Fractal dimensions of pacing and grip force in drawing and handwriting production

We performed a repeated measures experiment to show that the pacing of a cyclic, ballistic drawing task has a fractal dimension. We also estimated the dimensionality of the force used to grip the drawing implement. Finally, we present an analysis of pediatric data to show that grip force has a fractal dimension in an actual handwriting task. In our experiment, subjects drew circles of varying sizes and at varying rates on a digitizing tablet, using a pen instrumented to measure radial force applied to its barrel. Subjects also drew circles in synchrony with a metronome. We found strong evidence for fractal scaling of both drawing period and grip force in the circle-drawing study. The dimensionality ranged from fractal Gaussian noise (fGn) to fractal Brownian motion, with Hurst coefficients clustering around the value for 1/f noise. When the subjects were required to synchronize their drawing with a metronome, the Hurst coefficient for the drawing period decreased, while the coefficient for grip force did not. This result indicates that independent processes control the variations in pacing and grip force. Grip force in the handwriting study also displayed fractal properties, with Hurst coefficients in the range of correlated fGn. We draw parallels between our handwriting measurements and studies of human gait.