There are certain aspects of Nature that inspire amazement when we look at them and even greater amazement when we analyze them even deeper.
The mighty sunflower is an amazing little piece of mathematical design, when we analyze the spiral shapes in which the seeds are laid out. I think most of us have heard of Fibonacci numbers: the sequence 1, 1, 2, 3, 5, 8, and so on, so that each number is the sum of the last two. When looking at the spiraling shapes in cauliflower, artichoke and the sunflower floret, as seen above, we see this sequence appear in front of our eyes.
Upon analysis, we see that those spirals pack florets as tight as can be, maximizing their ability to gather sunlight for the plant. But how do plants like sunflowers create such perfect floret arrangements, and what does it have to do with Fibonacci numbers? A plant hormone called auxin, which spurs the growth of leaves, flowers, and other plant organs, is the key: Florets grow where auxin flows. This has been modelled mathematically by researchers to demonstrate the Fibonacci spiral count is the optimal dense-packing strategy.
How to Count the Spirals
The sunflower seed pattern used by the Museum of Mathematics contains many spirals. If you count the spirals in a consistent manner, you will always find a Fibonacci number (0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, …). Below are the three most natural ways to find spirals in this pattern. Note that the black pattern is identical in all the images on this page. Only the colored lines indicating the selected spirals are different.
The red lines show 34 spirals of seeds.
Choosing another slope, the green lines show 55 spirals of seeds.
And choosing a very shallow slope, the blue lines show 21 spirals of seeds.
– See more about this at: http://momath.org/home/fibonacci-numbers-of-sunflower-seed-spirals/#sthash.XF0YpZoT.dpuf
Hope you enjoyed this bit of in-depth view of the sunflower!