Disk florets of yellow chamomile (Anthemis tinctoria) with spirals indicating the arrangement drawn in. (Photo credit: Wikipedia)
I have known about the beauty of the pattern of seeds in the heads of sunflowers for a long time now, but still stare in wonder just as I did when I saw it the first time. You count the number of spirals in each direction and find that they are two consecutive numbers in the Fibonacci Sequence.
I recently heard that the pattern also includes the Golden Angle. This is when you divide up 360 degrees into two angles in the Golden Ratio. The smaller angle is the Golden Angle which is irrational and measures 137.508… degrees. The seed pattern is formed by seeds being ‘fired’ from the centre of the flower head outwards one at a time. The angle that each seed heads off from the centre when measured from the last one is the Golden Angle.
For a bit of fun I thought I’d write a computer simulation of this procedure to see if I could replicate the pattern. I then also changed the angle of consecutive seeds to plus and minus one degree from the Golden Angle to see how sensitive the pattern is to the angle. The results are surprising!
It seems as though the seed pattern is extremely sensitive to the angle that the seeds are released! Therefore we must conclude that sunflowers are great admirers of the beauty of mathematics! They are applied mathematicians at heart, putting their knowledge into a wonderful real world application!
