Advertisement

Hierarchical Cellular Automata Methods

  • Adam DunnEmail author
Chapter
Part of the Understanding Complex Systems book series (UCS)

Abstract

Many real-world spatial systems involve interacting processes that operate over more than scale. Whilst there has been a strong growth in knowledge about multiscale systems in many disciplines, the advent of coupled, multiresolution, multiscale and hierarchical cellular automata has been recent in comparison. Here, the structural definition of a cellular automaton is augmented with an abstraction operator, which transforms the cellular automaton into a hierarchy of cellular spaces. Simple propagation is used as a familiar and common behavioural phenomenon in several examples of behavioural specification. The purpose of this chapter is to provide the basics of a general framework, from which may be constructed for specific applications. Simple examples from landscape ecology are used to elucidate the methods.

Keywords

Cellular Automaton Seed Dispersal Landscape Ecology Cellular Automaton Delaunay Triangulation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    V. Ahl, T. F. H. Allen, Hierarchy Theory: A Vision, Vocabulary and Epistemology (Colombia University Press, New York, NY, 1996)Google Scholar
  2. 2.
    A. Alexandridis, D. Vakalis, C.I. Siettos, G.V. Bafas, A cellular automata model for forest fire spread prediction: The case of the wildfire that swept through Spetses Island in 1990. Appl. Math. Comput. 204(1), 191–201 (2008)CrossRefzbMATHMathSciNetGoogle Scholar
  3. 3.
    H. Andrén, Effects of landscape composition on predation rates at habitat edges, Mosaic Landscapes and Ecological Processes (Chapman & Hall, London 1995), pp. 225–255Google Scholar
  4. 4.
    A. Brandt, Multiscale scientific computation: Review 2001. Multiscale and Multiresolution Methods: Theory and Applications, vol. 20 (Springer, Heidelberg, 2001), pp. 1–95Google Scholar
  5. 5.
    A.W. Burks, Essays on Cellular Automata (University of Illinois Press, Champaign, IL 1970)zbMATHGoogle Scholar
  6. 6.
    M.L. Cadenasso, S.T.A. Pickett, K.C. Weathers, C.G. Jones, A framework for a theory of ecological boundaries. BioScience 53(8), 750–758 (2003)CrossRefGoogle Scholar
  7. 7.
    Q.W. Chen, F. Ye, Unstructured cellular automata and the application to model river riparian vegetation dynamics. Lecture Notes in Computer Science, ACRI 2008, vol. 5191 (Springer, Heidelberg, 2008), pp. 337–344Google Scholar
  8. 8.
    A.G. Dunn, J.D. Majer, In response to the continuum model for fauna research: A hierarchical, patch-based model of spatial landscape patterns. Oikos 116(8), 1413–1418 (2007)CrossRefGoogle Scholar
  9. 9.
    A.G. Dunn, J.D. Majer, Simulating weed propagation via hierarchical, patch-based cellular automata. Lecture Notes in Computer Science, ICCS 2007, vol. 4487 (Springer, Heidelberg 2007), pp. 762–769Google Scholar
  10. 10.
    A.G. Dunn, G.J. Milne, Modelling wildfire dynamics via interacting automata. Lecture Notes in Computer Science, ACRI 2004, vol. 3305 (Springer, Heidelberg 2004), pp. 395–404Google Scholar
  11. 11.
    D.G. Green, N. Klomp, G. Rimmington, S. Sadedin, Complexity in Landscape Ecology, Landscape Series (Springer, Heidelberg 2006)Google Scholar
  12. 12.
    J. Halton, G. B. Smith, Algorithm 247: Radical-inverse quasi-random point sequence. Comm ACM 7(12), 701–702 (1964)CrossRefGoogle Scholar
  13. 13.
    C.A.R. Hoare, Communicating sequential processes. Commun. ACM 21(8), 666–677 (1978)CrossRefzbMATHMathSciNetGoogle Scholar
  14. 14.
    A. Hoekstra, E. Lorenz, J.-L. Falcone, B. Chopard, Towards a complex automata framework for multi-scale modeling: Formalism and the scale separation map. Computational Science ICCS 2007 (Springer LNCS, Heidelberg 2007), pp. 922–930Google Scholar
  15. 15.
    E.P. Holland, J.N. Aegerter, C. Dytham, G.C. Smith, Landscape as a model: The importance of geometry. PLoS Comput Biol 3(10), e200 (2007)CrossRefMathSciNetGoogle Scholar
  16. 16.
    R.A. Ims, Movement patterns related to spatial structures. Mosaic Landscapes and Ecological Processes (Chapman & Hall, London, 1995), pp. 85–109Google Scholar
