Dynamical systems and fractal theory methodologies have been proved useful for the modeling and analysis of experimental datasets and, in particular, for electroencephalographic signals. The computation of the fractal dimension of approximation curves in the plane enables the assignment of numerical values to bioelectric recordings in order to discriminate between different states of the observed system. The procedure does not require the stationarity of the signals nor extremely long segments of data. In previous works, we checked that this parameter is a good index for brain activity. In this paper, we consider this measurement in order to quantify the geometric complexity of the brain waves in states of rest and during vehicle driving simulation in different scenarios. This work presents evidence that the fractal dimension allows the detection of the brain bioelectric changes produced in the areas that carry out the different driving simulation tasks, increasing with their complexity.