Polygonal planforms and phyllotaxis on plants

P. D. Shipman, A. C. Newell

Research output: Contribution to journalArticlepeer-review

51 Scopus citations


We demonstrate how phyllotaxis (the arrangement of leaves on plants) and the ribbed, hexagonal, or parallelogram planforms on plants can be understood as the energy-minimizing buckling pattern of a compressed sheet (the plant's tunica) on an elastic foundation. The key idea is that the elastic energy is minimized by configurations consisting of special triads of periodic deformations. We study the conditions that lead to continuous or discontinuous transitions between patterns, state testable predictions, and suggest experiments to test the theory.

Original languageEnglish (US)
Pages (from-to)154-197
Number of pages44
JournalJournal of Theoretical Biology
Issue number2
StatePublished - Sep 21 2005


  • Biomechanics
  • Pattern formation
  • Phyllotaxis

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Biochemistry, Genetics and Molecular Biology(all)
  • Immunology and Microbiology(all)
  • Agricultural and Biological Sciences(all)
  • Applied Mathematics


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