Publication Cover
Dynamical Systems
An International Journal
Volume 27, 2012 - Issue 4
275
Views
9
CrossRef citations to date
0
Altmetric
Original Articles

Cellular automata on irregular tessellations

&
Pages 411-430 | Received 27 Jun 2011, Accepted 28 Jun 2012, Published online: 14 Aug 2012

References

  • von Neumann , J . 1951 . “ The general and logical theory of automata ” . In Cerebral Mechanisms in Behaviour: The Hixon Symposium , Edited by: Jeffress , LA . 1 – 32 . New York : Wiley .
  • Gardner , M . 1971 . Mathematical games: The fantastic combinations of John Conway's new solitaire game ‘life’ . Sci. Amer. , 223 : 120 – 123 .
  • Kaneko , K . 1993 . Theory and Applications of Coupled Map Lattices , Chichester : John Wiley & Sons .
  • Shereshevsky , MA . 1991 . Lyapunov exponents for one-dimensional cellular automata . J. Nonlinear Sci. , 2 : 1 – 8 .
  • Wolfram , S . 1994 . Cellular Automata and Complexity , Boulder, CO : Westview Press .
  • Doran , RJ and Laffan , SW . 2005 . 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 : 133 – 152 .
  • Milne , J and Fu , SC . 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
  • White , SH , del Rey , AM and Sanchez , GR . 2007 . Modeling epidemics using cellular automata . Appl. Math. Comput. , 186 : 193 – 202 .
  • Baltzer , H , Braun , PW and Köhler , W . 1998 . Cellular automata models for vegetation dynamics . Ecol. Modell. , 107 : 113 – 125 .
  • Dewdney , A . 1984 . Sharks and fish wage an ecological war on the toroidal planet . Sci. Amer. , 251 : 14 – 22 .
  • Mallet , DG and De Pillis , LG . 2006 . A cellular automata model of tumour-immune system interactions . J. Theor. Biol. , 239 : 334 – 350 .
  • Preziosi , L . 2003 . Cancer Modelling and Simulation , Boca Raton, FL : Chapman & Hall .
  • Qi , A , Zheng , X , Du , C and An , B . 1993 . A cellular automaton model of cancerous growth . J. Theor. Biol. , 161 : 1 – 12 .
  • Picioreanu , C , van Loosdrecht , MCM and Heijnen , JJ . 1998 . Mathematical modeling of biofilm structure with a hybrid differential-discrete cellular automaton approach . Biotechnol. Bioeng. , 58 : 101 – 116 .
  • Pizarro , G , Griffeath , D and Noguera , DR . 2001 . Quantitative cellular automaton model for biofilms . J. Environ. Eng. , 127 : 782 – 789 .
  • Van der Weeën , P , Baetens , JM and De Baets , B . 2011 . Design and parameterization of a stochastic cellular automaton describing a chemical reaction . J. Comp. Chem. , 32 : 1952 – 1961 .
  • Alexandridis , A , Vakalis , D , Siettos , C and Bafas , G . 2008 . 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 : 191 – 201 .
  • Berjak , SG and Hearne , JW . 2002 . An improved cellular automaton model for simulating fire in a spatially heterogeneous Savanna system . Ecol. Modell. , 148 : 133 – 151 .
  • Encinas , LH , White , SH , del Rey , AM and Sánchez , GR . 2007 . Modelling forest fire spread using hexagonal cellular automata . Appl. Math. Modell. , 31 : 1213 – 1227 .
  • Chopard , B , Luthi , PO and Queloz , PA . 1996 . Cellular automata model of car traffic in a two-dimensional street network . J. Phys. A: Math. Gen. , 29 : 2325 – 2336 .
  • Tonguz , OK , Viriyasitavat , W and Bai , F . 2009 . Modeling urban traffic: A cellular automata approach . IEEE Comm. Mag. , 47 : 142 – 150 .
  • Batty , M . 2001 . “ Cellular dynamics: modelling urban growth as a spatial epidemic ” . In Geocomputational Modelling , Edited by: Fischer , MM and Leung , Y . 109 – 141 . Berlin : Springer .
  • Kier , LB , Seybold , P and Cheng , C . 2005 . Modelling Chemical Systems using Cellular Automata , Dordrecht , , The Netherlands : Springer .
  • Schiff , JL . 2008 . Cellular Automata: A Discrete View of the World , Chichester : John Wiley & Sons .
  • Berec , L . 2002 . Techniques of spatially explicit individual-based models: Construction, simulation and mean-field analysis . Ecol. Modell. , 150 : 55 – 81 .
  • Carter , B . 2009 . “ Cellular automata on triangular, pentagonal and hexagonal tessellations ” . In Encyclopedia of Complexity and Systems Sciences , Edited by: Meyers , RA . 892 – 900 . Heidelberg : Springer .
  • D'Ambrosio , D , Di Gregorio , S and Iovine , G . 2003 . Simulating debris flows through a hexagonal cellular automata model: SCIDDICAS3−hex . Nat. Hazard. Earth Syst. Sci. , 3 : 545 – 559 .
  • Margenstern , M . 2008 . On a characterization of cellular automata in tilings of the hyperbolic plane . Int. J. Found. Comp. Sci. , 19 : 1235 – 1257 .
