## A Photo a Day by Bill Heller

#### Mathematical Precision of Nature Photos Monday, August 1, 2005
Fibonacci Daisy

I really like flowers that are a little irregular like this one and another of my favorite daisies. But there is an interesting contrast in this one. Although the petals are quite wild, the center is incredibly orderly. In fact it is orderly to a mathematical precision.

There is a sequence of numbers that predicts very closely these kinds of shapes in nature. It is called the Fibonacci Sequence. Anything from the number of scales on each successive row of a pine cone and the leaves on a tree to the parts of the center of a daisy. The sequence is very easy to create. Each number is the sum of the previous two numbers in the sequence. So starting with 0, 1 and adding them together you get 0, 1, 1. Next you add 1 and 1 and get 0, 1, 1, 2 and so on...

``` 0,1,1,2 | | 1+2=3 | | | 2+3=5 | | | | 3+5=8 | | | | | 5+8=13 | | | | | | 8+13=21 | | | | | | | 13+21=34 | | | | | | | |  21+34=55 | | | | | | | |  |  34+55=89 | | | | | | | |  |  |  |  | 0,1,1,2,3,5,8,13,21,34,55,89 ```

So if you were to start in the very center of the daisy, called the "Capitulum". You would probably find one individual flower (the Capitulum is actually a cluster of small flowers. So, a single daisy is actually a group of very small flowers botanically speaking). Moving out from that first flower in concentric circles you would find each row contains 1 then 2 then 3 flowers and so on. It may not be exact, but more times than not you will find it is very close.