Abstract
Photographs of mistletoe (Viscum album L.) berries taken by a permanently fixed camera during their development in autumn were subjected to an outline shape analysis by fitting path curves using a mathematical algorithm from projective geometry. During growth and maturation processes the shape of mistletoe berries can be described by a set of such path curves, making it possible to extract changes of shape using one parameter called Lambda. Lambda describes the outline shape of a path curve. Here we present methods and software to capture and measure these changes of form over time. The present paper describes the software used to automatize a number of tasks including contour recognition, optimization of fitting the contour via hill-climbing, derivation of the path curves, computation of Lambda and blinding the pictures for the operator. The validity of the program is demonstrated by results from three independent measurements showing circadian rhythm in mistletoe berries. The program is available as open source and will be applied in a project to analyze the chronobiology of shape in mistletoe berries and the buds of their host trees.
Highlights
Patterns and forms in animals and plants have fascinated mankind from the dawn of science in ancient Greece, and motivated thinkers and scientists at the beginning of the scientific revolution
Amazing correlations continue to be found between forms and patterns in nature and certain fields in mathematics [2], and modeling has developed into a viable instrument for revealing the lawfulness of biological processes
The program is freely available as open source at http://www.feiten.de/LambdaFit/
Summary
Patterns and forms in animals and plants have fascinated mankind from the dawn of science in ancient Greece, and motivated thinkers and scientists at the beginning of the scientific revolution. Patterns and forms seemed ideal for exploring the hidden plan of God in nature [1], with mathematics the tool of choice for revealing these ‘‘divine thoughts’’. Amazing correlations continue to be found between forms and patterns in nature and certain fields in mathematics [2], and modeling has developed into a viable instrument for revealing the lawfulness of biological processes. Rhythms of plant growth and development, the synchronicity of cell division and DNA replication are scrutinized, as are gene expression and enzymatic activity in correlation with time or season. Biological rhythms can be found phenotypically in plant organs such as buds or berries [3]
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