Abstract
Mathematical modeling of growing multicellular structures creates the problem of solving systems of equations in which not only the values of variables, but the equations themselves, may change over time. We consider this problem in the framework of Lindenmayer systems, a standard formalism for modeling plants, and show how parametric context-sensitive L-systems can be used to numerically solve growing systems of coupled differential equations. We illustrate our technique with a developmental model of the multicellular bacterium Anabaena.
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de Koster, C.G., Lindenmayer, A.: Discrete and continuous models for heterocyst differentiation in growing filaments of blue-green bacteria. Acta Biotheoretica 36, 249–273 (1987)
Giavitto, J.-L., Michel, O.: Modeling the topological organization of cellular processes. BioSystems 70, 149–163 (2003)
Hammel, M., Prusinkiewicz, P.: Visualization of developmental processes by extrusion in space-time. In: Proceedings of Graphics Interface 1996, pp. 246–258 (1996)
Karwowski, R.: Improving the process of plant modeling: The L+C modeling language. PhD thesis, University of Calgary (2002)
Karwowski, R., Prusinkiewicz, P.: Design and implementation of the L+C modeling language. Electronic Notes in Theoretical Computer Science 86.2 (2003)
Lindenmayer, A.: Mathematical models for cellular interaction in development, Parts I and II. Journal of Theoretical Biology 18, 280–315 (1968)
Lindenmayer, A.: Adding continuous components to L-systems. In: Rozenberg, G., Salomaa, A. (eds.) L Systems. LNCS, vol. 15, pp. 53–68. Springer, Heidelberg (1974)
Mitchison, G.J., Wilcox, M.: Rules governing cell division in Anabaena. Nature 239, 110–111 (1972)
Press, W.H., Teukolsky, S.A., Wetterling, W.T.: Numerical recipes in C: The art of scientific computing, 2nd edn. Cambridge University Press, Cambridge (1988)
Prusinkiewicz, P., Hammel, M., Mjolsness, E.: Animation of plant development. In: Proceedings of SIGGRAPH 93 (Anaheim, California, August 1–6, 1993), New York. ACM SIGGRAPH, pp. 351–360 (1993)
Prusinkiewicz, P., Lindenmayer, A.: The algorithmic beauty of plants. Springer, New York (1990), With Hanan, J.S., Fracchia, F.D., Fowler, D.R., de Boer, M.J.M., Mercer, L
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Federl, P., Prusinkiewicz, P. (2004). Solving Differential Equations in Developmental Models of Multicellular Structures Expressed Using L-systems. In: Bubak, M., van Albada, G.D., Sloot, P.M.A., Dongarra, J. (eds) Computational Science - ICCS 2004. ICCS 2004. Lecture Notes in Computer Science, vol 3037. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24687-9_9
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DOI: https://doi.org/10.1007/978-3-540-24687-9_9
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