Applied Spatial Analysis and Policy

, Volume 2, Issue 1, pp 65–83 | Cite as

A Fuzzy Cellular Automata Urban Growth Model (FCAUGM) for the City of Riyadh, Saudi Arabia. Part 1: Model Structure and Validation

  • Khalid Al-Ahmadi
  • Alison Heppenstall
  • Jim Hogg
  • Linda See


Managing and modelling urban growth is a multi-faceted problem. Cities are now recognised as complex systems through which non-linear processes, emergence and self-organisation occur. The design of a system that can handle these complexities is a challenging prospect. This paper presents an urban planning application for the city of Riyadh, Saudi Arabia. At the core of the application is a Fuzzy Cellular Automata Urban Growth Model (FCAUGM) which is generally capable of simulating the complexities of urban growth. The chief components of the model are outlined and quantitative and qualitative methods of validation are described. The results of the validation show that the model is to a large extent successful at replicating the spatial patterns over time for Riyadh although closer examination reveals several minor anomalies which cannot readily be explained. The authors conclude that the model offers significant benefits for simulating urban growth and change, for urban planning and decision-support for policy makers and others, but further research will be necessary on methods of validating and interpreting the detailed results.


Cellular automata Urban growth Riyadh Saudi Arabia Fuzzy logic Fuzzy set theory Satellite remote sensing Sequential remote sensing 


