The box-counting (BC) algorithm is one of the most popular methods for calculating the fractal dimension (FD) of binary data. FD analysis has many important applications in the biomedical field, such as cancer detection from 2D computer axial tomography images, Alzheimer's disease diagnosis from magnetic resonance 3D volumetric data, and consciousness states characterization based on 4D data extracted from electroencephalography (EEG) signals, among many others. Currently, these kind of applications use data whose size and amount can be very large, with high computation times needed to calculate the BC of the whole datasets. Fast Box-Counting software is a very efficient parallel implementation of the BC algorithm for its execution on Graphics Processing Units (GPU) using the CUDA technology. This software can process 2D, 3D, and 4D data and has been tested on several platforms with different hardware configurations. Fast Box-Counting can achieve speedups of up to 92.38x (2D), 57.27 (3D) and 75.73x (4D) with respect to the corresponding CPU single.thread implementations of the box-counting algorithm. Against an OpenMP multihread CPU implementation, Fast Box-Counting can achieve speedups of up to 16.12x (2D), 6.86x (3D) and 7.49x(4D). Compared to previous GPU implementation of the BC algorithm in 3D, Fast Box-Counting can achieve speedups of up to 4.79x.