Phyllotaxis, pushed pattern-forming fronts, and optimal packing

Matthew Pennybacker, Alan C. Newell

Research output: Contribution to journalArticlepeer-review

17 Scopus citations


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.

Original languageEnglish (US)
Article number248104
JournalPhysical review letters
Issue number24
StatePublished - Jun 13 2013

ASJC Scopus subject areas

  • General Physics and Astronomy


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