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.
Keywords
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.
Preview
Unable to display preview. Download preview PDF.
References
- 1.M.C. Cross, H. Greenside, Pattern Formation and Dynamics in Nonequilibrium Systems (Cambridge UP, Cambridge, 2009)Google Scholar
- 2.M. Kuecken, A.C. Newell, Europhys. Lett. 68, 141 (2005)CrossRefADSGoogle Scholar
- 3.G.A.A. Dosio, F. Tardieu, O. Turc, New Phytol. 170, 711 (2006)CrossRefGoogle Scholar
- 4.W. Hofmeister, Allegmeine Morphologie der Gewachse, Handbuch der Physiologischen Botanik (Engelmann, Leipzig, 1868)Google Scholar
- 5.S. Douady, Y. Couder, J. Theor. Biol. 178, 178 (1996)Google Scholar
- 6.S. Douady, Y. Couder, J. Theor. Biol. 178, 255 (1996)CrossRefGoogle Scholar
- 7.S. Douady, Y. Couder, J. Theor. Biol. 178, 295 (1996)CrossRefGoogle Scholar
- 8.M. Snow, R. Snow, Proc. Roy. Soc. B 139, 545 (1952)CrossRefADSGoogle Scholar
- 9.A.C. Newell, P.D. Shipman, J. Stat. Phys. 121, 5 (2005)CrossRefMathSciNetGoogle Scholar
- 10.A.C. Newell, P.D. Shipman, Analysis and Applications 6, 4 (2008)CrossRefMathSciNetGoogle Scholar
- 11.A.C. Newell, P.D. Shipman, Z. Sun, J. Theor. Biol. 251, 421 (2008)CrossRefGoogle Scholar
- 12.A.C. Newell, P.D. Shipman, Z. Sun, Plant Signal. Behav. 8, 511 (2008)Google Scholar
- 13.P.D. Shipman, A.C. Newell, Phys. Rev. Lett. 92, 168102 (2004)CrossRefADSGoogle Scholar
- 14.P.D. Shipman, A.C. Newell, J. Theor. Biol. 236, 154 (2005)CrossRefMathSciNetGoogle Scholar
- 15.P.D. Shipman, Phys. Rev. E 81, 031905 (2010)CrossRefADSGoogle Scholar
- 16.P. Green, C. Steele, S. Rennich, Ann. Bot. 77, 515 (1996)CrossRefGoogle Scholar
- 17.P.B. Green, Am. J. Bot. 86, (1999)Google Scholar
- 18.R.S. Smith, S. Guyomarc’h, T. Mandel, D. Reinhardt, C. Kuhlemeier, P. Prusinkiewicz, PNAS 103, 1301 (2006)CrossRefADSGoogle Scholar
- 19.H. Jönsson, M.G. Heisler, B.E. Shapiro, E.M. Meyerowitz, E. Mjolsness, PNAS 103, 1633 (2006)CrossRefADSGoogle Scholar
- 20.P.B. de Reuille, I. Bohn-Courseau, K. Ljung, H. Morin, N. Carraro, C. Godin, J. Traas, Proc. Natl. Acad. Sci. 103, 1627 (2006)CrossRefADSGoogle Scholar
- 21.D. Reinhardt, T. Mandel, C. Kuhlemeier, Plant Cell. 12, 507 (2000)CrossRefGoogle Scholar
- 22.P. Atela, C. Golé, S. Hotton, J. Nonlinear Sci. 12, 641 (2002)CrossRefzbMATHADSMathSciNetGoogle Scholar
- 23.S. Hotton, Ph.D. thesis, University of California-Santa Cruz, 1999Google Scholar
- 24.A.H. Church, On the Relation of Phyllotaxis to Mechanical Laws (Williams and Norgate, 1904)Google Scholar
- 25.Z. Csahok, C. Misbah, Europhys. Lett. 47, 331 (1999)CrossRefADSGoogle Scholar
- 26.O. Hamant, M. Heister, H. Jönsson, P. Krupinski, M. Uyttewaal, P. Bokov, F. Corson, P. Sahlin, A. Boudaoud, E.M. Meyerowitz, Y. Couder, J. Traas, Science 332, 1650 (2008)CrossRefADSGoogle Scholar
- 27.S. Hotton, V. Johnson, J. Wilbarger, K. Zwieniecki, P. Atela, C. Golé, J. Dumais, J. Plant Growth Reg. 25, (2006) Google Scholar
- 28.L. Pismen, A. Nepomnyashchy, Europhys. Lett. 27, 433 (1994)CrossRefADSGoogle Scholar
Copyright information
© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2010