A growth-controlled model of the shape of a sunflower head

Mathematical Biosciences

Volumn 187, Issue 2, 2004, Pages 205-221

  Yeatts, F R ^a  

^a Department of Metallurgical and Materials Engineering   (United States)

Author keywords

Continued fraction; Differential geometry; Inflorescence morphogenesis; Mathematical model; Phyllotaxis

Indexed keywords

FUNCTIONS; MATHEMATICAL MODELS; SURFACE PROPERTIES; TISSUE;

FLORAL PARTS; SUNFLOWER;

PLANTS (BOTANY);

FLOWER; GEOMETRY;

ARTICLE; BIOLOGICAL MODEL; CALCULATION; COMPARATIVE STUDY; FLORET; GROWTH, DEVELOPMENT AND AGING; INFLORESCENCE; MATHEMATICAL ANALYSIS; MATHEMATICAL MODEL; PLANT GROWTH; PLANT MORPHOLOGY; PLANT TISSUE; SUNFLOWER;

HELIANTHUS;

EID: 0347931774     PISSN: 00255564     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mbs.2003.09.002     Document Type: Article

References (19)

1. Cutter E.G. Recent experimental studies of the shoot apex and shoot morphogenesis. Bot. Rev. 31:1965;7.
2. Hernandez L.F., Palmer J.H. Regeneration of the sunflower capitulum after cylindrical wounding of the receptacle. Am. J. Bot. 75(9):1988;1253.
3. Richards F.J. Phyllotaxis: its quantitative expression and relation to growth in the apex. Philos. Trans. Roy. Soc. London. 235(B):1951;509.
4. Thornley J.H.M. Phyllotaxis: a mechanistic model. Ann. Bot. 39:1975;491.
5. Bursill L.A., Xudong F. Close-packing of growing discs. Mod. Phys. Lett. B. 2:1988;1245.
6. Meinhardt H. Mechanisms of biological pattern formation and the constraints imposed by growth. Garcia-Ruiz J.M.et al. Growth Patterns in Physical Sciences and Biology. 1993;277 Plenum, New York.
7. Douady S., Couder Y. Phyllotaxis as a dynamical self organizing process. Part I: the spiral modes resulting from time-periodic iterations. J. Theor. Biol. 178:1996;255.
8. Phyllotaxis as a dynamical self organizing process. Part II: the spontaneous formation of a periodicity and the coexistence of spiral and whorled patterns. J. Theor. Biol. 178:1996;275.
9. Phyllotaxis as a dynamical self organizing process. Part III: the simulation of the transient regimes of ontogeny. J. Theor. Biol. 178:1996;295.
10. Thompson D'A.W. On Growth and Form (1942). 1992;Dover, Mineola, NY.
11. Jean R.V. Phyllotaxis. 1994;Cambridge University, Cambridge, UK.
12. Jean R.V., Barabe' D. Symmetry in Plants. 1998;World Scientific, Singapore.
13. Prusinkiewicz P., Lindenmayer A. The Algorithmic Beauty of Plants. 1990;Springer, New York, NY.
14. Bravais L., Bravais A. Essai sur la disposition des feuilles curviseriees. Ann. Sci. Nat. Biol. Veg. 7:1837;42. 193, 291; 8, 11.
15. Bravais L., Bravais A. Essai sur la disposition generale des feuilles rectiseriees. Ann. Sci. Nat. Bot. 12(5-14):1839;65.
16. Khinchin A.Y. Continued Fractions. 1964;University of Chicago, Chicago, IL.
17. Olds C.D. Continued Fractions. 1963;Random House, New York, NY.
18. Vogel H. A better way to construct the sunflower head. Math. Biosci. 44:1979;179.
19. Yeatts F.R. Another look at parastichies. Math. Biosci. 144:1997;71.