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Interior chamber walls of ammonites range from smoothly undulating surfaces in some taxa to complex surfaces, corrugated on many scales, in others. The ammonite suture, which is the expression of the intersection of these walls on the exterior of the shell, has been used to assess anatomical complexity. We used the fractal dimension to measure sutural complexity and to investigate complexity over evolutionary time and showed that the range of variation in sutural complexity increased through time. In this paper we extend our analyses and consider two new parameters that measure the range of scales over which fractal geometry is a satisfactory metric of a suture. We use a principal components analysis of these parameters and the fractal dimension to establish a two-dimensional morphospace in which the shapes of sutures can be plotted and in which variations and evolution of suture morphology can be investigated. Our results show that morphospace coordinates of ammonitic sutures correspond to visually perceptible differences in suture shape. However, three main classes of sutures (goniatitic, ceratitic, and ammonitic) are not unambiguously discriminated in this morphospace. Interestingly, ammonitic sutures occupy a smaller morphospace than other suture types (roughly one-half of the morphospace of goniatitic and ceratitic sutures combined), and the space they occupied did not change dimensions from the Jurassic to the late Cretaceous.We also compare two methods commonly used to measure the fractal dimension of linear features: the Box method and the Richardson (or divider) method. Both methods yield comparable results for ammonitic sutures but the Richardson method yields more precise results for less complex sutures.

The spatial distributions of agmatic complexes and other features thought to be associated with major crustal structures may be important sources of information about large‐scale structural patterns. However, attempts to incorporate these features into quantitative analyses of linear features have used arbitrary or inaccurate criteria to judge hypothetical geological relationships. In this paper, features of limited spatial extent are considered pointlike, and the concept of a probabilistic lattice point distribution is used to formulate a statistical method that leads to a quantitative and reproducible analysis of directional patterns based solely on the locations of the points. Thus this analysis is independent of linear patterns and provides a measure of the directional information intrinsic to point patterns. The procedure determines the most likely trends of structural anisotropies; Monte Carlo simulations of random point patterns provide a reference distribution from which confidence levels can be determined. Applications to published data for magmatic complexes, magnetic contour closures, and structural change points are used as examples. The results suggest that there has been a tendency to overestimate the amount of information available from point patterns.

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