a plant puts out a new shoot, that shoot has to grow two months before it is strong enough to support branching. If it branches every month after that at the growing point, we get the picture shown here
A plant that grows very much like this is the "sneezewort": Achillea ptarmica.
The most irrational number = Divina proportio
there is a precise sense in which some irrational numbers are more irrational than others.
This phenomenon has had important consequences in the organization of the natural world. In packing seeds around a core, many plants choose the strategy of placing each one at the most irrational angle .
Rotation through the most irrational angle leads to seed packing patterns
with numbers of left- and right-diagonal rows given by consectutive Fibonacci numbers http://plus.maths.org/issue3/fibonacci/ Nature uses spirals to prevent overcrowding