Examples of phyllotaxis (literally "leaf order")

Phyllotaxis is the property of some kind of visual regularity showing up in the arrangements of leaves on a plant, or any plant organs that have been sequentially produced.
The spirals that are visible in the patterns are called parastichies.

Here are some actual photos:

Norway Spruce needles. Pictures are about 2mm across

Future hair in an artichoke heart

The Romanesqueco