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.

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

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


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Details

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.

References

[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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