Cellular automata on irregular tessellations

Dynamical Systems

Volumn 27, Issue 4, 2012, Pages 411-430

  Baetens, Jan M ^a   De Baets, Bernard ^a  

^a GHENT UNIVERSITY   (Belgium)

Author keywords

cellular automata; discrete dynamical systems; enumeration; formalism; irregular tessellations

Indexed keywords

DISCRETE DYNAMICAL SYSTEMS; ENUMERATION; ENUMERATION SCHEMES; FORMALISM; GRAPH REPRESENTATION; ILLUSTRATIVE EXAMPLES; IRREGULAR TESSELLATIONS; MODELLING TOOLS;

DYNAMICAL SYSTEMS;

CELLULAR AUTOMATA;

EID: 84867797937     PISSN: 14689367     EISSN: 14689375     Source Type: Journal    
DOI: 10.1080/14689367.2012.711300     Document Type: Article

References (56)

1. J. von Neumann, The general and logical theory of automata, in Cerebral Mechanisms in Behaviour: The Hixon Symposium, L.A. Jeffress, ed., Wiley, New York, 1951, pp. 1-32.
2. M. Gardner, Mathematical games: The fantastic combinations of John Conway's new solitaire game 'life', Sci. Amer. 223 (1971), pp. 120-123.
3. K. Kaneko, Theory and Applications of Coupled Map Lattices, John Wiley & Sons, Chichester, 1993.
4. M.A. Shereshevsky, Lyapunov exponents for one-dimensional cellular automata, J. Nonlinear Sci. 2 (1991), pp. 1-8.
5. S. Wolfram, Cellular Automata and Complexity, Westview Press, Boulder, CO, 1994.
6. R.J. Doran and S.W. Laffan, Simulating the spatial dynamics of foot and mouth disease outbreaks in feral pigs and livestock in Queensland, Australia, using a susceptible-infected-recovered cellular automata model, Prev. Vet. Med. 70 (2005), pp. 133-152. (Pubitemid 40841370)
7. J. Milne and S.C. Fu, Epidemic modelling using cellular automata, Proceedings of the 1st Australian Conference on Artificial Life'03 (ACAL 03), University of New South Wales, Canberra, Australia, December 2003, pp. 43-57.
8. S.H. White, A.M. del Rey, and G.R. Sanchez, Modeling epidemics using cellular automata, Appl. Math. Comput. 186 (2007), pp. 193-202. (Pubitemid 46437385)
9. H. Baltzer, P.W. Braun, and W. Köhler, Cellular automata models for vegetation dynamics, Ecol. Modell. 107 (1998), pp. 113-125. (Pubitemid 28228958)
10. A. Dewdney, Sharks and fish wage an ecological war on the toroidal planet, Sci. Amer. 251 (1984), pp. 14-22.
11. D.G. Mallet and L.G. De Pillis, A cellular automata model of tumour-immune system interactions, J. Theor. Biol. 239 (2006), pp. 334-350.
12. L. Preziosi, Cancer Modelling and Simulation, Chapman & Hall, Boca Raton, FL, 2003.
13. A. Qi, X. Zheng, C. Du, and B. An, A cellular automaton model of cancerous growth, J. Theor. Biol. 161 (1993), pp. 1-12.
14. C. Picioreanu, M.C.M. van Loosdrecht, and J.J. Heijnen, Mathematical modeling of biofilm structure with a hybrid differential-discrete cellular automaton approach, Biotechnol. Bioeng. 58 (1998), pp. 101-116. (Pubitemid 28103346)
15. G. Pizarro, D. Griffeath, and D.R. Noguera, Quantitative cellular automaton model for biofilms, J. Environ. Eng. 127 (2001), pp. 782-789. (Pubitemid 32818662)
16. P. Van der Weeën, J.M. Baetens, and B. De Baets, Design and parameterization of a stochastic cellular automaton describing a chemical reaction, J. Comp. Chem. 32 (2011), pp. 1952-1961.
