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Describing the shapes of fern leaves: A fractal geometrical approach

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Abstract

Fractal geometry offers a new approach to describing the morphology of fern leaves. Traditional morphology is based on the Euclidean concept of shape as an area defined by a boundary. This approach has not proven successful with fern leaves because they are so elaborate. Fractal geometry treats forms as relationships between parts rather than as areas. In fern fronds there are often constant relationships between parts. Four fractal methodologies for describing these relations within leaves are explored in this paper. These include recursive line branching algorithms, iterated function systems (IFS), modifications of IFS, and L-systems. The methods are evaluated by comparing their results with measurements and appearances of various ferns. Fractal methods offer objective, quantifiable and succinct descriptions of fern-leaves. We conclude that fractal geometry offers simple descriptions of some elaborate fern shapes and that it will probably have application in investigating different aspects of ferns and other organisms.

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Authors and Affiliations

  1. Department of Developmental and Cell Biology, University of California, 92717, Irvine, CA, USA

    Richard D. Campbell

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  1. Richard D. Campbell
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Campbell, R.D. Describing the shapes of fern leaves: A fractal geometrical approach. Acta Biotheor 44, 119–142 (1996). https://doi.org/10.1007/BF00048419

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  • DOI: https://doi.org/10.1007/BF00048419

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