Well since I already mentioned the proportions, there is no secret.
Let me follow up on Al's question by stating it in a different way. Let's say I gave you this image and said "there is a branch there on the left that I'd like you to complete by drawing on the blue box. I want you to draw a branch that hangs down so that the entire design is in balance":
If you buy into the theory of the Golden Mean, you will draw Gene's design... which EXACTLY fits the proportions of the Golden Mean. Note that I didn't even INCLUDE that option (at least initially) and yet someone suggested it.
Is this the "only" design? Of course not! Is this the "perfect" design? That is up to interpretation. But it is a ratio that people are drawn to... and if you understand it you can use it in your work - to either match it or distance yourself from it.
The problem, though, is that you're only measuring one aspect of the tree.
The very first picture that you posted (in post 12) perfectly satisfied the golden mean in one sense (the ratio of the bottom of the foliage mass to the height). But most of us don't like it. On the "Gene tree", the left side still fits the golden mean, but the right side does not. Many of us seem to like that tree quite a bit. The big difference is the asymmetry in the foliage mass across the trunk between the two trees.
I think the "true" (or truer, perhaps) test of the golden ratio would be to take tree image #1 from post 12 and bring the foliage mass both up and down, changing the ratio but keeping the symmetry - because by introducing the asymmetry you're really changing many other factors in the design.
And that's where the complexity really comes in with real trees. How does one quantify the effects of asymmetry and how it relates to or interacts with other measurements?
Maybe that's a topic for a later thread.