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Use of fractal dimensions to quantify coral shape

Abstract

A morphometrical method to quantify and characterize coral corallites using Richardson Plots and Kaye’s notion of fractal dimensions is presented. A Jurassic coral species (Aplosmilia spinosa) and five Recent coral species were compared using the Box-Counting Method. This method enables the characterization of their morphologies at calicular and septal levels by their fractal dimensions (structural and textural). Moreover, it is possible to determine differences between species of Montastraea and to tackle the high phenotypic plasticity of Montastraea annularis. The use of fractal dimensions versus conventional methods (e.g., measurements of linear dimensions with a calliper, landmarks, Fourier analyses) to explore a rugged boundary object is discussed. It appears that fractal methods have the potential to considerably simplify the morphometrical and statistical approaches, and be a valuable addition to methods based on Euclidian geometry.

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Acknowledgments

We are greatly indebted to the staff of thin-section preparation: Vlado Grečo from the Institute of Geology at Berne, and to Michel Lemoine of the Muséum National d’Histoires Naturelles at Paris for impregnation of Recent coral skeletons with artificial resin. Finally, we are grateful to Martin Engi (Berne), for reviewing our French–German English, and to our reviewers for their constructive remarks. This research was funded by the Swiss National Science Foundation (grant 21-61834.00).

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Correspondence to B. Martin-Garin.

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Communicated by Geology Editor B. Riegl.

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Martin-Garin, B., Lathuilière, B., Verrecchia, E.P. et al. Use of fractal dimensions to quantify coral shape. Coral Reefs 26, 541–550 (2007). https://doi.org/10.1007/s00338-007-0256-4

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  • DOI: https://doi.org/10.1007/s00338-007-0256-4

Keywords

  • Fractal
  • Corallite
  • Method
  • Morphology
  • Variability