Talk:Phyllotaxis

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[edit] Fibonacci numbers and phyllotaxis

I put some discssuion of the appearance of Fibonacci numbers and the golden ratio in phyllotaxis at Talk:Fibonacci number/Phyllotaxis. Some of it might be useful here once this article is fleshed out a little more. -- Dominus 15:40, 11 Mar 2004 (UTC)

I'm new but having read Talk:Fibonacci number/Phyllotaxis, I don't know why the arrangement of leaves on a stalk isn't just one more example of those things that are .618... of another or 1.618 times the other.

There are going to be a lot of appearances of φ in the world. Some of these are coincidences, where it seems that there is no particular reason why it should be 1.6 rather than 1.7 or 1.5 or 23. For example, is your navel really 1/φ of the way up your body? Not so far as anyone can tell. Maybe it is about three-fifths of the way up, but there's no reason to identify that 3/5 with anything related to φ.

Other appearances of φ, however, are not coincidences; there will be some reason why they appear, and when the number that is actually measured differs from φ, we can view that as a deviation. The distribution of leaves on the stem is one of these, because there's a simple mechanism that leads to favorable leaf placement. Leaf placement is more favorable for certain angles than for other angles, and the optimal leaf placement is achieved when the angle is 360/φ. So it seems clear that the appearance of φ here is not a coincidence, because plants that distribute their leaves with the 360/φ angle will tend to outcompete plants that distribute their leaves in some other way, and the closer the plant can get to the uniform 360/φ angle, the more successful it will tend to be. -- Dominus 14:34, 13 Jun 2005 (UTC)