The fractal dimension of the phase space representation of the EEG of 8 clinical patients undergoing general anesthesia is determined. An attempt is made to correlate the trends in EEG dimensional complexity with the depth of anesthesia. While the EEG showed marked changes in dimensional complexity when passing through anesthetic stages, a uniform depth-dimension trend consistent with the eight patients was not observed. The only significant trend observed was a distinct change in dimension for individual EEG's with anesthesia. The dimensional complexities measured were very high and non-convergent, so that the presence of a fractal attractor in the EEG was not evident in this analysis. The observed trends were the close correlation of both brain hemispheres simultaneously exhibiting the same degree of dimensional complexity, and the close correlation of change in EEG spectral edge frequency with change in dimension with anesthesia.