How universal are Fibonacci patterns?

• Published in: The European physical journal. D, Atomic, molecular, and optical physics Vol. 62; no. 1; pp. 5 - 17
• Main Authors: Shipman, P.D., Sun, Z., Pennybacker, M., Newell, A.C.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer-Verlag 01-03-2011
• Subjects: Applications of Nonlinear Dynamics and Chaos Theory; Atomic; Flowers; Integers; Leaves; Molecular; Optical and Plasma Physics; Physical Chemistry; Physics; Physics and Astronomy; Quantum Information Technology; Quantum Physics; Scientists; Spectroscopy/Spectrometry; Spintronics; Spirals; Tips; Linear Growth Rate; Shoot Apical Meristem; Discrete Dynamical System; Fibonacci Sequence; Planar Pattern
• ISSN: 1434-6060; 1434-6079
• DOI: 10.1140/epjd/e2010-00271-8

.
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.