Abstract
Map L-systems with dynamic interpretation have been successfully applied to the modeling of the development of two-dimensional cell layers [3, 4]. We extend this technique to three-dimensional cellular structures. The seminal notion of three-dimensional cyclic edge-label-controlled OL-systems, termed cellworks, was introduced by A. Lindenmayer [8]. We provide an alternative definition of cellworks using markers, and use it as a formal basis for a simulation program. Cell geometry is viewed as the result of mechanical cell interactions due to osmotic pressure and wall tension. Developmental sequences can be animated by considering periods of continuous expansion delimited by instantaneous cell divisions. As an example, the method is applied to visualize the development of a three-dimensional epidermal cell layer.
Preview
Unable to display preview. Download preview PDF.
References
M. J. M. de Boer. Analysis and computer generation of division patterns in cell layers using developmental algorithms. PhD thesis, University of Utrecht, the Netherlands, 1989.
L. Fox and D. F. Mayers. Numerical solution of ordinary differential equations. Chapman and Hall, London, 1987.
F. D. Fracchia, P. Prusinkiewicz, and M. J. M. de Boer. Animation of the development of multicellular structures. In N. Magnenat-Thalmann and D. Thalmann, editors, Computer Animation '90, pages 3–18, Tokyo, 1990. Springer-Verlag.
F. D. Fracchia, P. Prusinkiewicz, and M. J. M. de Boer. Visualization of the development of multicellular structures. In Proceedings of Graphics Interface '90, pages 267–277, 1990.
B. E. S. Gunning. Microtubules and cytomorphogenesis in a developing organ: The root primordium of Azolla pinnata. In O. Kiermayer, editor, Cytomorphogenesis in plants, Cell Biology Monographs 8, pages 301–325. Springer-Verlag, Wien, 1981.
R. W. Korn. Positional specificity within plant cells. J. Theoretical Biology, 95:543–568, 1982.
A. Lindenmayer. Mathematical models for cellular interaction in development, Parts I and II. Journal of Theoretical Biology, 18:280–315, 1968.
A. Lindenmayer. Models for plant tissue development with cell division orientation regulated by preprophase bands of microtubules. Differentiation, 26:1–10, 1984.
A. Lindenmayer. An introduction to parallel map generating systems. In H. Ehrig, M. Nagl, A. Rosenfeld, and G. Rozenberg, editors, Graph-grammars and their application to computer science, pages 27–40. Springer-Verlag, 1987. Lecture Notes in Comp. Sci. 291.
A. Lindenmayer and G. Rozenberg. Parallel generation of maps: developmental systems for cell layers. In V. Claus, H. Ehrig, and G. Rozenberg, editors, Graph-grammars and their application to computer science and biology, pages 301–316. Springer-Verlag, Berlin, 1979. Lecture Notes in Comp. Sci. 73.
H. B. Lück and J. Lück. Vers une metrie des graphes evolutifs, representatifs d'ensembles cellulaires. In H. Le Guyader and T. Moulin, editors, Actes du premier seminaire de l'Ecole de Biologie Théorique du CNRS, pages 373–398. Ecole Nat. Sup. de Techn. Avanc., Paris, 1981.
J. Lück and H. B. Lück. 3-dimensional plant bodies by double wall map and stereomap systems. In H. Ehrig, M. Nagl, and G. Rozenberg, editors, Graph-grammars and their application to computer science, pages 219–231. Springer-Verlag, 1983. Lecture Notes in Comp. Sci. 153.
J. Lück and H. B. Lück. Double-wall cellwork systems for plant meristems. In this volume, 1990.
A. Nakamura, A. Lindenmayer, and K. Aizawa. Some systems for map generation. In G. Rozenberg and A. Salomaa, editors, The Book of L, pages 323–332. Springer-Verlag, Berlin, 1986.
P. Prusinkiewicz and J. S. Hanan. Lindenmayer systems, fractals, and plants. Springer-Verlag, New York, 1989. Lecture Notes in Biomathematics 79.
W. Sierpiński. Sur une courbe dont tout point est un point de ramification. Comptes Rendus hebdomadaires des séances de l'Académie des Sciences, 160:302–305, 1915. Reprinted in W. Sierpiński, Oeuvres choisies, S. Hartman et al., editors, pages 99–106, PWN — Éditions Scientifiques de Pologne, Warsaw, 1975.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1991 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Fracchia, F.D., Prusinkiewicz, P. (1991). Physically-based graphical interpretation of marker cellwork L-systems. In: Ehrig, H., Kreowski, HJ., Rozenberg, G. (eds) Graph Grammars and Their Application to Computer Science. Graph Grammars 1990. Lecture Notes in Computer Science, vol 532. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0017400
Download citation
DOI: https://doi.org/10.1007/BFb0017400
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-54478-4
Online ISBN: 978-3-540-38395-6
eBook Packages: Springer Book Archive