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Fibonacci or quasi-symmetric phyllotaxis. Part II: botanical observations

100%

Douady S., Gole C.

Acta Societatis Botanicorum Poloniae

2016

tom 85

nr 4

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 numbers reduced the complexity of the study and created a proliferation of generalizations, among others the simple geometric model of lattices. Unfortunately, these simple descriptive method runs into difficulties when dealing with patterns presenting 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 present 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.

Fibonacci or quasi-symmetric phyllotaxis. Part I: why?

80%

Gole C., Dumais J., Douady S.

Acta Societatis Botanicorum Poloniae

2016

tom 85

nr 4

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 distinct types of solutions: the classical Fibonacci-like ones, and also more irregular configurations exhibiting nearly equal number of helices in a quasi-square packing, 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.

Ograniczanie wyników

2 Acta Societatis Botanicorum Poloniae

2 Douady S.

2 Gole C.

1 Dumais J.

2 2016

Wyniki wyszukiwania

Fibonacci or quasi-symmetric phyllotaxis. Part II: botanical observations

Fibonacci or quasi-symmetric phyllotaxis. Part I: why?