Both simple and complex suture patterns of shelled cephalopods can be described when points along the pattern are described by parametric equations, and transformed to produce two separate Fourier series. The amplitudes of series for each suture pattern can be represented as either a point or a vector in multidimensional space. Subtle differences, even in nautilitic suture patterns, are clearly separated by this representation. Preliminary results from two applications of the method indicate its usefulness to provide insight into the organisms' development and phylogeny. Plotting the spectral power of angular (phi) versus vertical (h) amplitudes for the patterns in an ontogenetic series creates a path. In ammonitids, the path indicates an abrupt transition from a sinusoidal (nautilitic) suture pattern to the development of a more complex and crenellated (ammonitic) pattern. Nearest neighbor analysis of the points in multidimensional space can be used to compare suture patterns for their underlying similarity. The relatedness of similarity to phylogeny is demonstrated for the preliminary data set. The angle between vectors representing the patterns is a potentially more informative metric of suture-pattern similarity than is the distance between points.