Document Type

Article

Publication Date

12-31-2016

Publication Title

Acta Societatis Botanicorum Poloniae

Abstract

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.

Keywords

phyllotaxis; Fibonacci, quasi-symmetry, disc-stacking model, irregular pattern

Volume

89

Issue

4

DOI

doi.org/10.5586/asbp.3533

Creative Commons License

Creative Commons Attribution 4.0 License
This work is licensed under a Creative Commons Attribution 4.0 License.

Included in

Mathematics Commons

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