Fractal dimension of time-indexed paths

摘要

Measuring animal track or other trajectories (for example, the track of a flowing particle) by divider method to obtain the fractal dimension without knowing the chronology of the points of the path, one can obtain erroneous results. The importance of time-indexing of the track’s point will be demonstrated by a simply geometrical example. Neglecting these indices, the error can be high enough to mask relevant differences between various movement paths.