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Fractal grain distribution in agglutinated foraminifera

Published online by Cambridge University Press:  20 May 2016

Kathryn Allen,
Stephen Roberts and
John W. Murray
Kathryn Allen
Affiliation:
Department of Geology, Southampton Oceanography Centre, Empress Dock, European Way, Southampton SO14 3ZH, United Kingdom. E-mail: Sr1@mail.soc.soton.ac.uk; jwm1@mail.soc.soton.ac.uk
Stephen Roberts
Affiliation:
Department of Geology, Southampton Oceanography Centre, Empress Dock, European Way, Southampton SO14 3ZH, United Kingdom. E-mail: Sr1@mail.soc.soton.ac.uk; jwm1@mail.soc.soton.ac.uk
John W. Murray
Affiliation:
Department of Geology, Southampton Oceanography Centre, Empress Dock, European Way, Southampton SO14 3ZH, United Kingdom. E-mail: Sr1@mail.soc.soton.ac.uk; jwm1@mail.soc.soton.ac.uk
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Abstract

A fractal geometry of clast size within the test wall in the Antarctic agglutinated foraminifera Hormosina mortenseni Cushman, 1910 and Cyclammina cancellata Brady, 1879 has been identified with the use of Scanning Electron Microscopic techniques. External surface and internal clast distributions in H. mortenseni display a self-similar distribution. C. cancellata has an internal self-similar grain arrangement, whereas the exterior surface shows an alternative grain distribution. Power law relationships between particle density and grain diameter enable values of fractal dimension (D) to be calculated; these “D-values” represent the absolute gradient of the power law relationship. The dimensions acquired from the foraminiferal study correspond well with those previously obtained from natural fractal geological structures and ideal fractals. The self-similar grain arrangement within walls of the foraminifera exists over three orders of magnitude, after which alternative methods of test wall construction are evident. This suggests that a limit exists where grain selection terminates. A self-similar grain distribution limits the amount of biologically produced adhesive material required by the foraminifera for constructing their tests.

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Type
Articles
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Paleobiology , Volume 24 , Issue 3 , Summer 1998, pp. 349 - 358
Copyright
Copyright © The Paleontological Society 

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References

Literature Cited

Babaie, H. A., Hadizadeh, J., and Babaie, A. 1995. Self similar cataclasis in the Saltville thrust zone, Knoxville, Tennessee. Journal of Geophysical Research 100:B9: 18075–18082.Google Scholar
Bender, H. 1992. Chamber formation and biomineralization in Textularia candeiana d'Orbigny (Sarcodina: Textulariina). Journal of Foraminiferal Research 22: 229–241.Google Scholar
1995. Test structure and classification in agglutinated foraminifera. pp. 27–70in Kaminski, M. A., Geroch, S., Gasinski, M. A. eds. Proceedings of the Fourth International Workshop on Agglutinated Foraminifera, Krakow, Poland, September 12-19, 1993 (Grzybowski Foundation Special Publication No. 3).Google Scholar
Bowser, S. S. and Bernhard, J. M. 1993. Structure, bioadhesive distribution and elastic properties of the test of Astramminarara (Protozoa; Foraminiferida). Journal of Eukaryotic Microbiology 40: 121–131.Google Scholar
Brady, H. B. 1879. Notes on some of the Reticularian Rhizopoda of the Challenger Expedition on new or little known arenaceous types. Quarterly Journal of Microscopical Science, New Series 19: 20–63.Google Scholar
Cushman, J. A. 1910. A monograph of the foraminifera of the North Pacific Ocean. Bulletin of the United States National Museum 71: 1–134.Google Scholar
Gefen, Y., Ahorony, A., Mandelbröt, B. B., and Kirkpatrick, S. 1981. Solvable fractal family, and its possible relation to the backbone at percolation. Physical Review Letters 47: 1771–1774.Google Scholar
Gooday, A. J., Nott, J. A., Davis, S., and Mann, S. 1995. Apatite particles in the test wall of the large agglutinated foraminifer Bathysiphon major (Protista). Journal of the Marine Biological Association 75: 469–481.Google Scholar
Grotzinger, J. P. and Rothman, D. H. 1996. An abiotic model for stromatolite morphogenesis. Nature 383: 423–424.Google Scholar
Haake, F-W. 1971. Ultrastructures of Miliolid walls. Journal of Foraminiferal Research 1: 187–189.Google Scholar
Heron-Allen, E. 1915. A short statement upon the theory, and the phenomena of purpose and intelligence exhibited by the protozoa, as illustrated by selection and behaviour in the foramininfera. Journal of Microscopy 6: 547–557.Google Scholar
Hoyez, B. 1992. Analyse fractale de la forme des grains de sable. Comptes Rendus de l'Académie des Sciences, Paris. 314: 945–951.Google Scholar
Jones, D. 1988. Fractal concrete. Nature 332:310.Google Scholar
J⊘rgensen, N. O. 1977. Wall structure of some arenaceous foraminifera from the Maastrichtian white chalk (Denmark). Journal of Foraminiferal Research 7: 313–321.Google Scholar
Lipps, J. J. 1973. Test structure in foraminifera. Annual Review of Microbiology 27: 471–488.Google Scholar
Loeblich, A. R. and Tappan, H. 1987. Foraminiferal genera and their classification. Van Nostrand Reinhold, New York.Google Scholar
Mandelbröt, B. B. 1982. P. 142 in The fractal geometry of nature. W. H. Freeman, New York.Google Scholar
Orford, J. D. and Whalley, W. B. 1983. The use of fractal dimension to quantify the morphology of irregularly shaped particles. Sedimentology 30: 655–668.Google Scholar
Petelin, V. P. 1970. Composition of agglutinated material in the tests of certain modern foraminifera. Oceanology 10: 46–55.Google Scholar
Pickering, G., Bull, J. M., and Sanderson, D. J. 1995. Sampling power law distributions. Tectonophysics 248: 1–20.Google Scholar
Podobina, V. M. 1990. Composition and microstructure of agglutinated foraminifer wall. In Hemleben, C., Kaminski, M. A., Kuhnt, W., Scott, D. B. eds. Palaeoecology, biostratigraphy, paleoceanography and taxonomy of agglutinated foraminifera. North Atlantic Treaty Organization ASI Series C (Mathematical and Physical Sciences) 327: 19–23. Kluwer Academic Publishers, Dordrecht, Netherlands.Google Scholar
Salami, M. B. 1976. Biology of Trochammina cf. T. quadriloba Höglund (1947) an agglutinating foraminifera. Journal of Foraminiferal Research 6: 142–153.CrossRefGoogle Scholar
Sammis, C., King, G., and Biegel, R. 1987. The kinematics of gouge deformation. Pure and Applied Geophysics 125: 777–812.Google Scholar
Sanderson, D. J. and Roberts, R. 1994. A fractal relationship between vein thickness and gold grade in drill core from La Codosera, Spain. Economic Geology 89: 168–173.Google Scholar
Smith, M. A. and Kaesler, R. L. 1969. Selection of adventitious test material by Reophax curtus (Foraminiferida). Journal of Paleontology 44: 953–957.Google Scholar
Smith, D. L. 1990. Implications of chaos, scale invariance, and fractal statistics in geology. Palaeogeography, Palaeoclimatology, Palaeoecology (Global and Planetary Change Section) 89: 301–308.Google Scholar
Voss, R. F. 1985. Random fractals. In Pynn, R., Skjeltorp, A. ds. Scaling phenomena in disordered systems. North Atlantic Treaty Organization ASI Series B (Physics) 133: 1–11. Plenum, New York.Google Scholar