Fractal correlation of initial trajectory dynamics vanishes at the movement end point in human rapid goal-directed movements

Many researchers have investigated the variability of discrete goal-directed movements. However, a possible time-dependent property for them has been ignored. We investigated the time-dependent property of the kinematic variability in human rapid goal-directed movements by using fractal analysis. The variability of the peak acceleration had fractal time correlation characterized by a non-negligible frequency-spectral exponent ( β =0.3). This β value was reduced at the peak velocity ( β =0.2) and nearly reached zero at the peak movement amplitude, indicating that the variability became white noise with no time correlation. A similar result was observed in the progress of the positional trajectory. The functional significance of this phenomenon for the goal-directed task demand is discussed.