Phyllotaxis as a dynamical self organizing process part II: The spontaneous formation of a periodicity and the coexistence of spiral and whorled patterns

Journal of Theoretical Biology

Volumn 178, Issue 3, 1996, Pages 275-294

  Douady, S ^a   Couder, Y ^a  

^a LABORATOIRE DE PHYSIQUE STATISTIQUE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; DYNAMICS; PATTERN GENERATOR; PERIODICITY; PLANT GROWTH; PRIORITY JOURNAL;

EID: 0029892224     PISSN: 00225193     EISSN: None     Source Type: Journal    
DOI: 10.1006/jtbi.1996.0025     Document Type: Article

References (41)

1. BRAVAIS, L. & BRAVAIS, A. (1837). Essai sur la disposition des feuilles curvisériées. Ann. Sci. Nat. 7, 42-110, Essai sur la disposition symmétrique des inflorescences. 193-221 and 291-348; Ann. Sci. Nat. 8, 11-42.
2. BRAVAIS, L. & BRAVAIS, A. (1837). Essai sur la disposition des feuilles curvisériées. Ann. Sci. Nat. 7, 42-110, Essai sur la disposition symmétrique des inflorescences. 193-221 and 291-348; Ann. Sci. Nat. 8, 11-42.
3. BRAVAIS, L. & BRAVAIS, A. (1837). Essai sur la disposition des feuilles curvisériées. Ann. Sci. Nat. 7, 42-110, Essai sur la disposition symmétrique des inflorescences. 193-221 and 291-348; Ann. Sci. Nat. 8, 11-42.
4. BRAVAIS, L. & BRAVAIS, A. (1839). Essai sur la disposition des feuilles rectisériées. Ann. Sci. Nat. 12, 5-14 and 65-77.
5. COUDER, Y. & DOUADY, S. (1993). Phyllotaxis: genetic determination and self organization. In: Organisation et Processus dans les Systèmes Biologiques, (Friedel, J. & Gros, F., eds) Technique et Documentation, Paris.
6. DOUADY, S. (1996). The packing efficiency of the phyllotaxic patterns on a cylinder. Preprint.
7. DOUADY, S. & COUDER, Y. (1992). Phyllotaxis as a physical self organised growth process. Phys. Rev. Lett. 68, 2098-2101.
8. DOUADY, S. & COUDER, Y. (1996a). Phyllotaxis as a self organizing iterative process: part (I) The spiral modes resulting from time periodic iterations. J. theor. Biol., 178, 255-274.
9. DOUADY, S. & COUDER, Y. (1996b). Phyllotaxis as a self organizing iterative process: part (III) The simulation of the transient regimes of ontogeny. J. theor. Biol., 178, 295-312.
10. DUTROCHET, R. J. H. (1834). Observations sur les variations accidentelles du mode suivant lequel les feuilles sont distribuées sur les tiges des végétaux. Nouv. Ann. Mus. Hist. Nat. 3, 161-200.
11. FRIEDMAN, D. (1992). On whorled/spiral phyllotaxis. In: Spiral Symmetry (Hargittai, I. & Pickover, C. A., eds) Singapore: World Scientific.
12. GREEN, P. B., HAVELANGE, A. & BERNIER, G. (1991). Floral morphogenesis in Anagallis: scanning electron micrograph sequences from individual growing meristems before, during and after the transition to flowering. Planta 185, 502-512.
13. HERNANDEZ, L. F., HAVELANGE, A., BERNIER, G. & GREEN, P. B. (1991). Growth behaviour of single epidermal cells during flower formation: sequential scanning electron micrographs provide kinematic patterns for Anagallis. Planta 185, 139-147.
14. HOFMEISTER, W. (1868). Allgemeine Morphologie der Gewâchse, Handbuch der Physiologishen Botanik, 1 Engelmann, Leipzig, 405-664.
15. LEVITOV, L. S. (1991a) Energetic approach to phyllotaxis. Europhys. Lett. 14, 533-539.
