Mathematical model of floret arrangement
Illustration of Vogel's model for n=1 ... 500
A model for the pattern of florets in the head of a sunflower was proposed by H. Vogel in 1979. This is expressed in polar coordinates 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 (55/144 of a circular angle, where 55 and 144 are Fibonacci numbers) and gives a close packing of florets. This model has been used to produce computer graphics representations of sunflowers.
Illustration of Vogel's model for n=1 ... 500
A model for the pattern of florets in the head of a sunflower was proposed by H. Vogel in 1979. This is expressed in polar coordinates 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 (55/144 of a circular angle, where 55 and 144 are Fibonacci numbers) and gives a close packing of florets. This model has been used to produce computer graphics representations of sunflowers.
