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Full-Text Articles in Physical Sciences and Mathematics
Fibonacci Or Quasi-Symmetric Phyllotaxis. Part Ii: Botanical Observations, Stéphane Douady, Christophe Golé
Fibonacci Or Quasi-Symmetric Phyllotaxis. Part Ii: Botanical Observations, Stéphane Douady, Christophe Golé
Mathematics Sciences: Faculty Publications
Historically, the study of phyllotaxis was greatly helped by the simple description of botanical patterns by only two integer numbers, namely the number of helices (parastichies) in each direction tiling the plant stem. The use of parastichy num- bers reduced the complexity of the study and created a proliferation of generaliza- tions, among others the simple geometric model of lattices. Unfortunately, these simple descriptive method runs into difficulties when dealing with patterns pre- senting transitions or irregularities. Here, we propose several ways of addressing the imperfections of botanical reality. Using ontogenetic analysis, which follows the step-by-step genesis of the pattern, …
Fibonacci Or Quasi-Symmetric Phyllotaxis. Part I: Why?, Christophe Golé, Jacques Dumais, Stéphane Douady
Fibonacci Or Quasi-Symmetric Phyllotaxis. Part I: Why?, Christophe Golé, Jacques Dumais, Stéphane Douady
Mathematics Sciences: Faculty Publications
The study of phyllotaxis has focused on seeking explanations for the occurrence of consecutive Fibonacci numbers in the number of helices paving the stems of plants in the two opposite directions. Using the disk-accretion model, first introduced by Schwendener and justified by modern biological studies, we observe two dis- tinct types of solutions: the classical Fibonacci-like ones, and also more irregular configurations exhibiting nearly equal number of helices in a quasi-square pack- ing, the quasi-symmetric ones, which are a generalization of the whorled patterns. Defining new geometric tools allowing to work with irregular patterns and local transitions, we provide simple …