  1. Al-Ahmadi, K., See, L. M., Heppenstall, A. J. & Hogg, J. (2008a). Calibration of a fuzzy cellular automata model of urban dynamics in Saudi Arabia. Ecological Complexity. doi: 10.1016/j.ecocom.2008.09.004.
  2. Al-Ahmadi, K., Heppenstall, A. J., Hogg, J. & See, L. M., (2008b). A Fuzzy Cellular Automata Urban Growth Model (FCAUGM) for the City of Riyadh, Saudi Arabia. Part 2: Scenario Testing. Applied Spatial Analysis and Policy Journal. doi: 10.1007/s12061-008-9019-z.
  3. Allen, P. M. (1997). Cities and regions as self-organizing systems: Models of complexity. Amsterdam: Gordon and Breach Science.Google Scholar
  4. Allen, P., & Sanglier, M. (1981). Urban evolution, self-organization, and decision making. Environment and Planning A, 13, 169–183.CrossRefGoogle Scholar
  5. Almeida, C., Monteiro, A., Camara, G., Soares-Filho, B., Cerqueira, G., Pennachin, C. & Batty, M. (2002). Empiricism and stochastics in cellular automaton modelling of urban land use dynamics. University College London, working paper 42, URL:, [Accessed 2006].
  6. Arriyadh Development Authority (ADA). (2004). Arriyadh metropolitan strategy plan: Part 2 state of the city, background and issues. Riyadh, Saudi Arabia.Google Scholar
  7. Barredo, J., Kasanko, M., McCormick, N., & Lavalle, C. (2003). Modelling dynamic spatial processes: Simulation of urban future scenarios through cellular automata. Landscape and Urban Planning, 64, 145–160.CrossRefGoogle Scholar
  8. Batty, M. (1974). Spatial entropy. Geographical Analysis, 6, 1–31.Google Scholar
  9. Batty, M. (1997). The computable city. International Planning Studies, 2, 155–173.CrossRefGoogle Scholar
  10. Batty, M. (2003) The emergence of cities: Complexity and urban dynamics. Centre for Advanced Spatial Analysis, University Collage London, working paper 64, URL:, [Accessed 2006].
  11. Batty, M. (2005). Cities and complexity: Understanding cities through cellular automata, agent-based models, and fractals. Cambridge: MA: MIT Press.Google Scholar
  12. Batty, M. (2007) Complexity in city systems: Understanding, evolution and design. Centre for Advanced Spatial Analysis, University Collage London, working paper 117, URL:, [Accessed 2007].
  13. Batty, M., & Longley, P. (1989). Urban growth and form: Scaling, fractal geometry and diffusion-limited aggregation. Environment and Planning A, 21, 1447–1472.CrossRefGoogle Scholar
  14. Batty, M., & Xie, Y. (1994). From cells to cities. Environment and Planning B, 21, 531–548.Google Scholar
  15. Benenson, I., & Torrens, P. M. (2004). Geosimulation automata-based modelling of urban phenomena. UK: John Wiley and Sons Ltd.Google Scholar
  16. Benenson, I., Omer, I., & Hatna, E. (2002). Entity-based modelling of urban residential dynamics: The case of Yaffo, Tel Aviv. Environment and Planning B, 29, 491–512.CrossRefGoogle Scholar
  17. Besussi, E., Cecchini, A., & Rinaldi, E. (1998). The diffused city of the Italian north-east: identification of urban dynamics using cellular automata urban models. Computers, Environment and Urban Systems, 22, 497–523.CrossRefGoogle Scholar
  18. Caruso, G., Peeters, D., Cavailhes, J., & Rounsevell, M. (2007). Spatial Configurations in a periurban city. A cellular automata-based microeconomic model. Regional Science and Urban Economics, 37, 542–567.CrossRefGoogle Scholar
  19. Cecchini, A. (1996). Urban modelling by means of cellular automata: generalized urban automata with the help on-line (AUGH) model. Environment and Planning B, 23, 721–732.CrossRefGoogle Scholar
  20. Cheng, J., & Masser, I. (2004). Understanding spatial and temporal process of urban growth: cellular automata modelling. Environment and Planning B, 31, 167–194.CrossRefGoogle Scholar
  21. Clarke, K. C., & Gaydos, L. J. (1998). Loose-coupling a cellular automaton model and GIS: Long-term urban growth prediction for San Francisco and Washington/Baltimore. International Journal of Geographical Information Science, 12, 699–714.CrossRefGoogle Scholar
  22. Clarke, K. C., Hoppen, S., & Gaydos, L. J. (1997). A self-modifying cellular automaton model of historical urbanization in the San Francisco Bay area. Environment and Planning B, 24(2), 247–261.CrossRefGoogle Scholar
  23. Couclelis, H. (1985). Cellular worlds: A framework for modelling micro-macro dynamics. Environment and Planning A, 17, 585–596.CrossRefGoogle Scholar
  24. Couclelis, H. (1997). From cellular automata to urban models: New principles for model development and implementation. Environment and Planning B, 24, l65–174.Google Scholar
  25. Franceschetti, G., Marano, S., Pasquino, N., & Pinto, I. (2000). Model for urban and indoor cellular propagation using percolation theory. Physical Review E, 61, 2228–2231.CrossRefGoogle Scholar
  26. Fritz, S., & See, L. (2005). Comparison of land cover maps using fuzzy agreement. International Journal of Geographical Information Science, 19, 787–807.CrossRefGoogle Scholar
  27. Jantz, C., & Goetz, S. (2005). Analysis of scale dependencies in an urban land-use-change model. International Journal of Geographical Information Science, 19, 271–241.CrossRefGoogle Scholar
  28. Lau, K. H., & Kam, B. H. (2005). A cellular automata model for urban land-use simulation. Environment and Planning B, 32, 247–263.CrossRefGoogle Scholar
  29. Lee, D. R., & Sallee, G. T. (1970). A method of measuring shape. The Geographical Review, 60, 555–563.CrossRefGoogle Scholar
  30. Li, X., & Yeh, A. G. (2000). Modelling sustainable urban development by the integration of constrained cellular automata and GIS. International Journal of Geographical Information Systems, 14, l31–152.Google Scholar
  31. Li, X., & Yeh, A. G. (2001). Calibration of cellular automata by using neural networks for the simulation of complex urban system. Environment and Planning A, 33, 1445–1462.CrossRefGoogle Scholar
  32. Li, X., & Yeh, A. G. (2002). Neural-network based cellular automata for simulating multiple land use changes using GIS. International Journal of Geographical Information Science, 16, 323–343.CrossRefGoogle Scholar
