The human body involves the complex interaction between many feedback systems. This is certainly indicative that we are basically a nonlinear organism. Recent developments in the understanding of nonlinear systems suggest that fractal (power law) relationships may be the rule, not the exception. In this article it is shown that the performance of male and female superior athletes exhibits a fractal relationship between world record running and swimming times and the distance of the event. Furthermore, the precision of this relationship is so accurate that the small deviations exhibited by data from a fractal fit might be explained using the dominant interplay between aerobic and anaerobic energy expenditure.