caa a22 4500 44586639X CHVBK 20180317145459.0 cr unu---uuuuu 170323e20110301xx s 000 0 eng 10.1140/epjd/e2010-00271-8 doi (NATIONALLICENCE)springer-10.1140/epjd/e2010-00271-8 How universal are Fibonacci patterns? [Elektronische Daten] [P.D. Shipman, Z. Sun, M. Pennybacker, A.C. Newell] Abstract.: 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. EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg, 2010 Shipman P.D. Department of Mathematics, Colorado State University, 80523-1874 Fort Collins, Colorado, USA aut Sun Z. Department of Mathematics, University of California-Irvine, California-Irvine, USA aut Pennybacker M. Program in Applied Mathematics, University of Arizona, Arizona, USA aut Newell A.C. Program in Applied Mathematics, University of Arizona, Arizona, USA aut The European Physical Journal D Springer-Verlag 62/1(2011-03-01), 5-17 1434-6060 62:1<5 2011 62 10053 https://doi.org/10.1140/epjd/e2010-00271-8 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1140/epjd/e2010-00271-8 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Shipman P.D. Department of Mathematics, Colorado State University, 80523-1874 Fort Collins, Colorado, USA aut NATIONALLICENCE 700 1- Sun Z. Department of Mathematics, University of California-Irvine, California-Irvine, USA aut NATIONALLICENCE 700 1- Pennybacker M. Program in Applied Mathematics, University of Arizona, Arizona, USA aut NATIONALLICENCE 700 1- Newell A.C. Program in Applied Mathematics, University of Arizona, Arizona, USA aut NATIONALLICENCE 773 0- The European Physical Journal D Springer-Verlag 62/1(2011-03-01), 5-17 1434-6060 62:1<5 2011 62 10053 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer