An algorithmic approach for simulating realistic irregular lattices

Working papers de economía (2013) ,Volume 1 ,Pages 1-25

Abstract

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.

Datasets

100 RI-Maps with 81 areas
100 RI-Maps with 100 areas
100 RI-Maps with 400 areas
100 RI-Maps with 900 areas
100 RI-Maps with 1600 areas
100 RI-Maps with 2500 areas
100 RI-Maps with 3600 areas
100 RI-Maps with 81, 100, 400, 900, 1600, 2500, and 3600 areas

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