The dimensional complexity or fractal dimension of the EEG recorded at 17 locations from the 10-20 system was studied using a very fast new algorithm. The paper contains 2 parts. First, the influence of several parameters (embedding dimension, delay time, high and low frequency cutoff, ADC precision and sweep length) on the estimation of dimensional complexity is investigated. Then it is shown that patients with Alzheimer's disease (n = 50) have significantly lower dimensional complexity than age-approximated non-demented controls (n = 42).