The Geometric and Dynamic Essence of Phyllotaxis

P. Atela

Mathematical Modelling of Natural Phenomena (2011)

  • Volume: 6, Issue: 2, page 173-186
  • ISSN: 0973-5348

Abstract

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We present a dynamic geometric model of phyllotaxis based on two postulates, primordia formation and meristem expansion. We find that Fibonacci, Lucas, bijugate and multijugate are all variations of the same unifying phenomenon and that the difference lies in the changes in position of initial primordia. We explore the set of all initial positions and color-code its points depending on the phyllotactic pattern that arises.

How to cite

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Atela, P.. "The Geometric and Dynamic Essence of Phyllotaxis." Mathematical Modelling of Natural Phenomena 6.2 (2011): 173-186. <http://eudml.org/doc/222373>.

@article{Atela2011,
abstract = {We present a dynamic geometric model of phyllotaxis based on two postulates, primordia formation and meristem expansion. We find that Fibonacci, Lucas, bijugate and multijugate are all variations of the same unifying phenomenon and that the difference lies in the changes in position of initial primordia. We explore the set of all initial positions and color-code its points depending on the phyllotactic pattern that arises. },
author = {Atela, P.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {phyllotaxis; fibonacci; pattern formation; primordia; meristem; Fibonacci},
language = {eng},
month = {3},
number = {2},
pages = {173-186},
publisher = {EDP Sciences},
title = {The Geometric and Dynamic Essence of Phyllotaxis},
url = {http://eudml.org/doc/222373},
volume = {6},
year = {2011},
}

TY - JOUR
AU - Atela, P.
TI - The Geometric and Dynamic Essence of Phyllotaxis
JO - Mathematical Modelling of Natural Phenomena
DA - 2011/3//
PB - EDP Sciences
VL - 6
IS - 2
SP - 173
EP - 186
AB - We present a dynamic geometric model of phyllotaxis based on two postulates, primordia formation and meristem expansion. We find that Fibonacci, Lucas, bijugate and multijugate are all variations of the same unifying phenomenon and that the difference lies in the changes in position of initial primordia. We explore the set of all initial positions and color-code its points depending on the phyllotactic pattern that arises.
LA - eng
KW - phyllotaxis; fibonacci; pattern formation; primordia; meristem; Fibonacci
UR - http://eudml.org/doc/222373
ER -

References

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  1. P. Atela, C. Gole, S. Hotton. A dynamical system for plant pattern formation: a rigorous analysis. J. Nonlinear Sci., 12 (2002), No. 9, 641–676.  Zbl1029.92004
  2. S. Douady, Y. Couder. Phyllotaxis as a physical self organized growth process. Phys. Rev. Lett., (1992), No. 68, 2098–2101.  
  3. S. Douady, Y. Couder. Phyllotaxis as a Self Organizing Iterative Process, Parts I, II and III. J. Theor. Biol., (1996), No. 178, 255–312.  
  4. W. Hofmeister. Allgemeine Morphologie der Gewachse, in Handbuch der Physiologishcen Botanik. Engelmann, Leipzig, (1868), No. 1, 405–664.  
  5. S. Hotton, V. Johnson, J. Wilbarger, K. Zwieniecki, P. Atela, C. Gole, J. Dumais. The possible and the actual in phyllotaxis: Bridging the gap between empirical observations and iterative models. Journal of Plant Growth Regulation, (2006), No. 25, 313–323.  
  6. R. V. Jean. Phyllotaxis, a Systemic Study in Plant Morphogenesis. Cambridge University Press, 1994.  Zbl0818.92001
  7. R.V. Jean, D. Barab, editors. Symmetry in Plants. World Scientific, Singapore, 1994.  
  8. L.S. Levitov. Energetic Approach to Phyllotaxis. Europhys. Lett., 14 (1991), No. 6, 533–539.  
  9. M. Snow, R. Snow. Minimum Areas and Leaf Determination. Proc. Roy. Soc., (1952), No. B139, 545–566.  
  10. G. van Iterson. Mathematische und Microscopisch-Anatamische Studien über Blattstellungen, nebst Betrshungen über den Schalenbau der miliolinen. G.-Fischer-Verlag, Jena, 1907.  Zbl38.0984.07

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