17. A. Alexandridis, D. Vakalis, C. Siettos, and G. Bafas, A cellular automata model for forest fire spread prediction: The case of the wildfire that swept through Spetses Island in 1990, Appl. Math. Comp. 204 (2008), pp. 191-201.
18. S.G. Berjak and J.W. Hearne, An improved cellular automaton model for simulating fire in a spatially heterogeneous Savanna system, Ecol. Modell. 148 (2002), pp. 133-151. (Pubitemid 34215649)
19. L.H. Encinas, S.H. White, A.M. del Rey, and G.R. Sánchez, Modelling forest fire spread using hexagonal cellular automata, Appl. Math. Modell. 31 (2007), pp. 1213-1227.
20. B. Chopard, P.O. Luthi, and P.A. Queloz, Cellular automata model of car traffic in a twodimensional street network, J. Phys. A: Math. Gen. 29 (1996), pp. 2325-2336.
21. O.K. Tonguz, W. Viriyasitavat, and F. Bai, Modeling urban traffic: A cellular automata approach, IEEE Comm. Mag. 47 (2009), pp. 142-150.
22. M. Batty, Cellular dynamics: modelling urban growth as a spatial epidemic, in Geocomputational Modelling, M.M. Fischer and Y. Leung, eds., Springer, Berlin, 2001, pp. 109-141.
23. L.B. Kier, P. Seybold, and C. Cheng, Modelling Chemical Systems using Cellular Automata, Springer, Dordrecht, The Netherlands, 2005.
24. J.L. Schiff, Cellular Automata: A Discrete View of the World, John Wiley & Sons, Chichester, 2008.
25. L. Berec, Techniques of spatially explicit individual-based models: Construction, simulation and mean-field analysis, Ecol. Modell. 150 (2002), pp. 55-81. (Pubitemid 34455289)
26. B. Carter, Cellular automata on triangular, pentagonal and hexagonal tessellations, in Encyclopedia of Complexity and Systems Sciences, R.A. Meyers, ed., Springer, Heidelberg, 2009, pp. 892-900.
27. 3-hex, Nat. Hazard. Earth Syst. Sci. 3 (2003), pp. 545-559. (Pubitemid 38362756)
28. M. Margenstern, On a characterization of cellular automata in tilings of the hyperbolic plane, Int. J. Found. Comp. Sci. 19 (2008), pp. 1235-1257.
29. N. Fatés and M. Morvan, Perturbing the topology of the game of life increases its robustness to asynchrony, Lect. Notes Comput. Sci. 3305 (2004), pp. 111-120. (Pubitemid 39742825)
30. A. Flache and R. Hegselmann, Do irregular grids make a difference? Relaxing the spatial regularity in cellular models in social dynamics, J. Art. Soc. Soc. Simul. 4 (2001). Available at http://jasss.soc.surrey.ac.uk/4/4/6.html
31. W. Shi and M.Y. Cheung Pang, Development of Voronoi-based cellular automata: an integrated dynamic model for geographical information systems, Int. J. Geograph. Inf. Sci. 14 (2000), pp. 455-474. (Pubitemid 30603252)
32. J.M. Baetens and B. De Baets, Phenomenological study of irregular cellular automata based on Lyapunov exponents and Jacobians, Chaos 20 (2010), Article no. 033112. Available at http://dx.doi.org/10.1063/1.3460362
33. S. Wolfram, Statistical mechanics of cellular automata, Rev. Mod. Phys. 55 (1983), pp. 601-644.
34. J. Weimar, Simulation with Cellular Automata, Logos-Verlag, Berlin, 1998.
35. E. Coppola, B. Tomassetti, L. Mariotti, M. Verdecchia, and G. Visconti, Cellular automata algorithms for drainage network extraction and rainfall assimilation, Hydrol. Sci. J. 52 (2007), pp. 579-592. (Pubitemid 46851541)
