An Approach to Cellular Automata Modelling in Modelica

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

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

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Ingår i: Proceedings of the 5th International Workshop on Equation-Based Object-Oriented Modeling Languages and Tools; April 19; University of Nottingham; Nottingham; UK

Linköping Electronic Conference Proceedings 84:15, s. 121-120

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Publicerad: 2013-03-27

ISBN: 978-91-7519-621-3 (print)

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


A new Modelica library; named CellularPDEVS; is introduced in this manuscript. This new library facilitates the description of one- and two-dimensional Cellular Automata (CA) models in Modelica. CellularPDEVS models have been specified using Parallel DEVS. The library has been implemented using the functionality of the DEVSLib library which supports the Parallel DEVS formalism in Modelica. CellularPDEVS allows the user to focus on describing the behavior of the cell and the characteristics of the cellular space. CellularPDEVS models are compatible with other DEVSLib models; facilitating the combination of CA; Parallel DEVS and other Modelica models. Three examples are presented: Wolfram’s rule 30 and 110; and the Conway’s Game of Life.


Modelica; Cellular Automata; Parallel DEVS; CellularPDEVS; DEVSLib


[1] Oscar Acuña; Carla Martin-Villalba; and Alfonso Urquia. Virtual-lab of a cement clinker cooler for operator training. In Proceedings of the 7th Vienna International Conference on Mathematical Modeling (MATHMOD); pages 331–336; Vienna; Austria; 2012.

[2] Karl J. Åström; Hilding Elmqvist; and Sven Erik Mattsson. Evolution of continuous-time modeling and simulation. In Proceedings of the 12th European Simulation Multiconference (ESM’98); pages 9–18; Manchester; UK; 1998.

[3] Alex Chung Hen Chow. Parallel DEVS: A parallel; hierarchical; modular modeling formalism and its distributed simulator. Transactions of the Society for Computer Simulation International; 13(2):55–67; 1996.

[4] Some free modeling and simulation resources. Dpto. Informática y Automática; UNED. http://www. euclides.dia.uned.es/; 2013.

[5] Stefan M.O. Fabricius and E. Badreddin. Hybrid dynamic plant performance analysis supported by extensions to the Petri Net library in Modelica. In Proceedings of the 4th Asian control Conference (ASCC); pages 41–50; Singapore; 2002.

[6] J.A. Ferreira and J.P. Estima de Oliveira. Modelling hybrid systems using StateCharts and Modelica. In Proceedings of the 7th IEEE International Conference on Emerging Technologies and Factory Automation; pages 1063–1069; 1999.

[7] Peter Fritzson. Principles of Object-Oriented Modeling and Simulation with Modelica 2.1. Wiley-IEEE Computer Society Pr; 2003.

[8] Niloy Ganguly; Biplab K Sikdar; Andreas Deutsch; Geoffrey Canright; and P Pal Chaudhuri. A survey on cellular automata. Technical report; 2003.

[9] Golly. http://golly.sourceforge.net; 2013.

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

[11] Andrew Ilachinski. Cellular Automata: A Discrete Universe. World Scientific; Singapore; 2001.

[12] Lemont B. Kier; Paul G. Seybold; and Chao-Kun Cheng. Modeling Chemical Systems using Cellular Automata. Springer; Dordrecht; The Netherlands; 2005.

[13] Jiri Kroc; Peter M.A. Sloot; and Alfons G. Hoekstra; editors. Simulating Complex Systems by Cellular Automata. Springer-Verlag; Berlin; 2010.

[14] Modelica Association. Modelica - An unified objectoriented language for physical systems modeling. Language specification version 3.1; 2012.

[15] Modelica Libraries. Modelica free and comercial libraries. http://www.modelica.org/libraries; 2013.

[16] Pieter J. Mosterman; Martin Otter; and Hilding Elmqvist. Modelling Petri Nets as local constraint equations for hybrid systems using Modelica. In Proceedings of the Summer Computer Simulation Conference; pages 314–319; 1998.

