Abstract
An application of fractal mathematics to the analysis of leaf shapes is presented. Six leaves randomly selected from nine tree species were used in the study. A video imaging method together with microcomputer-based image processing was used to generate leaf outlines. A fractal analysis program was written to calculate the fractal dimensions of the leaves. Recalling a leaf outline from a diskette and specifying both the starting position on it (e.g., the beginning of the petiole) and six step lengths (explained later), the program then generates the fractal dimension according to the theory described. The results show that the fractal dimension is sensitive to leaf shape variations within a species. For example, two types of ginkgo leaves (one with and one without a notch in the middle of the leaf outline) showed distinctly different fractal values. Similar sensitivity to shape change was observed among the leaves of white oak, red oak, and sugar maple where such variables as width to length ratio and the degree of jaggedness of the leaf caused a departure of the fractal value from the average.
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Claims 3
Claim · model-written summary
The fractal dimension of leaves is sensitive to leaf shape variations within a species of tree.
Verbatim
e1“Six leaves randomly selected from nine tree species were used in the study”
e2“The results show that the fractal dimension is sensitive to leaf shape variations within a species”
Claim · model-written summary
Two types of ginkgo leaves, with and without a notch, gave distinctly different fractal values.
- Outcome
- fractal valuese3
- Qualifier
- distinctly differente3
- Comparator
- one with and one without a notch in the middle of the leaf outlinee3
GinkgoOrganisms pictured · Representative pictures of the matched species, not figures from the paper.
Verbatim
e3“two types of ginkgo leaves (one with and one without a notch in the middle of the leaf outline) showed distinctly different fractal values”
Claim · model-written summary
Width to length ratio and leaf jaggedness caused the fractal value of white oak, red oak and sugar maple leaves to depart from the average.
- Taxon
- white oak, red oak, and sugar maple
_(14092717698).jpg?width=60)
Quercus rubra
Quercus alba
Acer saccharume4 - Outcome
- fractal valuee4
- Qualifier
- width to length ratio and the degree of jaggednesse4
- Comparator
- averagee4
Organisms pictured · Representative pictures of the matched species, not figures from the paper.
_(14092717698).jpg?width=500)
Verbatim
e4“Similar sensitivity to shape change was observed among the leaves of white oak, red oak, and sugar maple where such variables as width to length ratio and the degree of jaggedness of the leaf caused a departure of the fractal value from the average”