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Applied Math Colloquium

Friday, February 7, 2014, 11:30 AM
Cullimore Lecture Hall, Lecture Hall II
New Jersey Institute of Technology

Phyllotaxis, pushed pattern fronts and optimal packing

Alan Newell

University of Arizona

Abstract

Understanding the wonderful patterns of phyllotactic configurations of leaves, flowers, spines, and bracts near the shoot apical meristems of plants has intrigued and fascinated natural scientists for over four hundred years. It is remarkable that only in recent decades have coherent explanations begun to emerge. But the story is far from over. In this lecture, I will review both the teleological and mechanistic explanations and show that in fact both lead to consistent outcomes. The main new result is that we have found that advancing patterns formed by instabilities with plain old physical and chemical origins leave in their wakes quasi periodic fields (such as those for auxin or stress concentrations) whose maxima (the places where new phylla most likely form) obey optimal packing rules. In short, instability generated patterns may be the mechanism by which plants and other organisms can pursue optimal strategies.