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An algorithmic approach for simulating realistic irregular lattices


  • Juan C. Duque


  • Alejandro Betancourt


  • Freddy Marin



There is a wide variety of computational experiments, or statistical simulations, in which regional scientists require regular and irregular lattices with a predefined number of polygons. While most commercial and free GIS software offer the possibility of generating regular lattices of any size, the generation of instances of irregular lattices is not a straightforward task. The most common strategy in this case is to find a real map that matches as closely as possible the required number of polygons. This practice is usually conducted without considering whether the topological characteristics of the selected map are close to those for an “average” map sampled in different parts of the world. In this paper, we propose an algorithm, RI-Maps, that combines fractal theory, stochastic calculus and computational geometry for simulating realistic irregular lattices with a predefined number of polygons. The irregular lattices generated with RI-Maps have guaranteed consistency in their topological characteristics, which reduces the potential distortions in the computational or statistical results due to an inappropriate selection of the lattices.

Suggested Citation

  • Juan C. Duque & Alejandro Betancourt & Freddy Marin, 2013. "An algorithmic approach for simulating realistic irregular lattices," Documentos de Trabajo CIEF 010937, Universidad EAFIT.
  • Handle: RePEc:col:000122:010937

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    References listed on IDEAS

    1. B N Boots, 1982. "Comments on the use of eigenfunctions to measure structural properties of geographic networks," Environment and Planning A, Pion Ltd, London, vol. 14(8), pages 1063-1072, August.
    2. Anselin, Luc & Bera, Anil K. & Florax, Raymond & Yoon, Mann J., 1996. "Simple diagnostic tests for spatial dependence," Regional Science and Urban Economics, Elsevier, vol. 26(1), pages 77-104, February.
    3. B N Boots, 1982. "Comments on the Use of Eigenfunctions to Measure Structural Properties of Geographic Networks," Environment and Planning A, , vol. 14(8), pages 1063-1072, August.
    4. Anselin, Luc & Moreno, Rosina, 2003. "Properties of tests for spatial error components," Regional Science and Urban Economics, Elsevier, vol. 33(5), pages 595-618, September.
    5. Pace, R. Kelley & LeSage, James P., 2004. "Chebyshev approximation of log-determinants of spatial weight matrices," Computational Statistics & Data Analysis, Elsevier, vol. 45(2), pages 179-196, March.
    6. Smirnov, Oleg & Anselin, Luc, 2001. "Fast maximum likelihood estimation of very large spatial autoregressive models: a characteristic polynomial approach," Computational Statistics & Data Analysis, Elsevier, vol. 35(3), pages 301-319, January.
    7. repec:cai:popine:popu_p1998_10n1_0240 is not listed on IDEAS
    8. Juan Duque & Jared Aldstadt & Ermilson Velasquez & Jose Franco & Alejandro Betancourt, 2011. "A computationally efficient method for delineating irregularly shaped spatial clusters," Journal of Geographical Systems, Springer, vol. 13(4), pages 355-372, December.
    9. Marsaglia, George & Tsang, Wai Wan & Wang, Jingbo, 2003. "Evaluating Kolmogorov's Distribution," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 8(i18).
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    More about this item


    RI-Maps; MR-Polygons; Regional Science; Lattices; Computation; Experiment;

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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