Phyllotaxis, disk packing and Fibonacci numbers

Phyllotaxis, the regular arrangement of leaves or flowers around a plant stem, is a distinctive example of developmental pattern formation in nature. The striking regularity of such patterns continues to be an object of fascination despite centuries of research by mathematicians, physicists and natural scientists. We investigate the ubiquity of the Fibonacci sequence in such systems using ideas from disk packing. Buds (blue dots) are introduced at the top of a surface which has the form of a growing stem. They migrate downwards, while conforming to three principles, applied locally: dense packing, homogeneity and continuity. Typical results are presented in the movie below.