We suggest that limits on the number of independent variables that play a role in controlling the shape of the seafloor can be obtained directly from bathymetry data. To obtain this information, seafloor topography is considered as a product of a larger system that produces the oceanic lithosphere. We hypothesize that this dynamical system is chaotic, and use bathymetric depth values to search for evidence of a strange attractor, the dimension of which approximates the number of degrees of freedom in the system. An analysis of Sea Beam multibeam data collected along a flow line of seafloor spreading in the Northeast Pacific Ocean indicates that the dynamical system that forms the topography (on the length scale of 100's of meters) has an underlying structure indicative of a high-order attractor. ¿ American Geophysical Union 1990