Covering fractals with constant radius tiles: Distribution functions and their implications for resource management

The need to optimize and rationally exploit, both fractally distributed natural resources and civil infrastructures, has led us to study the covering of random fractals with circular tiles of a fixed radius. The study has been carried out for different fractal dimensions and radii of the tiles. From the study it is deduced that the fractal mass enclosed by the circular tiles follows a parabolic fractal distribution, which depends only on two parameters. In addition, the distribution parameters have been expressed in terms of fractal dimension and radius of the tiles. Therefore, it is possible to estimate the fractal mass enclosed by the circular tiles of a given radius, once the fractal dimension is known. Consequently, the distribution allows a rational and optimal management of the resources located on the fractal. (c) 2020 Elsevier Ltd. All rights reserved.