The fractal branching of an arborescent sponge

The fractal properties of specimens of a planar branching sponge Raspailia inaequalis (Porifera, Demospongiae) were determined by analysing digitised photographs. The specimens, collected from a single site in northeastern Ne w Zealand, had a wide range of morphology. Three different fractal methods were used: box counting; a method that gives the scaling of branch length w ith distance from the base of the fan; and an allometric analysis of the de pendence of frontal area on specimen size. All three approaches gave a simi lar value for the fractal dimension. The conjecture that the specimens have a fractal branching structure is consistent with the results of a Horton a nalysis of their branching pattern. There is a significant relationship bet ween fractal dimension and number of fingers, which implies that a simple c ount of the number of fingers is as useful for discriminating between indiv iduals as the more complex fractal analysis. Using this relation, sponges f rom a site with less water movement are inferred to have a lower fractal di mension. This result is in agreement with the predictions of the Kaandorp m odel of sponge growth.