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Complex Automata: Multi-scale Modeling with Coupled Cellular Automata

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Simulating Complex Systems by Cellular Automata

Part of the book series: Understanding Complex Systems ((UCS))

Abstract

Cellular Automata (CA) are generally acknowledged to be a powerful way to describe and model natural phenomena [1–3]. There are even tempting claims that nature itself is one big (quantum) information processing system, e.g. [4], and that CA may actually be nature’s way to do this processing [5–7]. We will not embark on this philosophical road, but ask ourselves a more mundane question. Can we use CA to model the inherently multi-scale processes in nature and use these models for efficient simulations on digital computers?

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References

  1. B. Chopard, M. Droz, Cellular Automata Modeling of Physical Systems (Cambridge University Press, Cambridge, 1998)

    Book  MATH  Google Scholar 

  2. A. Deutsch, S. Dormann, Cellular Automaton Modeling of Biological Pattern Formation: Characterization, Applications, and Analysis (Birkhäuser, Basel, 2005)

    Google Scholar 

  3. P. Sloot, A. Hoekstra, Modeling dynamic systems with cellular automata, ed. by P. Fishwick Handbook of Dynamic System Modeling, Chapter 21 (Chapman & Hall/CRC, London/Boca Rabin, FL, 2007)

    Google Scholar 

  4. S. Lloyd, Phys. Rev. Lett. 23, 237901 (2002)

    Article  MathSciNet  Google Scholar 

  5. K. Zuse, Int. J. Theor. Phys. 21, 580–600 (1982)

    Article  Google Scholar 

  6. K. Zuse, Rechnender Raum, http://www.idsia.ch/∼juergen/digitalphysics.html

  7. S. Wolfram, A New Kind of Science (Wolfram Media, Inc., Champaign, IL, 2002)

    MATH  Google Scholar 

  8. D. Bader, Petascale Computing: Algorithms and Applications (Chapman & Hall/CRC, London/Boca Rabin, FL, 2008)

    Google Scholar 

  9. A. Hoekstra, S. Portegies Zwart, M. Bubak, P. Sloot, Towards distributed petascale computing, ed. by D. Bader, Petascale Computing: Algorithms and Applications, Chapter 8 (Chapman & Hall/CRC, London/Boca Rabin, FL, 2008)

    Google Scholar 

  10. P. Sloot, D. Frenkel, H. van der Vorst et al., White paper on computational e-science, studying complex systems in silico, a national research invitiative (2007), http://www.science.uva.nl/research/pscs/papers/archive/Sloot2007a.pdf

  11. Special Issue on Multiphysics modeling, IEEE Comput. Sci. Eng. 7 14–53, (2005)

    Google Scholar 

  12. SIAM Multiscale Model Simul, http://epubs.siam.org/sam-bin/dbq/toclist/MMS

  13. Int J Multiscale Comput Eng, http://www.edata-center.com/journals/61fd1b191cf7e96f.html

  14. A. Finkelstein, J. Hetherington, O. Margoninski, P. Saffrey, R. Seymour, A. Warner, IEEE Comput. 37, 26–33 (2004)

    Article  Google Scholar 

  15. D. Noble, Science 295, 1678–1682 (2002)

    Article  Google Scholar 

  16. B. Di Ventura, C. Lemerle, K. Michalodimitrakis, L. Serrano, Nature 443, 527–533 (2006)

    Article  Google Scholar 

  17. P. Hunter, W. Li, A. McCulloch, D. Noble, IEEE Comput. 39, 48–54 (2006)

    Article  Google Scholar 

  18. P. Sloot, A. Tirado-Ramos, I. Altintas, M. Bubak, C. Boucher, IEEE Comput. 39, 40–46 (2006)

    Article  Google Scholar 

  19. S. Smye, R. Clayton, Med. Eng. Phys. 24, 565–574 (2002)

    Article  Google Scholar 

  20. G. Ingram, I. Cameron, K. Hangos, Chem. Eng. Sci., 59, 2171–2187 (2004)

    Article  Google Scholar 

  21. E. Weinan, X. Li, W. Ren, E. Vanden-Eijnden, Commun. Comput. Phys. 2, 367–450 (2007)

    MATH  MathSciNet  Google Scholar 

  22. R. White, Modeling multi-scale processes in a cellular automata framework, ed. by J. Portugali, Complex Artificial Environments, Simulation, Cognition and VR in the Study and Planning of Cities, (Springer, New York, NY, 2006) pp. 165–177

    Google Scholar 

  23. B. Ribba, T. Alarcón, K. Marron, P. Maini, Z. Agur, The use of hybrid cellular automata models for improving cancer therapy, ed. by P. Sloot, B. Chopard, A. Hoekstra: Cellular Automata, 6th International Conference on Cellular Automata, ACRI 2004, LNCS, vol. 3305 (Springer, Heidelberg, 2004), pp. 444–453

    Google Scholar 

  24. C. Lin, Y. Lai, Phys. Rev. E. 62, 2219–2225 (2000)

    Article  Google Scholar 

  25. N. Baas, T. Helvik, Adv. Compl. Syst. 8, 169–192 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  26. N. Israeli, N. Goldenfeld, Phys. Rev. Let. 92, 074105 (2004)

    Article  Google Scholar 

  27. A. Hoekstra, E. Lorenz, J.L. Falcone, B. Chopard, Towards a complex automata framework for multi-scale modeling: Formalism and the scale separation map, ed. by Y. Shi, D. van Albada, J. Dongarra, P. Sloot, ICCS 2007, Part I, Lecture Notes in Computer Science, vol. 4487 (Springer, Heidelberg, 2007), pp. 922–930

