Abstract
This paper shows how to solve a system of differential equations controlling the development of a dynamical system based on finite element method and L-Systems. Our methods leads to solve a linear system of equations by propagating the flow of information throughout the structure of the developing system in a natural way. The method is illustrated on the growth of a branching system whose axes bend under their own weight.
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
Allen, M., Prusinkiewicz, P., DeJong, T.M.: Using L-systems for modeling source-sink interactions, architecture and physiology of growing trees: the L-PEACH Model. New Phyotologist 166, 869–880 (2005)
Bathe, K.: Finite Element Procedures. Prentice Hall (1996)
Boudon, F., Pradal, C., Cokelaer, T., Prusinkiewicz, P., Godin, C.: L-Py: an L-system simulation framework for modeling plant architecture development base on a dynamic language. Frontiers in Plant Science 3(76) (2012)
Chou, P.C., Pagano, N.J.: Elasticity: tensor, dyadic, and engineering approaches. Courier Dover Publications (1992)
Costes, E., Smith, C., Renton, M., Guédon, Y., Prusinkiewicz, P., Godin, C.: MAppleT: simulation of apple tree development using mixed stochastic and biomechanical models. Functional Plant Biology 35(10) (2008)
Featherstone, R.: Efficient Factorization of the Joint-Space Inertia Matrix for Branched Kinematic Trees. The International Journal of Robotics Research 24(6), 487–500 (2005)
Federl, P., Prusinkiewicz, P.: 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.) ICCS 2004. LNCS, vol. 3037, pp. 65–72. Springer, Heidelberg (2004)
Godin, C., Sinoquet, H.: Functional-structural plant modelling. The New Phytologist 166(3), 705–708 (2005)
Hemmerling, R., Evers, J.B., Smoleňova, K., Buck-Sorlin, G., Kurth, W.: Extension of the GroIMP modelling platform to allow easy specification of differential equations describing biological processes within plant models. Computers and Electronics in Agriculture 92(C), 1–8 (2013)
Jirasek, C., Prusinkiewicz, P., Moulia, B.: Integrating biomechanics into developmental plant models expressed using L-systems. Plant Biomechanics 24(9), 614–624 (2000)
Peiró, J., Sherwin, S.: Finite Difference, Finite Element and Finite Volume Methods for Partial Differential Equations. In: Springer Netherlands Handbook of Materials Modeling, Dordrecht, pp. 2415–2446 (2005)
Press, W.H., Teukolsky, S.A., Vettering, W.T., Flannery, B.P.: Numerical Recipes: The art of scientific computing. Cambridge University Press (1987)
Prusinkiewicz, P.: Geometric modeling without coordinates and indices. In: IEEE Computer Society Proceedings of the IEEE Shape Modeling International, pp. 3–4 (2002)
Prusinkiewicz, P.: Modeling plant growth and development. Modeling plant growth and development 7(1), 79–83 (2004)
Prusinkiewicz, P., Allen, M., Escobar-Gutierrez, A., DeJong, T.M.: Numerical methods for transport-resistance sink-source allocation models. Frontis 22, 123–137 (2007)
Prusinkiewicz, P. and Lindenmayer, A.: The algorithmic beauty of plants. Springer (1990)
Prusinkiewicz, P., Runions, A.: Computational models of plant development and form. The New Phytologist 193(3), 549–569 (2012)
Taylor-Hell, J.: Incorporating biomechanics into architectural tree models. In: 18th Brazilian Symposium on Computer Graphics and Image Processing, SIBGRAPI 2005. IEEE (2005)
Vos, J., Evers, J.B., Buck-Sorlin, G.H., Andrieu, B., Chelle, M., de Visser, P.H.B.: Functional-structural plant modelling: a new versatile tool in crop science. Journal of Experimental Botany 61(8), 2101–2115 (2010)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Bernard, JP., Gilles, B., Godin, C. (2014). Combining Finite Element Method and L-Systems Using Natural Information Flow Propagation to Simulate Growing Dynamical Systems. In: Dediu, AH., Lozano, M., Martín-Vide, C. (eds) Theory and Practice of Natural Computing. TPNC 2014. Lecture Notes in Computer Science, vol 8890. Springer, Cham. https://doi.org/10.1007/978-3-319-13749-0_19
Download citation
DOI: https://doi.org/10.1007/978-3-319-13749-0_19
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-13748-3
Online ISBN: 978-3-319-13749-0
eBook Packages: Computer ScienceComputer Science (R0)