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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.

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

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References

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