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The Geometric and Dynamic Essence ofPhyllotaxis

Published online by Cambridge University Press:  01 March 2011

P. Atela
P. Atela*
Affiliation:
Department of Mathematics, Smith College, Northampton, MA 01063, USA
*
⋆E-mail: [email protected]
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Abstract

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

Keywords

phyllotaxisfibonaccipattern formationprimordiameristem
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 6 , Issue 2: Modelling of plant growth , 2011 , pp. 173 - 186
Copyright
© EDP Sciences, 2011

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References

Références

Atela, P., Gole, C., Hotton, S.. A dynamical system for plant pattern formation: a rigorous analysis. J. Nonlinear Sci., 12 (2002), No. 9, 641–676. CrossRefGoogle Scholar
Douady, S., Couder, Y.. Phyllotaxis as a physical self organized growth process. Phys. Rev. Lett., (1992), No. 68, 2098–2101. CrossRefGoogle ScholarPubMed
Douady, S., Couder, Y.. Phyllotaxis as a Self Organizing Iterative Process, Parts I, II and III. J. Theor. Biol., (1996), No. 178, 255–312. CrossRefGoogle Scholar
Hofmeister, W.. Allgemeine Morphologie der Gewachse, in Handbuch der Physiologishcen Botanik. Engelmann, Leipzig, (1868), No. 1, 405–664. Google Scholar
Hotton, S., Johnson, V., Wilbarger, J., Zwieniecki, K., Atela, P., Gole, C., Dumais, J.. 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. CrossRefGoogle Scholar
R. V. Jean. Phyllotaxis, a Systemic Study in Plant Morphogenesis. Cambridge University Press, 1994.
R.V. Jean, D. Barab, editors. Symmetry in Plants. World Scientific, Singapore, 1994.
Levitov, L.S.. Energetic Approach to Phyllotaxis. Europhys. Lett., 14 (1991), No. 6, 533–539. CrossRefGoogle Scholar
Snow, M., Snow, R.. Minimum Areas and Leaf Determination. Proc. Roy. Soc., (1952), No. B139, 545–566. CrossRefGoogle Scholar
G. van Iterson. Mathematische und Microscopisch-Anatamische Studien über Blattstellungen, nebst Betrshungen über den Schalenbau der miliolinen. G.-Fischer-Verlag, Jena, 1907.