[17] Modelica standard library. http://www.modelica. org/libraries/Modelica; February 2010.

[18] David O’Sullivan and Paul M. Torrens. Cellular models of urban systems. In S. Bandini and T. Worsch; editors;Theoretical and Practical Issues on Cellular Automata. Springer-Verlag; London; 2000.

[19] Martin Otter; Karl-Erik Årzén; and Isolde Dressler. State- Graph - a Modelica library for hierarchical state machines. In Proceedings of the 4th International Modelica Conference; pages 569–578; Hamburg; Germany; 2005.

[20] Tiziano Pulecchi and Francesco Casella. HyAuLib: modelling hybrid automata in Modelica. In Proceedings of the 6th International Modelica Conference; pages 239– 246; Bielefeld; Germany; 2008.

[21] Stewart Robinson; Richard E. Nance; Ray J. Paul; Michael Pidd; and Simon J.E. Taylor. Simulation model reuse: definitions; benefits and obstacles. Simulation Modelling Practice and Theory; 12(7-8):479 – 494; 2004. Simulation in Operational Research.

[22] Jean-François Rouhaud. Cellular automata and consumer behaviour. European Journal of Economic and Social Systems; 14:37–52; 2000.

[23] Miguel A. Rubio; Alfonso Urquia; and Sebastian Dormido. Dynamic modelling of PEM fuel cells using the fuelcelllib Modelica library. Mathematical and Computer Modelling of Dynamical Systems; 16(3):165–194; 2010.

[24] Victorino Sanz. Hybrid System Modeling Using the Parallel DEVS Formalism and the Modelica Language. PhD thesis; E.T.S.I. Informática; UNED; Madrid; Spain; 2010.

[25] Victorino Sanz; Alfonso Urquia; François E. Cellier; and Sebastian Dormido. System modeling using the Parallel DEVS formalism and the Modelica language. Simulation Modeling Practice and Theory; 18(7):998–1018; 2010.

[26] Victorino Sanz; Alfonso Urquia; and Sebastian Dormido. Parallel DEVS and process-oriented modeling in Modelica. In Proceedings of the 7th International Modelica Conference; pages 96–107; Como; Italy; 2009.

[27] Joel L. Schiff. Cellular Automata: A Discrete View of the World. Wiley-Interscience; New York; NY; USA; 2008.

[28] Stanislaw Ulam. Random processes and transformations. In Sets; Numbers and Universes. MIT Press; Cambridge; 1974.

[29] John von Neumann. The general and logical theory of automata. In Collectd Works; volume 5. Macmillan; New York; 1963.

[30] John von Neumann. Theory of self-reproducing automata. University of Illinois Press; Urbana and London; 1966.

[31] Gabriel Wainer. CD++: A toolkit to develop DEVS models. Software: Practice and Experience; 32(13):1261–1306; 2002.

[32] Gabriel A.Wainer. Discrete-Event Modeling and Simulation - A Practitioner’s Approach. CRC Press; Boca Raton; FL; USA; 2009.

[33] Dieter A. Wolf-Gladrow; editor. Lattice Gas Cellular Automata and Lattice Boltzmann Models: An Introducction. Springer-Verlag; Berlin; 2000.

[34] Stephen Wolfram. Cellular Automata and Complexity: Collected Papers. Addison-Wesley; 1994.

[35] Stephen Wolfram. A New Kind of Science. Wolfram Media Inc.; Champain; IL; USA; 2002.

[36] Benard P. Zeigler and Hessam S. Sarjoughian; editors.Guide to Modeling and Simulation of Systems of Systems. Springer-Verlag; London; 2013.

[37] Bernard P. Zeigler; Tag Gon Kim; and Herbert Prähofer. Theory of Modeling and Simulation. Academic Press; Inc.; Orlando; FL; USA; 2000.

[38] Bernard P. Zeigler and Hessam S. Sarjoughian. Introduction to DEVS modeling & simulation with JAVA: Developing component-based simulation models; 2003.

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