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. 2015 Mar 24;6:172. doi: 10.3389/fpls.2015.00172

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Copyright © 2015 Dutilleul, Han, Valladares and Messier.

This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

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Illustration of three successive steps in the cube-counting procedure of fractal dimension estimation, i.e., the steps in which one of the smallest cubes to contain the entire skeletal branching pattern of a miniature coniferous tree (here, Microbiota decussata Gold Spot) is divided into (A) 8 = 2 × 2 × 2; (B) 64 = 4 × 4 × 4; and (C) 512 = 8 × 8 × 8 cubes which have a sidelength equal to (A) 1/2; (B) 1/4; and (C) 1/8 of the sidelength of the start cube (438). The counting of the cubes that have a non-empty intersection with at least one branch segment provides C(s) at the corresponding sidelengths and scales in Equation (1); see also the 2nd, 3rd, and 4th data points from left to right in Figure 6B, for log(1/s) = log(1/219), log(1/110), log(1/55) (after rounding of s to the nearest integer) and log(C(s)) = log(8), log(38), log(150), respectively.