Structural Complexity in Mussel Beds: the Fractal Geometry of Surface Topography

Student Authors

Brian R. Rusignuolo '98, Gettysburg College

Document Type


Publication Date



Environmental Studies


Seafloor topographic complexity is ecologically important because it provides habitat structure and alters boundary-layer flow over the bottom. Despite its importance, there is little agreement on how to define and measure surface complexity. The purpose of this investigation was to utilize fractal geometry of vertical cross-section profiles to characterize the surface topography of the soft-bottom mussel bed (Mytilus edulisL.) at Bob’s Cove, ME, USA. Mussels there have been shown previously to have spatially ordered fractal characteristics in the horizontal plane. Two hypotheses were tested. The first was that the bed surface is fractal over the spatial scale of 1.44–200 mm, with fractal dimension less than or equal to 1.26, the value for the Koch curve, our model for bed profiles. The second was that bed surface topography (i.e., in vertical profile) is less complex than the mussel bed spatial pattern (i.e., aerial view in the horizontal plane). Both hypotheses were supported. Cross-sections of plaster casts of the bed produced 88 surface profiles, all of which were fractal over the entire spatial scale of more two orders of magnitude employed in the analysis. Fractal dimension values (D) for individual profiles ranged from 1.031 to 1.310. Fractal dimensions of entire casts ranged up to mean (1.242±0.046) and median (1.251) values similar to 1.26, the theoretical value of the Koch curve. The bed surface was less complex than the bed spatial pattern because every profile hadD


Original version is available from the publisher at: http://www.sciencedirect.com/science/article/pii/S0022098100002859

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