Acta Societatis Botanicorum Poloniae
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 explanations for the emergence of these two states within the same elementary model. A companion paper will provide a wide array of plant data analyses that support our view.
phyllotaxis; Fibonacci, quasi-symmetry, disc-stacking model, irregular pattern
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Golé, Christophe; Dumais, Jacques; and Douady, Stéphane, "Fibonacci or Quasi-Symmetric Phyllotaxis. Part I: Why?" (2016). Mathematics and Statistics: Faculty Publications, Smith College, Northampton, MA.