I'm not sure leaf morphology matters. Let me look in my files, I may find
something about this.
> The Golden Spiral, the Golden Rectangle, and the Magic Ratio are all
> designations of some elusive phenomenon that is extremely widespread in nature
> and in human life. The phenomenon appears in astronomy, oceanography,
> biology, architecture, art, and music. It is found in the curving arms of spiral
> of galaxies; the curling lip of a wave, the shoreline of Cape Cod; in the
> arrangements of florets of a sunflower, seeds in pine cones, the arrangements of
> leaves on a plant's stalk, and the number of petals in a daisy; in the "exquisitely
> beautiful molluscan shells" (Thompson, 1942), the shape of a snail's shell and that
> of a chambered nautilus; in a ram's horn, a parrot's beak, a lion's claw; in the
> Great Pyramid of Egypt, the front elevation of the Parthenon, in Greek vases and
> statues, in classical art; in the proportions found in musical chords; in the
> proportions of the human body. The phenomenon is too widespread in too many
> different circumstances to be discounted as mere chance (Hoffer E., "A magic ratio
> recurs throughout art and nature" _Smithsonian Magazine_1975, p. 120), although
> none of the examples is exactly perfect in nature.
The human things you mentioned (architecture, art, etc) are because the Greeks
were fascinated with the golden ratio and it pops in in classical art a lot.
Many of the natural cases have to do with the relationship between phi and the
logarithmic spiral (I refer you to http://www.mhri.edu.au/~pdb/other/phi/). These
are equiangular spirals and are thus seen in shells, horns, claws, beaks, etc.
because they're minumum energy configurations for growth.
> Has anyone found anywhere a general naturalistic explanation of the Magic
> Ratio? I'd like a reference if anyone has one. Does it have a function in
> nature, or is it just there? Does the Magic Ratio fit Dembski's "complex
> specified information" criterion for intelligent design? Its generality and
> ubiquity, it seems to me, argue for design.
I don't think it's anymore surprising than pi which also pops up all over the
place in unexpected places. It arouses my wonder that the natural world is so
orderly as well but there are naturalistic explanations as well.
Anyway, there has been work explaining these observations but I'd have to dig
to get references which will have to wait until next week since I'm going down
to D.C. for the weekend in a couple of hours. If you have access to a library,
you might try searching back issue of Scientific American since I know they've
done more than one article on this.
-- Steven H. Schimmrich Physical Sciences Department firstname.lastname@example.org (office) Kutztown University email@example.com (home) 217 Grim Science Building 610-683-4437, 610-683-1352 (fax) Kutztown, Pennsylvania 19530 http://home.earthlink.net/~schimmrich/