  33. Liu, Y., & Phinn, S. R. (2003). Modelling urban development with cellular automata incorporating fuzzy-set approaches. Computer, Environment and Urban Systems, 27, 637–658.CrossRefGoogle Scholar
  34. Makse, H., Havlin, S., & Stanley, H. (1995). Modelling urban growth patterns. Nature, 377, 608–612.CrossRefGoogle Scholar
  35. Openshaw, S., & Openshaw, C. (1997). Artificial intelligence in geography. New York: Wiley.Google Scholar
  36. Pontius, R., Huffaker, D., & Denman, K. (2004). Useful techniques of validation for spatially explicit land-change model. Ecological Modelling, 179, 445–461.CrossRefGoogle Scholar
  37. Portugali, J. (2000). Self-Organization and the city. Berlin: Springer-Verlag.Google Scholar
  38. Rykiel, E. J. (1996). Testing ecological models: The meaning of validation. Ecological Modelling, 90, 229–244.CrossRefGoogle Scholar
  39. Soares-Filho, B., Coutinho-Cerqueira, G., & Lopes-Pennachin, C. (2002). DINAMICA— stochastic cellular automata model designed to simulate the landscape dynamics in an Amazonian colonization frontier. Ecological Modelling, 154, 217–235.CrossRefGoogle Scholar
  40. Sun, Z. (2005). LEAM: Extended cellular automata model of urban land-use change. In the Proceedings of the 8th International Conference on GeoComputation, University of Michigan,USA. URL:, [Accessed 2005].
  41. Tobler, W. (1979). Cellular geography. In S. Gale, & G. Olsson (Eds.), Philosophy in Geography (pp. 379–386). Dordrecht, The Netherlands: Reidel.Google Scholar
  42. Torrens, P. M. (2000a). How cellular models of urban systems work. CASA Centre for Advanced Spatial Analysis, University College London, working paper 28, URL:, [Accessed 2005].
  43. Torrens, P. M. (2000b). How land-use transport models work. Centre for Advanced Spatial Analysis, University College London, working paper 20, URL:, [Accessed 2005].
  44. Torrens, P. M., & Benenson, I. (2005). Geographic automata systems. International Journal of Geographical Information Science, 19, 385–412.CrossRefGoogle Scholar
  45. Torrens, P. M., & O’Sullivan, D. (2001). Cellular automata and urban simulation: Where do we go from here? Environment and Planning B, 28, 163–168.CrossRefGoogle Scholar
  46. Verburg, P. H. (2004). Land use change modelling: Current practice and research priorities. GeoJournal, 61, 309–324.CrossRefGoogle Scholar
  47. Walsh, S. J., Entwisle, B., Rindfuss, R. R., & Page, P. H. (2006). Spatial simulation modelling of land use/land cover change scenarios in northeastern Thailand: A cellular automata approach. Journal of Land Use Science, 1, 5–28.CrossRefGoogle Scholar
  48. Ward, D. P., Murray, A. T., & Phinn, S. R. (2000). A stochastically constrained cellular model of urban growth. Computer, Environment and Urban Systems, 24, 539–558.CrossRefGoogle Scholar
  49. White, R., & Engelen, G. (1993). Cellular automata and fractal urban form: A cellular modelling approach to the evolution of urban land-use. Environment and Planning A, 25, 1175–1199.CrossRefGoogle Scholar
  50. White, R., & Engelen, G. (1997). Cellular automata as the basis of integrated dynamic regional modelling. Environment and Planning B, 24, 235–246.CrossRefGoogle Scholar
  51. White, R., & Engelen, G. (2000). High-resolution integrated modelling of the spatial dynamics of urban and regional systems. Computer, Environment and Urban Systems, 24, 383–400.CrossRefGoogle Scholar
  52. White, R., Engelen, G., & Uljee, I. (1997). The use of constrained cellular automata for high-resolution modelling of urban land-use dynamics. Environment and Planning B, 24, 323–343.CrossRefGoogle Scholar
  53. Wilson, A. G. (1970). Entropy in urban and regional modelling. London: Pion.Google Scholar
  54. Wilson, A. G. (1976). Catastrophe theory and urban modelling: An application to modal choice. Environment and Planning A, 8, 351–356.CrossRefGoogle Scholar
  55. Wilson, A. G. (1981). Catastrophy theory and bifurcation. Berkeley, California: University of California Press.Google Scholar
  56. Wong, D., & Fotheringham, A. (1990). Urban systems as examples of bounded chaos: Exploring the relationship between fractal dimension, rank-size, and rural-to-urban migration. Geografiska Annaler B, Human Geography, 72, 89–99.CrossRefGoogle Scholar
  57. Wolfram, S. (1994). Cellular automata and complexity. MA: Addison-Wesley, Reading.Google Scholar
  58. Wolfram, S. (2002). A new kind of science. London: Champaign, Wolfram Media.Google Scholar
  59. Wu, F., & Webster, C. J. (1998). Simulation of land development through the integration of cellular automata and multi-criteria evaluation. Environment and Planning B, 25, 103–126.CrossRefGoogle Scholar
  60. Wu, F. (1998a). An experiment on the generic polycentricity of urban growth in acellular automatic city. Environment and Planning B, 25, 731–752.CrossRefGoogle Scholar
  61. Wu, F. (1998b). Simulating urban encroachment on rural land with fuzzy-logic-controlled cellular automata in a geographical information system. Journal of Environmental Management, 53, 293–308.CrossRefGoogle Scholar
  62. Wu, F. (1998c). SimLand: A prototype to simulate land conversion through the integrated GIS and CA with AHP-derived transition rules. International Journal of Geographical Information Science, 12, 63–82.CrossRefGoogle Scholar
  63. Wu, F. (2002). Calibration of stochastic cellular automata: The application to rural-urban land conversions. International Journal of Geographical Information Science, 16, 795–818.CrossRefGoogle Scholar
  64. Yeh, A., & Li, X. (2001). Measurement and monitoring of urban sprawl in a rapidly growing region using entropy. Photogrammetric Engineering and Remote Sensing, 67, 83–89.Google Scholar
  65. Ziehr, C. (2005). Fundamental of geography. Education Course, Northeastern State University. URL:,[Accessed 2005].

Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  • Khalid Al-Ahmadi
    • 1
  • Alison Heppenstall
    • 2
  • Jim Hogg
    • 2
  • Linda See
    • 2
  1. 1.The Centre for GISKing Abdulaziz City for Science and TechnologyRiyadhKingdom of Saudi Arabia
  2. 2.School of GeographyUniversity of LeedsLeedsUK

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