Abstract
In a variety of physical systems in which there is growth, patterns are spontaneously generated. Since it is also during their growth that living entities acquire their shapes, it is tempting to consider possible relations between the two types of morphogenesis. This direction of research was initiated by D’Arcy Thompson (1917) in his classical book “On Growth and Form”. To the present day it is still an important and open problem. The fact that biological growth is under the control of genetic factors does not abolish the fact that it also obeys the laws of physics. Many situations of biological morphogenesis can thus involve an interplay between genetic determination and physical self-organisation. This is, of course, well beyond the field of the present article. We limit ourselves here to the description of some recent results concerning branches and meshworks in physical systems and discuss a few biological systems, mostly in botany, where these results may be relevant.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
C. Allain and L. Limat, Phys. Rev. Lett 74 (1995) 2981–2984.
G.S. Avery, Amer. J. Bot. 20 (1933) 513–564.
J. Bataille, Rev. Inst. Pétrole 23 (1968) 1349–1364.
M. Ben Amar, Phys. Rev. A. 41 (1990) 2080–2092.
M. Ben Amar, Phys. Rev. A 44 (1991) 3673–3685.
M. Ben Amar, V. Hakim, M. Mashaal and Y. Couder, Phys. Fluids A 3 (1991) 2039–2042.
Ben Jacob, H. Schmueli, O. Shochet and A. Tenenbaum, Physica A 187 (1992) 378–424.
E. Blackman, Ann. Bot 35 (1971) 653–665.
P. Bouissou, A. Chiffaudel, B. Perrin and P. Tabeling, Europhys. Lett. 13 (1990) 89–94.
R.L. Chuoke, P. Van Meurs and C. Van der Pol, AIME 216 (1959) 188–194.
Y. Couder, Perspectives in Fluid Dynamics (Cambridge University Press, 2000).
Y. Couder, F. Argoul, A. Arnéodo, J. Maurer and M. Rabaud, Phys. Rev. A 42 (1990) 3499–3503.
Y. Couder, L. Pauchard, M. Adda-Bedia, C. Allain and S. Douady, On the self-organisation of leaf venation (1999) Preprint.
W. D’Arcy Thompson, On growth and Form, Vols. 1 and 2 (Cambridge University Press, 1917), Edition of 1952.
S. Douady and Y. Couder, J. Theor. Biol. 178 (1996) 255–312.
K. Esau, Plant Anatomy (John Wiley, New York, 1953).
H. Fujikawa and M. Matsushita, J. Phys. Soc. Jpn. 60 (1991) 88–94.
L.J. Gibson and M.F. Ashby, Proc. Roy. Soc. London A 383 (1982) 43–59.
P.B. Green, Int. J. Plant Sci. 153 (1992) S59-S75.
A. Groisman and E. Kaplan, Europhys. Lett. 25 (1994) 415–420.
Z. Hejnowicz and A. Sievers, J. Exp. Bot. 46 (1995) 1045–1053.
L.J. Hickey, Amer. J. Bot. 60 (1973) 17–33.
P. Huerre, Perspectives in Fluid Dynamics (Cambridge University Press, 2000).
D. Kessler, J. Koplik and H. Levine, Adv. Phys. 37 (1988) 255–339.
U. Kutschera, Physiologia Plantaram 77 (1989) 157–163.
E. Lajeunesse and Y. Couder, J. Fluid Mech. 419 (2000) 125–149.
P.M. Lintilhac and T.B. Vesecky, Amer. J. Bot. 68 (1981) 1222–1230.
G.H. Mitchison, Sci 196 (1977) 270–275.
G.J. Mitchison, Proc. Roy. Soc. London B 207 (1980) 79–109.
H. Meinhardt, Models of pattern formation and their application to plant development, in Positional controls in plant development, edited by W. Barlow and D.J. Carr (Cambridge University Press, 1984).
W.W. Mullins and R.F. Sekerka, J. Appl. Phys. 35 (1964) 444–451.
T. Nelson and N. Dengler, The Plant Cell 9 (1997) 1121–1135.
L. Pauchard, F. Parisse and C. Allain, Phys. Rev. E 59 (1999) 3737–3740.
P. Pelcé, Dynamics of Curved Fronts (Academic Press, San Diego, 1988).
W.S. Peters and A.D. Tomos, Ann. Bot. 77 (1996) 657–665.
Y. Pomeau and M. Ben Amar, Dendritic growth and related topics, in Solids far from equilibrium, edited by C. Godrèche (Cambridge University Press, 1992).
X.W. Quian and H.Z. Cummins, Phys. Rev. Lett. 64 (1990) 3038–3041.
M. Rabaud, Y. Couder and N. Gerard, Phys. Rev. A 37 (1988) 935–947.
T. Sachs, Pattern formation in plant tissues (Cambridge University Press, Cambridge, 1991).
H. Thomé, M. Rabaud, V. Hakim and Y. Couder, Phys. Fluids A 1 (1989) 224–240.
T. Witten and L.M. Sander, Phys. Rev. B 27 (1983) 5686–5697.
Ya.B. Zel’dovich, A.G. Istratov, N.I. Kidin and V.B. Librovich, Combust. Sci. Technol. 24 (1980) 1–13.
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Couder, Y. (2001). Patterns with Open Branches or Closed Networks: Growth in Scalar or Tensorial Fields. In: Fleury, V., Gouyet, JF., Léonetti, M. (eds) Branching in Nature. Centre de Physique des Houches, vol 14. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-06162-6_1
Download citation
DOI: https://doi.org/10.1007/978-3-662-06162-6_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-41888-7
Online ISBN: 978-3-662-06162-6
eBook Packages: Springer Book Archive