Functional Magnetic Resonance Imaging (fMRI) is a powerful non-invasive tool for localizing and analyzing brain activity. This study focuses on one very important aspect of the functional properties of human brain, specifically the estimation of the level of parallelism when performing complex cognitive tasks. Using fMRI as the main modality, the human brain activity is investigated through a purely data-driven signal processing and dimensionality analysis approach. Specifically, the fMRI signal is treated as a multi-dimensional data space and its intrinsic ‘complexity’ is studied via dataset fractal analysis and blind-source separation (BSS) methods. One simulated and two real fMRI datasets are used in combination with Independent Component Analysis (ICA) and fractal analysis for estimating the intrinsic (true) dimensionality, in order to provide data-driven experimental evidence on the number of independent brain processes that run in parallel when visual or visuomotor tasks are performed. Although this number is can not be defined as a strict threshold but rather as a continuous range, when a specific activation level is defined, a corresponding number of parallel processes or the casual equivalent of ‘cpu cores’ can be detected in normal human brain activity.