Phyllotaxis: Its geometry and dynamics

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 57, Issue 4, 1998, Pages 4589-4593

  Liaw, Sy Sang ^a  

^a NATIONAL CHUNG HSING UNIVERSITY   (Taiwan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 11744320382     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.57.4589     Document Type: Article

References (12)

1. R. V. Jean, Phyllotaxis: A Systemic Study in Plant Morphogenesis (Cambridge University Press, Cambridge, 1994).
2. See, for example, H. Vogel, Math. Biosci. 44, 179 (1979).
3. R. V. Jean, J. Number Theory 29, 206 (1988).JNUTA9
4. S. Douady and Y. Couder, Phys. Rev. Lett. 68, 2098 (1992).
5. If we number the order of appearance of primordium by n, and denote its distance to the center of apex by rn. The plastochrone ratio R is defined as the ratio of the distances of two successive primordia on the genetic spiral, namely, R=rn/rn+1. According to the botanical observation, the plastochrone ratio decreases during the development of a plant. The parameter g is defined as eg=R. Geometrically, to construct a pair of opposed spirals of parastichy numbers (i, j), there exists an algebraic relation between ln R, the divergence angle, and the two numbers i and j. Thus g=ln R is a more convenient parameter for constructing models.
6. J. C. Schoute, Recl. Trav. Bot. Neerl., 10, 153 (1913).
7. G. J. Mitchison, Science 196, 270 (1977).
8. G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 5th ed. (Clarendon, Oxford, 1979).
9. See Phyllotaxis: A Systemic Study in Plant Morphogenesis (Ref. 1), Chap. 7.
10. B. Zagorska-Marek, Can. J. Bot. 63, 1844 (1985).
11. See Phyllotaxis: A Systemic Study in Plant Morphogenesis (Ref. 1), Chap. 6.
12. See the discussion in Phyllotaxis: A Systemic Study in Plant Morphogenesis (Ref. 1), Chap. 8.