Dandelion spiral

Golden flowers, a special arrangement of seeds in spirals based on the golden ratio, are common in the plant world. I was looking at dandelion and suspected there was one underneath the white fluffy seed parachutes. I blew on it a few times to find out and sure enough, there's a golden spiral under those seeds. Nice!

Here's a pdf file of a paper I wrote some years ago on the mathematics of these spirals: http://www.mike-naylor.com/naylor-seeds.pdf. And here's a nice video by Vi Hart: http://youtu.be/ahXIMUkSXX0

 

 

Here I've drawn in two sets of spirals, 8 and 13. The set of spiral with 21 arms is fairly easy to see also.