Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-11-27T11:59:52.888Z Has data issue: false hasContentIssue false
  • English
  • Français

Fractal geometry of ammonoid sutures

Published online by Cambridge University Press:  08 February 2016

Timothy M. Lutz  and
George E. Boyajian
Timothy M. Lutz
Affiliation:
Department of Geology and Astronomy, West Chester University, West Chester, Pennsylvania 19383, [email protected]
George E. Boyajian
Affiliation:
Department of Geology, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6316, [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

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.

Type
Articles
Information
Paleobiology , Volume 21 , Issue 3 , Summer 1995 , pp. 329 - 342
Copyright
Copyright © The Paleontological Society 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Literature Cited

Bayer, U. 1985. Pattern recognition problems in geology and paleontology. Springer, Berlin.Google Scholar
Boyajian, G. E. 1990. The fractal dimensions of ammonite sutures and their evolutionary significance. Geological Society of America Abstracts with Programs 22:308–309.Google Scholar
Boyajian, G. E. 1991. The fractal dimensions of ammonite sutures through geologic time. Geological Society of America (North-Central) Abstracts with Programs 23:38.Google Scholar
Boyajian, G. E., and Lutz, T. 1992. Evolution of biological complexity and its relation to taxonomic longevity in the Ammonoidea. Geology 20:983–986.2.3.CO;2>CrossRefGoogle Scholar
Canfield, D. J., and Anstey, R. L. 1981. Harmonic analysis of cephalopod suture patterns. Journal of Mathematical Geology 13:23–35.CrossRefGoogle Scholar
Checa, A. 1986. Dynamic analysis of sutural changes in Aspidoceratidae (Ammonitina). Neues Jahrbuch für Geologie und Paläontologie Monatshefte, pp. 275–283.Google Scholar
Dutch, S. I. 1993. Linear Richardson plots from non-fractal data sets. Mathematical Geology 25:737–751.CrossRefGoogle Scholar
Feder, J. 1988. Fractals. Plenum, New York.CrossRefGoogle Scholar
Foote, M. 1991. Morphologic patterns of diversification: examples from trilobites. Palaeontology 34:461–485.Google Scholar
Foote, M. 1992. Rarefaction analysis of morphological and taxonomic diversity. Paleobiology 18:1–16.CrossRefGoogle Scholar
Garcia-Ruiz, J. M., Checa, A., and Rivas, P. 1990. On the origin of ammonite sutures. Paleobiology 16:349–354.CrossRefGoogle Scholar
Hewitt, R. A., and Westermann, G. E. G. 1986. Function of complexly fluted septa in ammonoid shells: I. Mechanical principles and functional models. Neues Jahrbuch für Geologie und Paläontologie, Abhandlungen 172:47–69.CrossRefGoogle Scholar
Hewitt, R. A., and Westermann, G. E. G. 1987. Function of complexity fluted septa in ammonoid shells: II. Septal evolution and conclusions. Neues Jahrbuch für Geologie und Paläontologie, Abhandlungen 174:135–169.Google Scholar
House, M. R., and Senior, J. R., eds. 1981. The Ammonoidea. Academic Press, London.Google Scholar
Jacobs, D. K. 1990. Sutural pattern and shell stress in Baculites with implications for other cephalopod shell morphologies. Paleobiology 16:336–348.CrossRefGoogle Scholar
Klinkenberg, B. 1994. A review of methods used to determine the fractal dimension of linear features. Mathematical Geology 26:23–46.CrossRefGoogle Scholar
Lehmann, U. 1981. The ammonites: their life and their world. Cambridge University Press.Google Scholar
Luppov, N. P., and Drushchits, V. V., eds., 1958. Osnovy paleontologii (Fundamentals of paleontology), Vol. 6: Mollusca-Cephalopoda II. Academy of Sciences, USSR.Google Scholar
Mandelbrot, B. B. 1983. The fractal geometry of nature. W. H. Freeman, New York.CrossRefGoogle Scholar
Raup, D. M. 1966. Geometric analysis of shell coiling: general problems. Journal of Paleontology 40:1178–1190.Google Scholar
Ruzhenstez, V. E., ed. 1962. Osnovy paleontolgii (Fundamentals of paleontology), Vol. 5: Mollusca-Cephalopoda I. Academy of Sciences, U.S.S.R.Google Scholar
Saunders, B. W., and Swan, A. R. H. 1984. Morphology and morphologic diversity of mid-Carboniferous (Namurian) ammonoids in time and space. Paleobiology 10:195–228.CrossRefGoogle Scholar
Seilacher, A. 1988. Why are nautiloid and ammonite sutures so different? Neues Jahrbuch für Geologie und Paläontologie Abhandlungen 177:41–69.Google Scholar
Swan, A. R. H., and Saunders, B. W. 1987. Function and shape in late Paleozoic (mid-Carboniferous) ammonoids. Paleobiology 13:297–311.CrossRefGoogle Scholar
Ward, P. 1980. Comparative shell shape distributions in Jurassic-Cretaceous ammonites and Jurassic-Tertiary nautilids. Paleobiology 6:32–43.CrossRefGoogle Scholar
Westermann, G. G. E. 1973. Strength of concave septa and depth limits of fossil cephalopods. Lethaia 6:383–403.CrossRefGoogle Scholar
Westermann, G. G. E. 1975. Model for origin, function, and fabrication of fluted cephalopod septa. Paläontologische Zeitschrift 49:235–253.CrossRefGoogle Scholar
Wiedmann, J. and Kullmann, J. 1980. Ammonoid sutures in ontogeny and phylogeny. Pp. 215–255in House, M. R. and Senior, J. R., eds., The Ammonoidea. Academic Press, London.Google Scholar