Physical Sciences and Mathematics Commons^™

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 …