What really interested me in these videos wasn't just the relationship, but that they'd figured out a mechanism for how the relationship was formed, and it something so apparently unrelated, ie the concentration of hormones as the individual 'bits' of the plant were forming and moving away from the meristem. At a given concentration, fibonacci numbers just appeared spontaneously. And, more to the point, if the concentration was slightly different, then numbers from a different number-sequence would appear, even on the same plant. Also, the way that it seems that way the leaves are arranged on a stem is controlled the same way.
Most herbicides are hormonal in effect. I wonder if there's any evidence of herbicide use effecting the patterns that form on plants?
Edit - I've finally found a pdf of an article about
Phyllotaxis, Fibonacci and Hormone Gradients
It's a bit technical, but I think I can read it...
Also, for anyone not in the mood for numbers or long words, this
video is just beautiful -
Nature by Numbers
Here's a still from the video...