title: Phyllotaxis, pushed pattern-forming fronts, and optimal packing.
abstract: We demonstrate that the pattern forming partial differential equation derived from the auxin distribution model proposed by Meyerowitz, Traas, and others gives rise to all spiral phyllotaxis properties observed on plants. We show how the advancing pushed pattern front chooses spiral families enumerated by Fibonacci sequences with all attendant self-similar properties, a new amplitude invariant curve, and connect the results with the optimal packing based algorithms previously used to explain phyllotaxis. Our results allow us to make experimentally testable predictions.
authors.affiliation: Department of Mathematics, University of Arizona, Tucson, Arizona 85721, USA.
authors.forename: Matthew
authors.initials: M
authors.lastname: Pennybacker
authors.affiliation: Department of Mathematics, University of Arizona, Tucson, Arizona 85721, USA.
authors.forename: Alan C
authors.initials: AC
authors.lastname: Newell
mesh_terms: D007210:Indoleacetic Acids / Q000378:metabolism; D008954:Models, Biological; D063245:Plant Development / Q000502:physiology*; D010944:Plants / Q000033:anatomy & histology / Q000378:metabolism
chemical_list: D007210:Indoleacetic Acids