  17. 17.
    N. Israeli, N. Goldenfeld, Coarse-graining of cellular automata, emergence, and the predictability of complex systems. Phys. Rev. E 73(2), 026203 (2006)CrossRefMathSciNetGoogle Scholar
  18. 18.
    P. Jordano, C. Garcia, J.A. Godoy, J.L. Garcia-Castaño, Differential contribution of frugivores to complex seed dispersal patterns. Proc. Natl. Acad. Sci. USA 104(9), 3278–3282 (2007)CrossRefGoogle Scholar
  19. 19.
    S. Levin, The problem of pattern and scale in ecology: The Robert H. MacArthur award lecture. Ecology 73, 1943–1967 (1992)CrossRefGoogle Scholar
  20. 20.
    D.B. Lindenmayer, J. Fischer, R. Hobbs, The need for pluralism in landscape models: A reply to Dunn and Majer. Oikos 116(8), 1419–1421 (2007)CrossRefGoogle Scholar
  21. 21.
    D.B. Lindenmayer, S. McIntyre, J. Fischer, Birds in eucalypt and pine forests: landscape alteration and its implications for research models of faunal habitat use. Biol. Conserv. 110, 45–53 (2003)CrossRefGoogle Scholar
  22. 22.
    R. Milner, Communication and Concurrency (Prentice-Hall, Inc., Upper Saddle River, NJ, USA, 1989)zbMATHGoogle Scholar
  23. 23.
    R. Nathan, Long-distance dispersal of plants. Science 313, 786–788 (2006)CrossRefGoogle Scholar
  24. 24.
    A. Okabe, B. Boots, K Sugihara, Spatial Tessellations – Concepts and Applications of Voronoi Diagrams (Wiley, New York, 2000)zbMATHGoogle Scholar
  25. 25.
    W.G. O’Regan, P.H. Kourtz, and S. Nozaki, Bias in the contagion analog to fire spread. Forest Sci. 22(1), 61–68 (1976)Google Scholar
  26. 26.
    B. Pfeifer, K. Kugler, M.M. Tejada, C. Baumgartner, M. Seger, M. Osl, M. Netzer, M. Handler, A. Dander, M. Wurz, A. Graber, and B. Tilg, A cellular automaton framework for infectious disease spread simulation. Open Med Inform J 2, 70–81 (2008)CrossRefGoogle Scholar
  27. 27.
    B. Schönfisch, Anisotropy in cellular automata. Biosystems 41(1), 29–41 (1997)CrossRefGoogle Scholar
  28. 28.
    W. Spataro, D. DŠAmbrosio, R. Rongo, G. A. Trunfio, An evolutionary approach for modelling lava flows through cellular automata. In Lecture Notes in Computer Science, ACRI 2004, vol. 3305. (Springer, Heidelberg 2004), pp. 725–734Google Scholar
  29. 29.
    C. D. Stansbury, Dispersal of the environmental weed Bridal Creeper, Asparagus asparagoides, by Silvereyes, Zosterops lateralis in south-western Australia. Emu 101, 39–45 (2001)CrossRefGoogle Scholar
  30. 30.
    A.L. Sullivan, I.K. Knight, A hybrid cellular automata/semi-physical model of fire growth. Asia-Pacific Conference on Complex Systems, Complex 09 (Cairns, Australia, 2004)Google Scholar
  31. 31.
    G.A. Trunfio, Predicting wildfire spreading through a hexagonal cellular automata model. Cellular Automata, LNCS (Springer, Heidelberg 2004), pp. 385–394Google Scholar
  32. 32.
    A. Vicari, H. Alexis, C. Del Negro, M. Coltelli, M. Marsella, C. Proietti, Modeling of the 2001 lava flow at Etna volcano by a cellular automata approach. Environ Model. Softw. 22(10), 1465–1471 (2007)CrossRefGoogle Scholar
  33. 33.
    J.R. Weimar, Coupling microscopic and macroscopic cellular automata. Parallel Comput. 27(5), 601–611 (2001). 375183CrossRefzbMATHGoogle Scholar
  34. 34.
    J.A. Wiens, N.C. Stenseth, B. Van Horne, R.A. Ims, Ecological mechanisms and landscape ecology. Oikos 66, 369–380 (1993)CrossRefGoogle Scholar
  35. 35.
    J. Wu, J.L. David, A spatially explicit hierarchical approach to modeling complex ecological systems: Theory and applications. Ecol. Modell. 153(1–2), 7–26 (2002)CrossRefGoogle Scholar
  36. 36.
    J. Wu, O. Loucks, From balance-of-nature to hierarchical patch dynamics: A paradigm shift in ecology. Q. Rev. Biol. 70, 439–466 (1995)CrossRefGoogle Scholar
  37. 37.
    B.P. Zeigler, Theory of Modeling and Simulation (Krieger Publishing, Melbourne, FL, USA, 1984)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.Centre for Health Informatics, University of New South Wales UNSWSydney NSWAustralia
  2. 2.Alcoa Research Centre for Stronger Communities, Curtin University of TechnologyPerthAustralia

Personalised recommendations