One thing Josh asked is, Does the sunflower picture contain arbirarily large vacant disks? Empirically it seems that it doesn't, and this makes intuitive sense, but can one prove this? Jim Propp On 3/24/12, Henry Baker <hbaker1@pipeline.com> wrote:
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
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun