Fibonacci or quasi-symmetric phyllotaxis. Part I: why?
Goles
C
author
Dumais
J
author
Douady
S
author
2016
English
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.
phyllotaxis
Fibonacci
quasi-symmetry
disc-stacking model
irregular pattern
WOS:000392930700006
exported from refbase (http://ficpubs.uai.cl/show.php?record=694), last updated on Wed, 11 Oct 2017 16:37:58 -0400
text
http://ficpubs.uai.cl/files/694_Gole_etal2016.pdf
10.5586/asbp.3533
Goles_etal2016
Acta Societatis Botanicorum Poloniae
Acta Soc. Bot. Pol.
2016
Polskie Towarzystwo Botaniczne
continuing
periodical
academic journal
85
4
34 pp
0001-6977