Skip to main content

Hierarchical Cellular Automata Methods

  • Chapter
  • First Online:

Part of the book series: Understanding Complex Systems ((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.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. V. Ahl, T. F. H. Allen, Hierarchy Theory: A Vision, Vocabulary and Epistemology (Colombia University Press, New York, NY, 1996)

    Google Scholar 

  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)

    Article  MATH  MathSciNet  Google Scholar 

  3. H. Andrén, Effects of landscape composition on predation rates at habitat edges, Mosaic Landscapes and Ecological Processes (Chapman & Hall, London 1995), pp. 225–255

    Google Scholar 

  4. A. Brandt, Multiscale scientific computation: Review 2001. Multiscale and Multiresolution Methods: Theory and Applications, vol. 20 (Springer, Heidelberg, 2001), pp. 1–95

    Google Scholar 

  5. A.W. Burks, Essays on Cellular Automata (University of Illinois Press, Champaign, IL 1970)

    MATH  Google Scholar 

  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)

    Article  Google Scholar 

  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. 337–344

    Google Scholar 

  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)

    Article  Google Scholar 

  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. 762–769

    Google Scholar 

  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. 395–404

    Google Scholar 

  11. D.G. Green, N. Klomp, G. Rimmington, S. Sadedin, Complexity in Landscape Ecology, Landscape Series (Springer, Heidelberg 2006)

    Google Scholar 

  12. J. Halton, G. B. Smith, Algorithm 247: Radical-inverse quasi-random point sequence. Comm ACM 7(12), 701–702 (1964)

    Article  Google Scholar 

  13. C.A.R. Hoare, Communicating sequential processes. Commun. ACM 21(8), 666–677 (1978)

    Article  MATH  MathSciNet  Google Scholar 

  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. 922–930

    Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  16. R.A. Ims, Movement patterns related to spatial structures. Mosaic Landscapes and Ecological Processes (Chapman & Hall, London, 1995), pp. 85–109

    Google Scholar 

  17. N. Israeli, N. Goldenfeld, Coarse-graining of cellular automata, emergence, and the predictability of complex systems. Phys. Rev. E 73(2), 026203 (2006)

    Article  MathSciNet  Google Scholar 

  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)

    Article  Google Scholar 

  19. S. Levin, The problem of pattern and scale in ecology: The Robert H. MacArthur award lecture. Ecology 73, 1943–1967 (1992)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  22. R. Milner, Communication and Concurrency (Prentice-Hall, Inc., Upper Saddle River, NJ, USA, 1989)

    MATH  Google Scholar 

  23. R. Nathan, Long-distance dispersal of plants. Science 313, 786–788 (2006)

    Article  Google Scholar 

  24. A. Okabe, B. Boots, K Sugihara, Spatial Tessellations – Concepts and Applications of Voronoi Diagrams (Wiley, New York, 2000)

    MATH  Google Scholar 

  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. 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)

    Article  Google Scholar 

  27. B. Schönfisch, Anisotropy in cellular automata. Biosystems 41(1), 29–41 (1997)

    Article  Google Scholar 

  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. 725–734

    Google Scholar 

  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)

    Article  Google Scholar 

  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. G.A. Trunfio, Predicting wildfire spreading through a hexagonal cellular automata model. Cellular Automata, LNCS (Springer, Heidelberg 2004), pp. 385–394

    Google Scholar 

  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)

    Article  Google Scholar 

  33. J.R. Weimar, Coupling microscopic and macroscopic cellular automata. Parallel Comput. 27(5), 601–611 (2001). 375183

    Article  MATH  Google Scholar 

  34. J.A. Wiens, N.C. Stenseth, B. Van Horne, R.A. Ims, Ecological mechanisms and landscape ecology. Oikos 66, 369–380 (1993)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  37. B.P. Zeigler, Theory of Modeling and Simulation (Krieger Publishing, Melbourne, FL, USA, 1984)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Adam Dunn .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Dunn, A. (2010). Hierarchical Cellular Automata Methods. 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_4

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-12203-3_4

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-12202-6

  • Online ISBN: 978-3-642-12203-3

  • eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)

Publish with us

Policies and ethics