The European Physical Journal D

, Volume 62, Issue 1, pp 5–17 | Cite as

How universal are Fibonacci patterns?

  • P.D. ShipmanEmail author
  • Z. Sun
  • M. Pennybacker
  • A.C. Newell


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.


Shoot Apical Meristem Discrete Dynamical System Linear Growth Rate Fibonacci Sequence Planar Pattern 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • P.D. Shipman
    • 1
    Email author
  • Z. Sun
    • 2
  • M. Pennybacker
    • 3
  • A.C. Newell
    • 3
    • 4
  1. 1.Department of MathematicsColorado State UniversityColoradoUSA
  2. 2.Department of MathematicsUniversity of California-IrvineCalifornia-IrvineUSA
  3. 3.Program in Applied Mathematics, University of ArizonaArizonaUSA
  4. 4.Department of MathematicsUniversity of ArizonaTucsonUSA

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