10 October 2012

Fibonacci Seed Head

Flower seed head fibonacci numbers

The other day I took a bucket of kitchen waste to the compost bin at the back of the garden. A fat and menacing spider had woven a web right across the path. I swear the silk was so thick it could have suspended the Severn Bridge, so being an urban wimp I backed away and looked for another way to get to the bin, but it's jungle out there at the moment. Fed by the rain and the little dribble of sunshine we are having everything is putting out a last desperate effort of growth. There is no bare earth to walk on at all. The heleniums have gone crazy; I reckon some of them are six foot tall. But although they may elegantly swish from side to side like an adolescent supermodel they have no real strength in them, and are no match for a hefty middle aged woman with a bucket of potato peelings in her hand. I heaved through into their green ranks. Unfortunately this was meant to be a ‘just nipping out’ job so I was wearing fluffy socks and the clogs that are too big. The supermodels took their revenge. They stuck out their skinny little roots and tripped me up, and I ended up flailing around in a stand of heleniums, one shoe off, onion skins stuck to my face and a fierce hope none of the neighbours were watching.

Feigning amusement I did in the end manage to top up the compost bin.

On the up side of the close encounter with the deceptively simple flowers an interesting discovery was made: the seed heads grow in a beautiful spiralling pattern. And with further googling it turns out this pattern is the result of some famous mathematical numbers called the Fibonacci sequence.

1, 2, 3, 5, 8, 13, 21, 34, 55, 89

The idea is you add the last two numbers together to get the next. For example, 5 + 8 = 13, 8 + 13 = 21.

Mathematicians and Mother Nature love this set of numbers. Mathematicians use them to do inscrutable things with algorithms, but nature uses them to efficiently pack in as many seeds as possible onto a flower head. As seeds grow from the centre they push out older seeds. This is done in an ordered way to ensure there are no gaps, or wasted space. The resultant pattern appears as arms of a spiral. The beauty of the pattern is a consequence of precise maths.

So to prove the point I’ve counted the spirals of one of my supermodels, and yes indeed, in this case there are 13 spirals. Flowers that have more seeds, such as sunflowers, show a counter-clockwise pattern of spiral arms as well. This can be just about seen here, with 21 arms, some of which are only three seeds long. And just to make things neat and tidy the flower has 13 petals.

fibonacci numbers in flower seed head
21 Counter-clockwise Spiral Arms

I am tempted to conclude this post by saying there is always order in apparent chaos, but then I have a 'flailing in the heleniums' flashback, and have to doubt that belief.