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Fractal dimension is useful to characterize the structure of spatial objects such as urban structures or river networks. However, fractal analysis is underutilized for point processes. This study aims at suggesting a method to generate fractal point processes. The procedure consists in a reverse box-counting method that is quite efficient since the relative error between the theoretical and produced fractal dimensions does not exceed 2% when the structure of the object is quite small. Beyond its goal to create point processes, this method provides also a way to explore the relationship between the fractal dimension and the classical methods of spatial analysis in geography.