Activities of daily living require maintaining upright posture within a variety of environmental constraints. A healthy postural control system can adapt to different environmental constraints. Afferent sensory information is used to determine where the body is in relation to the gravitational vertical and efferent motor commands make corrections with the goal of keeping the center of mass within the base of support. The purpose of this research was to understand how vision, direction of translation, and the temporal correlation of the support surface stimuli affected the persistence characteristics of postural dynamics on short and long time scales. Ten healthy young adults performed a standing task with either eyes open or closed, oriented anteriorly or mediolaterally while the support surface underwent structured translations based on different levels of temporal correlation-white noise (no correlation), pink noise (moderate correlation), and red noise and sinusoidal movements (strong correlations). Center of pressure velocity was analyzed using fractal analysis to determine the dynamics of postural control. On the short time scale, persistence was shown to be stronger with eyes closed, in the mediolateral direction, and when the structure of translation contained stronger temporal correlation. On the long time scale, anti-persistence was stronger with eyes closed, in the mediolateral direction, and for all structures of movement except red noise. This study provides deeper insight into the flexibility existing in human movement responses to structured environmental stimuli through the fractal analysis of movement variability.