/0411597v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

5 pages, 8 figues

Scientific paper

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.

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