[fvirexi]

I only meant it as a possible explanation for why it wouldn't be unreasonable to think phi appears often in nature. I don't really have enough knowledge of nature to say if it's the case.

Distribute the seeds of a sunflower radially, placing one seed every 360*x degrees, gradually increasing radius. If x=a/b, after placing b seeds, you will be back to the initial position and the next b seeds will be (radially) shaded from the first b seeds (which I admit, might not be how shading works in practice). If x is irrational, but closely approximated by a/b, the seeds won't line up perfectly, but still enough to shade quite a bit. If x is phi, then they will shade as little as theoretically possible (I think.. This is by no means a proof, just some thoughts). IIRC, the "sunflower seed pattern" is actually achieved only if you simulate such a seed placing with x close to phi.

[jules]

This is trying to find meaning where there is none. I don't think shading of seeds has any impact on the evolutionary fitness, even if we assume that light is coming in radially which is of course not true at all. Furthermore, even if we make the two (clearly incorrect) assumptions that sunflowers do care about shading of the seeds and that light does come in radially, that does not even constitute a convincing argument that the seeds grow in that pattern. Here is a far more convincing argument along the same lines. Plants care about getting energy. They get energy by absorbing sunlight. Black absorbs the most light. Ergo, plants are black.

[fvirexi]

Good point. The reason why few to no plants are not black is a very interesting problem, which I haven't heard an answer to.

Still, the number phi has very unique properties, considering its SCF. And the sequence of fibonacci ratios is not an arbitrary sequence converging to it. Whether anything has evolved to utilize this or not, I can not say.

[jameshart]

Thing is, Phi's not really all that interesting. It's just a simple root of a quadratic, no more 'mystical' than the square root of five. It doesn't 'emerge' from arithmetic the way e or pi do. It's a fixed point of the sequence of operations: 'take a number; invert it; add one; repeat'... that's, sort of interesting, but 'add one' isn't a very special operation - why not add 12? or add pi? or add phi?

Take a number, invert it, add two, repeat... eventually you get root 2 + 1. And the inverse of that is root 2 - 1! That's pretty magical! Kind of more magical than 'half plus root 5 over 2', anyway. Maybe root 2 + 1 is the platinum ratio!