Although there is an extensive literature on the study of the neural correlates of consciousness (NCC) this is a subject that is far from being considered over. In this paper we present a novel experimental paradigm, based on binocular rivalry, to study internally and externally generated conscious experiences. We called this procedure bimodal rivalry. In addition, and assuming the non-linear nature of the EEG signals, we propose the use of fractal dimension to characterize the complexity of the EEG signal associated with each percept. Analysis of the data showed a significant difference in complexity between the internally generated and externally generated percepts. Moreover, EEG complexity was dissimilar for externally generated auditory and visual percepts. These results support fractal dimension analyses as a new tool to characterize conscious perception.