Document Type

Article

Publication Date

12-31-2016

Publication Title

Acta Societatis Botanicorum Poloniae

Abstract

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, and crystallographic analysis, which reveal irregularity in its details, we show how to derive more information from a real botanical sample, in particular, about its irregularities and transitions. We pres- ent several examples, from the first explicit visualization of a normal Fibonacci parastichy number increase, to more exotic ones, including the quasi-symmetric patterns detected in simulations. We compare these observations qualitatively with the result of the disk-packing model, presenting evidence for the relevance of the model.

Keywords

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

Volume

85

Issue

4

DOI

doi. org/10.5586/asbp.3534

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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