By Alan Newell, University of Arizona

Man's curiosity and fascination with the wonderful architectures seen near the shoot apical meristems (SAM's) of plants goes back almost two thousand years. Renaissance scientists such as Kepler and daVinci were intrigued and Kepler was one of the first to note that spiral plant patterns had connections with Fibonacci sequences. It is remarkable, despite continued interest over the centuries, that only recently have quantitative explanations emerged which enjoy broad acceptance. In this talk, I will review the progress to date, and discuss both teleological explanations based upon the observations of Hofmeister and encoded in the works of Douady and Couder, and mechanistic explanations which seek to model the relevant biochemistry and mechanics at work near the SAM. The former approach argues that new phylla (flowers, seeds, bracts, etc.) are placed according to some optimization principle. The latter approach leads to instability driven pattern forming systems in which either the plant growth hormone auxin field or the local stress field have quasiperiodic structures at whose maxima new phylla are likely to be initiated. Whereas the latter model is richer than the former in that one obtains field rather than configuration information and because it addresses the connection between phyllotactic configurations and surface morphologies, one of the stunning and surprising outcomes of our work is that both approaches lead to absolutely consistent outcomes. It may very well be that nature employs pattern forming systems to achieve optimal outcomes not just in plants but in many organisms.