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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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We present an improved method for determining statistically significant alignments of pointlike features. One of the principal such methods now in use, the two‐point azimuth method, depends on a homogeneous distribution of points over the region of interest. Modification of this approach by use of the relatively new statistical technique of kernel density estimation permits treatment of heterogeneous point distributions without introducing substantial dependence on choice of the grid employed in the test for significance of apparent preferred orientations. The improved method can selectively reveal alignments on different spatial scales and can suggest the locations of alignments as well as their orientation. We use this method to analyze the spatial distribution of 416 vents, largely of Pleistocene age, in the Pinacate volcanic field, Sonora, Mexico, just east of the northern end of the Gulf of California. Apart from a few sets of aligned cinder cones, the distribution of Pinacate vents appears nearly random on aerial and space photography. However, when treated statistically, old Pinacate vents exhibit structural control trending approximately N10°E throughout the field and in all its subareas. In contrast, vents with ages estimated by comparison with dated cones to be younger than about 0.4 Ma show not only the N10°E control but also N20°W and N55°W alignments significant at the 95% confidence level. The N10° alignment probably reflects the current Basin and Range horizontal stress regime in this particular area, which is atop the mantle magma source of the Pinacate lavas. The N55°W direction is related to a major regional fracture of that orientation passing through the middle of the field and possibly related to normal faults associated with opening of the adjacent Gulf of California. The distribution of vents relative to the fracture trace is consistent with magma having been guided upward along a SW dipping fault plane. The origin of the N20° W alignment is unknown but of pre‐Pleistocene heritage. We found no evidence to support control of the Pinacate vent alignments parallel to rifting or transform directions in the adjacent Gulf. Intrusion along N20°W and N55°W fractures at or since about 0.4 m.y. ago could reflect either a shift in the crustal stress field or an increase in magma pressure in Pinacate conduits that allowed magma to ascend along structures that were not parallel to the maximum horizontal compressive stress.

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