1D/2D Cellular Automata Modeling with Modelica

Victorino Sanz
Dpto. Informática y Automática, ETSI Informática, UNED, Madrid, Spain

Alfonso Urquia
Dpto. Informática y Automática, ETSI Informática, UNED, Madrid, Spain

Alberto Leva
Dipartimento di Elettronica, Informazione e Bioingegneria, Politecnico di Milano, Milano, Italy

Ladda ner artikelhttp://dx.doi.org/10.3384/ecp14096489

Ingår i: Proceedings of the 10th International Modelica Conference; March 10-12; 2014; Lund; Sweden

Linköping Electronic Conference Proceedings 96:51, s. 489-498

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Publicerad: 2014-03-10

ISBN: 978-91-7519-380-9

ISSN: 1650-3686 (tryckt), 1650-3740 (online)


Cellular Automata (CA) can be used to describe dynamic phenomena dependent of the spatial coordinates. This approach exhibits two main advantages: CA models are conceptually simple and can be simulated very efficiently. A new Modelica library named CellularAutomataLib is presented. It facilitates describing one- and two-dimensional CA in Modelica; and interfacing these CA models with other Modelica models. Simulation performance and large model support have been highest priority in the design of the library. To achieve these goals; the CA internal description is programmed in C and it is consequently hidden to the modeling environment; which is released from the burden of causalizing and manipulating the millions of equations that typically compose CA models. The library architecture and use are discussed in this manuscript. Two examples illustrate the library use: heat diffusion on a chip and spread of an epidemic disease. CellularAutomataLib is freely available at http://www.euclides.dia.uned.es.


Cellular Automata; Hybrid Models; Modelica


[1] von Neumann J. Theory of self-reproducing automata. Univ. of Illinois Press, Urbana and London, 1966.

[2] Ilachinski A. Cellular Automata: A Discrete Universe. World Scientific, Singapore, 2001.

[3] Schiff J.L. Cellular Automata: A Discrete View of the World. Wiley-Interscience, New York, USA, 2008.

[4] Wolfram S. A New Kind of Science. Wolfram Media Inc., Champain, IL, USA, 2002.

[5] Vangheluwe H.L.M., Vansteenkiste G.C. The cellular automata formalism and its relationship to DEVS. In: In 14th European Simulation Multi-conference (ESM.

[6] Hötzendorfer H., Estelberger W., Breitenecker F., Wassertheurer S. Three-dimensional cellular automaton simulation of tumour growth in inhomogeneus oxygen environment. Mathematical and Computer Modelling of Dynamical Systems, 15:pp. 177–189, 2009.

[7] O’Sullivan D., Torrens P.M. Cellular Models of Urban Systems. In: S. Bandini, T. Worsch, eds., Theoretical and Practical Issues on Cellular Automata. Springer-Verlag, London, 2000.

[8] Kier L.B., Seybold P.G., Cheng C.K. Modeling Chemical Systems using Cellular Automata. Springer, Dordrecht, The Netherlands, 2005.

[9] Rouhaud J.F. Cellular automata and consumer behaviour. European Journal of Economic and Social Systems, 14:pp. 37–52, 2000.

[10] Kroc J., Sloot P.M., Hoekstra A.G., eds. Simulating Complex Systems by Cellular Automata. Springer-Verlag, Berlin, 2010.

[11] Ganguly N., Sikdar B.K., Deutsch A., Canright G., Chaudhuri P.P. A Survey on Cellular Automata. Tech. rep., 2003.

[12] Fritzson P. Principles of Object-Oriented Modeling and Simulation with Modelica 2.1. Wiley-IEEE Computer Society Pr, 2003.

[13] Sanz V., Urquia A. An Approach to Cellular Automata Modeling in Modelica. In: Proceedings of the 5th International Workshop on Equation-Based Object-Oriented Modeling Languages and Tools, pp. 121–130. Nottingham, UK, 2013.

[14] Sanz V., Urquia A., Cellier F.E., Dormido S. System Modeling Using the Parallel DEVS Formalism and the Modelica language. Simulation Modeling Practice and Theory, 18(7):pp. 998–1018, 2010.

[15] Sanz V., Urquia A., Dormido S. Parallel DEVS and Process-Oriented Modeling in Modelica. In: Proceedings of the 7th International Modelica Conference, pp. 96–107. Como, Italy, 2009.

[16] Zeigler B.P., Kim T.G., Prähofer H. Theory of Modeling and Simulation. Academic Press, Inc., Orlando, FL, USA, 2000.

[17] Sanz V. Hybrid System Modeling Using the Parallel DEVS Formalism and the Modelica Language. Ph.D. thesis, ETSI Informática, UNED, Madrid, Spain, 2010.

[18] Zimmer D. Module-Preserving Compilation of Modelica Models. In: Proceedings of the 7th International Modelica Conference, pp. 880–889. Como, Italy, 2009.

[19] Modelica Association. Modelica - An Unified Object-Oriented Language for Physical Systems Modeling. Language Specification version 3.3, 2013. URL http://www.modelica.org/documents.

[20] Williams T., Kelley C. Gnuplot 4.6: An Interactive Plotting Program, 2012. URL http://www.gnuplot.info.

[21] White S.H., del Rey A.M., Sanchez G.R. Modeling epidemics using cellular automata. Applied Mathematics and Computation, 186(2007):pp. 193–202, 2007.

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