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Phyllotaxis, Pushed Pattern-Forming Fronts, and Optimal Packing

Matthew Pennybacker and Alan C. Newell
Phys. Rev. Lett. 110, 248104 – Published 13 June 2013
Physics logo See Synopsis: How Plants Do Their Math
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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.

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  • Received 12 December 2012

DOI:https://doi.org/10.1103/PhysRevLett.110.248104

© 2013 American Physical Society

Synopsis

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How Plants Do Their Math

Published 13 June 2013

New simulations better explain how Fibonacci patterns can emerge from the biochemical processes driving a plant’s growth.

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Authors & Affiliations

Matthew Pennybacker* and Alan C. Newell

  • Department of Mathematics, University of Arizona, Tucson, Arizona 85721, USA

  • *pennybacker@math.arizona.edu

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Issue

Vol. 110, Iss. 24 — 14 June 2013

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