16. LEVITOV, L. S. (1991b). Phyllotaxis of flux lattices in layered superconductors. Phys. Rev. Lett. 66, 224-227.
17. MEDFORD, J. I., BEHRINGER, F. J., CALLOS, J. D. & FELDMANN, K. A. (1992). Normal and abnormal development in the Arabidopsis vegetative shoot apex. Plant Cell 4, 631-643.
18. MEICENHEIMER, R. D. (1979). Changes in Epilobium phyllotaxy induced by N-1-naphtylphthalamic acid and α-4-chlorophenoxy-isobutiric acid. Am. J. Botany 66, 557-569.
19. MEICENHEIMER, R. D. (1982). Change in Epilobium phyllotaxy during the reproductive transition. Am. J. Botany 69, 1108-1118.
20. MEICENHEIMER, R. D. & ZAGORSKA-MAREK, B. (1989). Consideration of the geometry of the phyllotaxic triangular units and discontinuous phyllotactic transitions. J. theor. Biol. 139, 359-368.
21. MEINHARDT, H. (1982). Models of Biological Pattern Formation. London: Academic Press.
22. MITCHISON, G. H. (1977). Phyllotaxis and the Fibonacci series. Science 196, 270-275.
23. RICHARDS, F. J. (1951). Phyllotaxis: its quantitative expression and relation to growth in the apex. Phil. Trans. Roy. Soc. B 225, 509-564.
24. RIDLEY, J. N. (1986). Ideal phyllotaxis on general surfaces of revolution. Math. Biosciences 79, 1-24.
25. SCHOUTE, J. C. (1913). Beiträge zur Blattstellungslehre. Rec. Trav. Bot. Néerl. 10, 153-339.
26. SCHOUTE, J. C. (1922). On whorled phyllotaxis (I) growth whorls. Rec. Trav. Bot. Néerl. 19, 184-206.
27. SCHOUTE, J. C. (1925). On whorled phyllotaxis (II) Late binding whorls of Peperomia. Rec. Trav. Bot. Néerl. 22, 128-172.
28. SCHOUTE, J. C. (1936). On whorled phyllotaxis (III) True and false whorls. Rec. Trav. Bot. Néerl. 33, 670-687.
29. SCHOUTE, J. C. (1938). On whorled phyllotaxis (IV) Early binding whorls. Rec. Trav. Bot. Néerl. 35, 416-558.
30. SNOW, M. & SNOW, R. (1933). Experiments on phyllotaxis, II, the effect of displacing a primordium. Phil. Trans. Roy. Soc. B222, 353-400.
31. SNOW, M. & SNOW, R. (1935). Experiments on phyllotaxis. III. Diagonal splits through decussate apices. Phil. Trans. Roy. Soc. B225, 63-94.
32. SNOW, M. & SNOW, R. (1952). Minimum areas and leaf determination. Proc. Roy. Soc. B139, 545-566.
33. SNOW, M. & SNOW, R. (1962). A theory of the regulation of phyllotaxis based on Lupinus albus. Phil. Trans. Roy. Soc. B244, 483-514.
34. TURING, A. M. (1952). The chemical basis of morphogenesis. Phil. Trans. Roy. Soc. B237, 37-72.
35. VAN ITERSON, G. (1907). Mathematische und Microscopisch-Anatomische Studien über Blattstellungen, nebst Betrachungen über den Schalenbau der Miliolinen. Iena: Gustav-Fischer-Verlag.
36. VEEN, A. H. & LINDENMAYER, A. (1977). Diffusion mechanism for phyllotaxy. Plant Physiol. 60, 127-139.
37. WARDLAW, C. W. (1968). Essays on Forms in Plants. Manchester: Manchester University Press.
38. WEISSE, A. (1894). Neue Beiträge zur mechanischen Blattstellungslehre. Jahrb. Wiss. Bot. 26, 236-294.
39. WILLIAMS, R. F. (1975). The Shoot Apex and the Leaf Growth. Cambridge: Cambridge University Press.
40. YOUNG, D. A. (1978). On the diffusion theory of phyllotaxis. J. theor. Biol. 71, 421-432.
41. ZAGORSKA-MAREK, B. (1987). Phyllotaxis triangular unit: phyllotaxic transitions as the consequences of the apical wedge disclinations in a crystal like pattern of the units. Acta Soc. Bot. Poloniae 56, 229-255.