In this study we examine the dynamic characteristics of the center of pressure (COP) profiles in quiet stance on various carpets through the framework of fractional Brownian motion. Four different carpets plus the force platform (which served as a control floor) were tested. Six healthy young subjects stood stationary in bare feet on each flooring condition under both eyes-open (EO) and eyes-closed (EC) conditions. A stabilogram diffusion analysis (SDA) was conducted in both anteroposterior and mediolateral directions to extract the dynamic features of the COP profiles. Two approximately linear regions (short-versus long-term regions) were found for all of the flooring conditions in the double logarithmic plot of the mean-square displacements versus time intervals, implying that a two-stage control scheme exists in regulating the posture. In general, a more compliant carpet was found to be associated with a shorter transitional time interval and a lower HL value (Hurst coefficient in the long-term region) under the EO condition, but to be correlated with a higher HS (Hurst coefficient in the short-term region) and a higher HL under the EC condition. While the hard floor of the force platform significantly decreased HL from the EO to the EC conditions, the alteration of visual environments did not substantially influence HL for a compliant carpet.