I agree with you. There are other methods  to solve the problem, but we choose box counting methods because it is easy and rapidly. That project was a first project for my students. I sent for them your sugestion and they are already studying.

Thanks

Thank you!

This is an important question.    In addition to the helpful answer given by @Maria Helena Rodrigues Gomes, there is a bit more to add.

A good introduction to the fractal dimension of a line is given in

https://www.researchgate.net/profile/Lexing_Xie/publication/221571569_Physics-motivated_features_for_distinguishing_photographic_images_and_computer_graphics/links/0c96052cff5ec17edd000000.pdf

See Figure 2.   Local fractal geometry is nicely introduced in Section 6.

See also:

https://www.researchgate.net/publication/262329476_Fractal_Estimation_Using_Extended_Triangularisation_and_Box_Counting_Algorithm_for_any_Geo-Referenced_Point_Data_in_GIS/figures?lo=1

Conference Paper Physics-motivated features for distinguishing photographic i...

Article Fractal Estimation Using Extended Triangularisation and Box ...

Thank you! I will read the papers.

In the meantime I found this reference:

A procedure to Estimate the Fractal Dimension of Wave

https://arxiv.org/abs/1003.5266forms

Thanks. More later. Rudi