Tuesday, August 26, 2008

Mathematical model of floret arrangement

A model for the pattern of florets in the head of a sunflower was proposed by H Vogel. This is expressed in polar coordinates

r = c \sqrt{n},
\theta = n \times 137.5^{\circ},

where θ is the angle, r is the radius or distance from the center, and n is the index number of the floret and c is a constant scaling factor. It is a form of Fermat's spiral. The angle 137.5° is related to the golden ratio and gives a close packing of florets. This model has been used to produce computer graphics representations of sunflowers.

From www.wikipedia.org

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