So perhaps this is a question that others have answered, but what springs to mind for me is: why? I get that trees that follow the Fibonacci sequence are more productive, but without an answer to why that is, it remains a bit of a kludge. I would love to see some explanation of why this configuration is optimal.
If leaves are space a rational number divisor a/b of 360 degrees around a trunk, then after b turns, leaves will directly shadow each other. To avoid this you need the amount of turn between leaves to be as difficult as possible to approximate by a rational number.
Using continued fractions we can see that the most difficult rational to approximate is
1 + 1/(1 + 1/(1 + 1/(...)))
which is (1+sqrt(5))/2 which is the Golden Ratio.
You can also get better packings by using the Fibonacci Spiral, which again gives the Golden Ratio:
Yeah, that's a bit fishy. Without an explanation, I'm skeptical that the Fibonacci sequence is actually important. Perhaps any branching arrangement of solar panels performs better than a flat one.
