I saw a recent TED Talk about Phyllotaxis, but when I Google searched for it, I couldn't find it. According to this talk, the Fibonacci sequence comes quite naturally in phyllotaxis, because when a branch on a plant splits off, Kirchoff's current law says that the water flow in the branches equals the water flow in the trunk. Since branches tend to split off one at a time, you get flow_{i-2}=flow_{i-1}+flow_{i}, etc. The sizes of the branches is organized to support this amount of flow. At 09:24 PM 3/23/2012, Stuart Anderson wrote:
A reference for some of that recent (and not so recent work - von Iterson) http://www.scribd.com/doc/39484505/Phyllotaxis
with real sunflowers evidently one needs to understand the dynamics of plant buds; 'primordia' which has been the subject of much recent research