The arrangements of phylla (leaves, flowers, seeds, bracts) on plants and their surface morphologies have intrigued and mystified scientists for over four hundred years. A special challenge has been to understand why on many plants such as the sunflower, the seeds lie on families of clockwise and counterclockwise spirals and that the numbers in each family belong not just to the integers but to a special subset known as Fibonacci numbers generated by starting with any two integers and defining each successive member as the sum of the previous two. Google sunflower images and count for yourselves. You will encounter beautiful sunflower seed heads with 21, 34 and 55 family spirals. Count them. One can generate this, the most common, Fibonacci sequence by beginning with 1,2 and obtain 1,2,3,5,8,13,21,34,55... .
Attempts to explain phyllotactic configurations fall into two categories. The teleological approach devises rules for positioning the next seed or flower so as to pack the seeds in some optimal fashion and is philosophically equivalent to saying the reason tigers have stripes is that it provides better camouflage. Now that may be the reason that striped tigers had an evolutionary advantage over unstriped ones, but nature has to use plain old physical and biochemical processes to achieve these outcomes. In plants, the mechanisms by which phylla are made involve instabilities which lead to a non uniform distribution of the hormone auxin (phylla initiation would occur at maxima of the auxin field) and non uniform stress fields in the vicinity of the plant's growth tips. The corresponding pattern then propagates as a front and creates potential sites for phylla initiation. What we have obtained is some stunning new results which demonstrate that the locations of the maxima of the instability generated pattern fields coincide with the point configurations generated by the teleologically inspired models. This suggests the exciting new idea that in many circumstances nstability generated patterns may be the mechanisms by which plants and other organisms can pursue optimal strategies. It also suggests alternative approaches to investigate many of the open challenges in optimal packing.
