On the Fundamental Theorem of Phyllotaxis

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Jean's fundamental theorem of phyllotaxis describes the relationship between the numbers of observed spirals in cylindrical lattices and the horizontal angle between successive vertical spots in the lattice.


In this Demonstration the divergence is calculated solely by the visible opposed parastichy (spiral line) pairs.


Contributed by: Dmitry Weise (June 2013)
Open content licensed under CC BY-NC-SA



The parastichies are the series of leaves that most readily catch the eye. The number of parastichies rises from the center to the periphery, following a Fibonacci sequence.

GCD is the greatest common divisor.

Divergence angle is the angle between two consecutive leaves.


[1] R. V. Jean, Phyllotaxis: A Systemic Study in Plant Morphogenesis, New York: Cambridge University Press, 2009.

[2] D. Weise. "Principle of Minimax and Rise Phyllotaxis (Mechanistic Phyllotaxis Model)." (Jun 6, 2013) www.mi.sanu.ac.rs/vismath/dima.

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