    Google Scholar 

  28. A. Hoekstra, E. Lorenz, J. Falcone, B. Chopard, Int. J. Multiscale Comp. Eng. 5, 491–502 (2007)

    Article  Google Scholar 

  29. A.G. Hoekstra, J-L. Falcone, A. Caiazzo, B. Chopard, Multi-scale modeling with cellular automata: The complex automata approach, ed. by H. Umeo et al., ACRI 2008, Lecture Notes in Computer Science, vol. 5191, (Springer, Berlin-Heidelberg, 2008), pp. 192–199

    Google Scholar 

  30. D. Evans, P. Lawford, J. Gunn, D. Walker, R. Hose, R. Smallwood, B. Chopard, M. Krafczyk, J. Bernsdorf, A. Hoekstra, Phil. Trans. Roy. Soc. A 366, 3343–3360 (2008)

    Article  Google Scholar 

  31. The Coast project, http://www.complex-automata.org

  32. B. Chopard, J-L. Falcone, R. Razakanirina, A.G. Hoekstra, A. Caiazzo, On the collision-propagation and gather-update formulations of a cellular automata rule, ed. by H. Umeo et al., ACRI 2008, Lecture Notes in Computer Science vol. 5191, (Springer, Berlin Heidelberg, 2008), pp. 144–251

    Google Scholar 

  33. J.A. Kaandorp, J.E. Kübler, The Algorithmic Beauty of Seaweeds, Sponges and Corals (Springer, Heidelberg, New York, 2001)

    Book  MATH  Google Scholar 

  34. R.M.H. Merks, A.G. Hoekstra, J.A. Kaandorp, P.M.A. Sloot, J. Theor. Biol. 224, 153–166 (2003)

    Article  MathSciNet  Google Scholar 

  35. R.M.H. Merks, A.G. Hoekstra, J.A. Kaandorp, P.M.A. Sloot, J. Theor. Biol. 228, 559–576 (2004)

    Article  MathSciNet  Google Scholar 

  36. G. Agha Actors: A Model of Concurrent Computation in Distributed Systems (MIT Press, Cambridge, MA, 1986)

    Google Scholar 

  37. J. Hegewald, M. Krafczyk, J. Tölke, A. Hoekstra, B. Chopard, An agent-based coupling platform for complex automata ICCS 2008, Krakow. Lecture Notes in Computer Science, vol. 5102, doi:10.1007/978-3-540-69387-1 (Springer, Berlin Heidelberg, 2008), pp. 227–233

    Google Scholar 

  38. S. Succi, The Lattice Boltzmann Equation for Fluid Dynamics and Beyond (Oxford University Press, Oxford, 2001)

    MATH  Google Scholar 

  39. D. Alemani, B. Chopard, J. Galceran, J. Buffle, Phys. Chem. Chem. Phys. 7, 1–11 (2005)

    Article  Google Scholar 

  40. A. Caiazzo, J-L. Falcone, B. Chopard, A.G. Hoekstra, Error investigations in complex automata models for reaction-diffusion systems, ed. by H. Umeo et al., ACRI 2008, Lecture Notes in Computer Science, vol. 5191, (Springer, Berlin Heidelberg, 2008), pp. 260–267

    Google Scholar 

  41. A. Caiazzo, J-L. Falcone, B. Chopard, A.G. Hoekstra, Asymptotic analysis of complex automata models for reaction-diffusion systems. Appl. Num. Maths 59, 2023–2034 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  42. A. Caiazzo, D. Evans, J.L. Falcone, J. Hegewald, E. Lorenz, B. Stahl, D. Wang, J. Bernsdorff, B. Chopard, J. Gunn, R. Hose, M. Krafczyk, P. Lawford, R. Smallwood, D. Walker, A.G. Hoekstra, Towards a complex automata multiscale model of in-stent restenosis, submitted to J. Comput. Sci.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Computational Science, Faculty of Science, University of Amsterdam, Science park 107, 1098, XG, Amsterdam, The Netherlands

    Alfons G. Hoekstra

  2. INRIA Rocquencourt – BP 105, F-78153, Le Chesnay Cedex, France

    Alfonso Caiazzo

  3. Computational Science Group, Faculty of Science, University of Amsterdam, Science park 107, 1098, XG, Amsterdam, The Netherlands

    Eric Lorenz

  4. Department of Computer Science, University of Geneva, 7 route de Drize, 1227, Carouge, Switzerland

    Jean-Luc Falcone & Bastien Chopard

Authors
  1. Alfons G. Hoekstra
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  2. Alfonso Caiazzo
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  3. Eric Lorenz
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  4. Jean-Luc Falcone
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  5. Bastien Chopard
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Corresponding author

Correspondence to Alfons G. Hoekstra .

Editor information

Editors and Affiliations

  1. Havlickova 482, Stahlavy, CZ 33203, Czech Republic

    Jiri Kroc

  2. Fac. Science, Informatics Institute, Universiteit Amsterdam, Kruislaan 403, Amsterdam, 1098 SJ, Netherlands

    Peter M.A. Sloot

  3. , Computational Science Faculty, University of Amsterdam, Science Park 107, Amsterdam, 1098 XG, Netherlands

    Alfons G. Hoekstra

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Hoekstra, A.G., Caiazzo, A., Lorenz, E., Falcone, JL., Chopard, B. (2010). Complex Automata: Multi-scale Modeling with Coupled Cellular Automata. In: Kroc, J., Sloot, P., Hoekstra, A. (eds) Simulating Complex Systems by Cellular Automata. Understanding Complex Systems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12203-3_3

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  • DOI: https://doi.org/10.1007/978-3-642-12203-3_3

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-12202-6

  • Online ISBN: 978-3-642-12203-3

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