2013 DiPerna Lectures

The 2013 DiPerna Lecture was given by Alan Newell (University of Arizona) on January 24, 2013, 4PM in 60 Evans.

Phyllotaxis as a pattern forming front

Abstract : Science is littered with the debris of unsolved or incompletely solved problems which many modern scientists ignore in their mad marches on to the new frontiers at the outermost reaches of the real and parallel universes and the worlds of fundamental particles and unified field theories. Simple everyday examples are the waves on the surface of the sea, the earth's magnetic field, the flux of turbulent water down a pipe as a function of pressure head and, of prime interest for this lecture, the intriguing and beautiful phyllotactic configurations near the growth shoots of most plants. The fact that in many cases, phylla (flowers, leaves, bracts, florets) lie on intersections of families of spirals enumerated by consecutive numbers from Fibonacci sequences has been known for over four hundred years, since the time of Kepler, but to date there is still no widely accepted theory which can explain all observations. Nevertheless in recent years there has been significant progress, both experimental and theoretical. In this lecture, I will outline what that progress has been and tell you about our (my colleagues in these efforts have been Matt Pennybacker, Patrick Shipman and Zhiying Sun) own idea which is that the phyllotactic configurations and surface deformations on plants are "pushed" pattern forming fronts initiated by instabilities with biochemical and mechanical origins. I will discuss the connections of our results with the cellular automata, optimal packing approaches of Adler, Douady and Couder and Atele, Gole and Hotton and also suggest circumstances in which Fibonacci patterns can be considered universal.