36. G.M. Crisci, G. Iovine, S.D. Gregorio, and V. Lupiano, Lava-flow hazard on the SE flank of Mt. Etna (Southern Italy), J. Volcanol. Geotherm. Res. 177 (2008), pp. 778-796.
37. D. D'Ambrosio and W. Spataro, Parallel evolutionary modelling of geological processes, Parallel Comput. 33 (2007), pp. 186-212. (Pubitemid 46428454)
38. D. Favis-Mortlock, A self-organizing dynamic systems approach to the simulation of rill initiation and development on hillslopes, Comput. Geosci. 24 (1998), pp. 353-372. (Pubitemid 28501968)
39. J.A. Parsons and M.A. Fonstad, A cellular automata model of surface water flow, Hydrol. Processes 21 (2007), pp. 2189-2195. (Pubitemid 47226122)
40. G. Valette, S. Prévost, L. Lucas, and J. Lonard, SoDA project: A simulation of soil surface degradation by rainfall, Comput. Graphics 30 (2006), pp. 494-506. (Pubitemid 43994145)
41. G.A. Trunfio, Predicting wildfire spreading through a hexagonal cellular automata model, Lect. Notes Comput. Sci. 3305 (2004), pp. 385-394. (Pubitemid 39742852)
42. M. Coleman, An Introduction to Partial Differential Equations with MATLAB, Chapman & Hall/CRC, Boca Raton, FL, 2005.
43. M. De Berg, O. Cheong, M. van Kreveld, and M. Overmars, Computational Geometry: Algorithms and Applications, 3rd ed., Springer, Berlin, 2008.
44. J. Van den Bulcke, J. Van Acker, and M. Stevens, Laboratory testing and computer simulation of blue stain growth on and in wood coatings, Int. Biodeterior. Biodegrad. 59 (2007), pp. 137-147. (Pubitemid 46162209)
45. Q. Chen and F. Ye, Unstructured cellular automata and the application to model river Riparian vegetation dynamics, Lect. Notes Comput. Sci. 5191 (2008), pp. 337-344.
46. D. Stevens and S. Dragićević, A GIS-based irregular cellular automata model of land-use change, Environ. Plan. B: Des. Plan. 34 (2007), pp. 708-724. (Pubitemid 47108928)
47. H. Couclelis, Cellular worlds: A framework for modeling micro-macro dynamics, Environ. Plan. A 17 (1985), pp. 585-596.
48. M.J. Fresnadillo, E. García, J.E. García, A. Martín, and G. Rodríguez, A SIS epidemiological model based on cellular automata on graphs, Lect. Notes Comput. Sci. 5518 (2009), pp. 1005-1062.
49. C. Marr and M.T. Hütt, Outer-totalistic cellular automata on graphs, Phys. Lett. A 373 (2009), pp. 546-549.
50. K. Tomita, H. Kurokawa, and S. Murata, Graph automata: Natural expression of selfreproduction, Physica D 171 (2002), pp. 197-210.
51. J. von Neumann and A.W. Burks, Theory of Self-Reproducing Automata, University of Illinois Press, Champaign, IL, 1966.
52. A. Deutsch and S. Dormann, Cellular Automaton Modeling of Biological Pattern Formation: Characterization, Applications, and Analysis, Birkhäuser, Bonn, 2005.
53. A. Ilachinski, Cellular Automata. A Discrete Universe, World Scientific, London, 2001.
54. S. Wolfram, A New Kind of Science, Wolfram Media, Champaign, IL, 2002.
55. J.M. Baetens and B. De Baets, On the topological sensitivity of cellular automata, Chaos 21 (2011), Article no. 023108. Available at http://dx.doi.org/ 10.1063/1.3535581
56. F. Bagnoli, R. Rechtman, and S. Ruffo, Damage spreading and Lyapunov exponents in cellular automata, Phys. Lett. A 172 (1992), pp. 34-38.