Now let's forget the moon and come back to Fibonacci.
Fibonacci was studying the reproduction of rabbits and he made the hypothesis that each generation was producing 1 couple and only one couple at each generation. In that case the ratio of two consecutive terms will be the solution of the equation x = x^2 +1 which would give 1.618.
But nature is not so simplist and if he had supposed 3 couples distributed on 3 generations the new magic number would be the solution of the equation x^3 = x^2 + x + 1 and would give a ratio of 1.839.
So the golden mean has no acquired universality at least on macroscopic scale where the initial conditions can be broadly numerous and that what makes richness of life possible !
It could be that on atomic scale golden ratio play a role as other universal constants but on macroscopic scale it has to be demonstrated case by case !
Fibonacci was studying the reproduction of rabbits and he made the hypothesis that each generation was producing 1 couple and only one couple at each generation. In that case the ratio of two consecutive terms will be the solution of the equation x = x^2 +1 which would give 1.618.
But nature is not so simplist and if he had supposed 3 couples distributed on 3 generations the new magic number would be the solution of the equation x^3 = x^2 + x + 1 and would give a ratio of 1.839.
So the golden mean has no acquired universality at least on macroscopic scale where the initial conditions can be broadly numerous and that what makes richness of life possible !
It could be that on atomic scale golden ratio play a role as other universal constants but on macroscopic scale it has to be demonstrated case by case !
- plants for sure follow fibonacci law for their leaves form a spiral in golden ratio proportion. But some plants don't and follow Lucas Law rather. This has to do with their gene coding which is a very precise mechanism. As for stock market there is no such known gene ... as far as I know 
