On Fibbonaci

Rating: 8/10 (4 February 2005)

I'm a physicist; I write fidgety reviews while my code is compiling and it's too late to do any real writing.
I'm commenting here because there actually is a theory on the origin of Fibbonaci series in plants, published recently in Physical Review Letters (92, 168102, 2004). The theory works best on cacti, as the author (and I) have observed in Arizona.
Spirals are built into the plant when it is very young: so young you can see them forming under an electron microscope. The dome of the growing plant buckles under pressure--you can see the same effect if you pinch a wide swath on the back of your hand, or stretch a piece of plastic. Buckling is often geometrically simple for the same reason soap bubbles form nature's most perfect sphere: it takes the easiest path.
Shipman found that when a new spiral forms, it has the same number of arms as the sum of pre-existing arms (the Fibbonaci sequence).
Whether the phyllotaxis (leaf arrangement) of cacti and sunflowers can be extended to other things, and whether the discovery is useful--I dunno.
A talk by Shipman (a living Max who has gone on to work at the Max Planck Institute) is, at the time I write, available at: http://online.itp.ucsb.edu/online/pattern_c03/shipman/
Note, incidentally, that the truth is both less artsy and more beautiful than presented in this movie and in the legions of pseudo-science that accompany this field.