  • Fatés , N and Morvan , M . 2004 . Perturbing the topology of the game of life increases its robustness to asynchrony . Lect. Notes Comput. Sci. , 3305 : 111 – 120 .
  • Flache , A and Hegselmann , R . 2001 . Do irregular grids make a difference? Relaxing the spatial regularity in cellular models in social dynamics . J. Art. Soc. Soc. Simul. , 4 Available at http://jasss.soc.surrey.ac.uk/4/4/6.html
  • Shi , W and Cheung Pang , MY . 2000 . Development of Voronoi-based cellular automata: an integrated dynamic model for geographical information systems . Int. J. Geograph. Inf. Sci. , 14 : 455 – 474 .
  • Baetens , JM and De Baets , B . 2010 . Phenomenological study of irregular cellular automata based on Lyapunov exponents and Jacobians . Chaos , 20 Article no. 033112. Available at http://dx.doi.org/10.1063/1.3460362
  • Wolfram , S . 1983 . Statistical mechanics of cellular automata . Rev. Mod. Phys. , 55 : 601 – 644 .
  • Weimar , J . 1998 . Simulation with Cellular Automata , Berlin : Logos-Verlag .
  • Coppola , E , Tomassetti , B , Mariotti , L , Verdecchia , M and Visconti , G . 2007 . Cellular automata algorithms for drainage network extraction and rainfall assimilation . Hydrol. Sci. J. , 52 : 579 – 592 .
  • Crisci , GM , Iovine , G , Gregorio , SD and Lupiano , V . 2008 . Lava-flow hazard on the SE flank of Mt. Etna (Southern Italy) . J. Volcanol. Geotherm. Res. , 177 : 778 – 796 .
  • D'Ambrosio , D and Spataro , W . 2007 . Parallel evolutionary modelling of geological processes . Parallel Comput. , 33 : 186 – 212 .
  • Favis-Mortlock , D . 1998 . A self-organizing dynamic systems approach to the simulation of rill initiation and development on hillslopes . Comput. Geosci. , 24 : 353 – 372 .
  • Parsons , JA and Fonstad , MA . 2007 . A cellular automata model of surface water flow . Hydrol. Processes , 21 : 2189 – 2195 .
  • Valette , G , Prévost , S , Lucas , L and Lonard , J . 2006 . SoDA project: A simulation of soil surface degradation by rainfall . Comput. Graphics , 30 : 494 – 506 .
  • Trunfio , GA . 2004 . Predicting wildfire spreading through a hexagonal cellular automata model . Lect. Notes Comput. Sci. , 3305 : 385 – 394 .
  • Coleman , M . 2005 . An Introduction to Partial Differential Equations with MATLAB , Boca Raton, FL : Chapman & Hall/CRC .
  • De Berg , M , Cheong , O , van Kreveld , M and Overmars , M . 2008 . Computational Geometry: Algorithms and Applications , 3 , Berlin : Springer .
  • Van den Bulcke , J , Van Acker , J and Stevens , M . 2007 . Laboratory testing and computer simulation of blue stain growth on and in wood coatings . Int. Biodeterior. Biodegrad. , 59 : 137 – 147 .
  • Chen , Q and Ye , F . 2008 . Unstructured cellular automata and the application to model river Riparian vegetation dynamics . Lect. Notes Comput. Sci. , 5191 : 337 – 344 .
  • Stevens , D and Dragićević , S . 2007 . A GIS-based irregular cellular automata model of land-use change . Environ. Plan. B: Des. Plan. , 34 : 708 – 724 .
  • Couclelis , H . 1985 . Cellular worlds: A framework for modeling micro-macro dynamics . Environ. Plan. A , 17 : 585 – 596 .
  • Fresnadillo , MJ , García , E , García , JE , Martín , A and Rodríguez , G . 2009 . A SIS epidemiological model based on cellular automata on graphs . Lect. Notes Comput. Sci. , 5518 : 1005 – 1062 .
  • Marr , C and Hütt , MT . 2009 . Outer-totalistic cellular automata on graphs . Phys. Lett. A , 373 : 546 – 549 .
  • Tomita , K , Kurokawa , H and Murata , S . 2002 . Graph automata: Natural expression of self-reproduction . Physica D , 171 : 197 – 210 .
  • von Neumann , J and Burks , AW . 1966 . Theory of Self-Reproducing Automata , Champaign, IL : University of Illinois Press .
  • Deutsch , A and Dormann , S . 2005 . Cellular Automaton Modeling of Biological Pattern Formation: Characterization, Applications, and Analysis , Bonn : Birkhäuser .
  • Ilachinski , A . 2001 . Cellular Automata. A Discrete Universe , London : World Scientific .
  • Wolfram , S . 2002 . A New Kind of Science , Champaign, IL : Wolfram Media .
  • Baetens , JM and De Baets , B . 2011 . On the topological sensitivity of cellular automata . Chaos , 21 Article no. 023108. Available at http://dx.doi.org/10.1063/1.3535581
  • Bagnoli , F , Rechtman , R and Ruffo , S . 1992 . Damage spreading and Lyapunov exponents in cellular automata . Phys. Lett. A , 172 : 34 – 38 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.