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Fourier packing ordinate: A univariate size-independent measurement of the polygonal packing variation in Paleozoic bryozoans

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Abstract

The Fourier packing ordinate provides a highly sensitive, univariate, and size-independent measurement of the polygonal packing variation in Paleozoic bryozoan colonies. It is potentially useful in quantifying a wide variety of natural packing arrays or polygonal networks, and is preferable to counting the sides of polygons, the frequency of triple or quadruple junctions, the nearest-neighbor statistic, measurements of surface area per unit cell, or individual harmonic amplitudes. Fourier shape analysis provides exact measurements of the levels of two- to six-fold rotational symmetry in all natural packing gradients. In bryozoans these symmetries are intercorrelated because as each order of symmetry is increasing, the previous order is decreasing. Shapes in these packing arrays are normally hybrids of two or more orders of rotational symmetry. The levels of rotational symmetry involved in these packing gradients are significantly correlated with a single principal component, the Fourier packing ordinate, which is independent of both size and cell boundary phenomena. Spatial analysis of the Fourier packing ordinate within an Ordovician bryozoan colony reveals both variation in packing caused by subcolony budding, as well as large scale trends which vary from the colony center to the free-growing margin.

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Authors and Affiliations

  1. Department of Geology, Michigan State University, 48824, East Lansing, Michigan, USA

    Robert L. Anstey

  2. Department of Geology, Indiana University—Purdue University at Indianapolis, 46202, Indiana, USA

    Joseph F. Pachut

Authors
  1. Robert L. Anstey
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  2. Joseph F. Pachut
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Anstey, R.L., Pachut, J.F. Fourier packing ordinate: A univariate size-independent measurement of the polygonal packing variation in Paleozoic bryozoans. Mathematical Geology 12, 139–156 (1980). https://doi.org/10.1007/BF01035245

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  • DOI: https://doi.org/10.1007/BF01035245

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