Saturday, August 27, 2011

Sunflowers



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.












6 comments:

Anonymous said...

pretty

mimi said...

Such friendly flowers. Love them!

Nana said...

Your sunflowers are lovely! They are so cheerful and tall! Who's that cute kid with them?? He's getting pretty tall too! Congrats on your first day of school, Conor!! love you!

Mindy said...

I think my head just exploded.

Anonymous said...

The mathematical model about blew my mind. Great photos!

My Advices said...

I bet you are good in math !!