# 4th Lorenz Kramer Memorial Lecture

## Phyllotaxis and Patterns on Plants

Prof. Dr. Alan C. Newell (University of Arizona, Tucson AZ, USA)

October 6, 2009

**Abstract:**

Phyllotaxis, the arrangement of phylla (leaves, stickers, bracts, florets) on plants has fascinated and intrigued natural scientists for over four hundred years. In particular, the eye is drawn to the fact that, on many plants, the phylla lie on families of spirals and these families are enumerated by members of Fibonacci sequences. I will try in this lecture to give you some understanding as to why this is so and how, as the plant grows, the numbers climb the Fibonacci sequence, discuss the circumstances under which the transitions are smooth or non smooth, the self similar nature of the patterns, their energy and packing efficiencies, which mechanisms or combinations of mechanisms are responsible for plant patterns in the first place, how universal in nature Fibonacci patterns are, and finally how transitions are made between Fibonacci and whorl dominated patterns.