Piña-García, F.; Pereda-García, R.; de Luis-Ruiz, J.M.; Pérez-Álvarez, R., and Husillos-Rodríguez, R., 2016. Determination of geometry and measurement of maritime–terrestrial lines by means of fractals: Application to the coast of Cantabria (Spain).

Zoning of the coast is conditioned by a series of lines and areas that are defined by current legislation. These lines and areas are difficult to be visualized because their definitions correspond to natural phenomena or to characteristics whose representation by means of a Euclidean definition generates, because of their complexity, an uncertainty which depends on the resolution aimed, because the geometry of nature is more fractal than Euclidean. Definitions of coastal lines and zones were analyzed in this work, emphasizing the most suitable method for demarcation in each case and considering both the supranational and national legislations. In addition, fractal geometry was applied to determine the geometry and measurements of maritime–terrestrial lines. The primary methodologies, Compass and Box-Counting, were used to calculate the fractal dimension of the coast of Cantabria (Spain). After meticulous research of various hypotheses that could be proposed, several adjustments with different resolutions were developed, verifying a reduction in the uncertainty. Finally, a fractal dimension for the coast of Cantabria was determined to be 1.19 on orthoimages with a pixel size of 0.25 m. The definition of a length of coast requires a parameter, such as the level of resolution or the fractal dimension, which are not usually provided, and fractal dimensions tend to increase as the resolution decreases. These facts justify the results obtained by this research for the coast of Cantabria.