How universal are Fibonacci patterns?

P. D. Shipman, Z. Sun, M. Pennybacker, A. C. Newell

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


Pattern patterns, or phyllotaxis, the arrangements of phylla (flowers, leaves, bracts, florets) in the neighborhood of growth tips, have intrigued natural scientists for over four hundred years. Prominent amongst the observed features is the fact that phylla lie on families of alternately oriented spirals and that the numbers in these families belong to subsets {m j } of the integers defined by the Fibonacci rule m j + 1 = m j + m j - 1. The corresponding patterns, which we call Fibonacci patterns, are widespread and universal on plants. Our goal in this paper is to ask if they may also be seen in other physical structures and to try to quantify the circumstances under which one may expect Fibonacci patterns to occur.

Original languageEnglish (US)
Pages (from-to)5-17
Number of pages13
JournalEuropean Physical Journal D
Issue number1
StatePublished - Mar 2011

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics


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