Inspecting a sunower head, one may notice first the
diamond-shaped seeds that tile the disk. Families of spirals catch the eye, and if one counts
the numbers of spirals in each family, one typically arrives at successive members of the Fibonacci
sequence 1, 1, 2, 3, 5, 8, ... The spiral families seem to blend into each other so that
lower members of the Fibonacci sequence are observed near the center of the disk and higher numbers
as one works one's way out. Yet, there is a self-similarity in that locally the pattern is
nearly the same throughout the disk. The arrangement of elements such as seeds on a
sunflower, leaves on plants, bracts on a pine cone, or aeroles on cacti, is referred to as
phyllotaxis, and it has long been observed that only a few classes of phyllotactic patterns are
commonly observed in nature. The same Fibonacci-spiral pattern, for example, is commonly
observed on pine cones and cacti. Why is it that only a few patterns dominate? And what
chemical or physical mechanisms are behind the formation of these patterns?
Through mathematical models for the formation of
phyllotactic patterns based on biochemical and biomechanical mechanisms, we suggest ways to
understand both universal aspects of phyllotactic patterns as well as how interacting mechanisms
can cooperate or compete to produce the array of patterns seen in nature.