The most effective way of preventing motor vehicle accidents caused by drowsy driving is through a better understanding of drowsiness itself. Prior research on the detection of symptoms of drowsy driving has offered insights on providing drivers with advance warning of an elevated risk of crash. The present study measured back and sitting pressures during a simulated driving task under both high and low arousal conditions. Fluctuation of time series of center of pressure (COP) movement of back and sitting pressure was observed to possess a fractal property. The fractal dimensions were calculated to compare the high and low arousal conditions. The results showed that under low arousal (the drowsiness state) the fractal dimension was significantly lower than what was calculated with high arousal. Accumulated drowsiness thus contributed to the loss of self-similarity and unpredictability of time series of back and sitting pressure measurement. Drowsiness further reduces the complexity of the posture control system as viewed from back and sitting pressure. Thus, fractal dimension is a necessary and sufficient condition of a decreased arousal level. It further is a necessary condition for detecting the interval or point in time with high risk of crash.