Emerging fractal properties in gorgonian growth forms (Cnidaria: Octocorallia)

Gorgonian growth has been hitherto studied mostly by investigating the influence of different environmental conditions on shape and orientation. We have made an attempt at analyzing the intrinsic growth properties of these organisms, by using a method capable of pointing out a fractal arrangement. Colony outlines of the gorgonian species Eunicella singularis, Eunicella cavolinii, Paramuricea clavata, and Lophogorgia ceratophyta have been digitized and their length measured by traveling along them with a series of logarithmically increasing steps. When this procedure is used on fractal lines, logarithmic plots of estimated length vs. step show linear trends, whose slope yields the fractal dimension. In gorgonian outlines, due to their limited multi-scale organization, we have found curved trends typical of non-fractal lines. However, non-linear regression analysis has shown that the degree of bending is variable from curve to curve, with differences among species. Also, in P. clavata and L. ceratophyta there is a positive correlation between the degree of development and the tendency to assume a fractal geometry. This suggests that gorgonian growth mechanisms retain a self-similar design, which becomes evident only in species combining a large size with a high branch density. Based on these data, possibilities of modeling biological patterns through fractal growth models are questioned.