Fractal time in animal behaviour: the movement activity of Drosophila

The organization of episodes of activity and inactivity of Drosophila melanogaster has a complex structure. Episodes of apparently continuous activity have shorter episodes of inactivity embedded within them. This pattern of activity has a self-similar structure; the activity record appears the same regardless of the time scale used. There is a power law dependence of the rate ‘constants’ that describes how the activity of flies turns on and off. As a consequence no natural time scale for the measurement of the activity level exists, and the amount of activity depends on the time scale of measurement. The observation of fractal time variability in animal behaviour may illuminate the processes that produce activity. Fractal time variation in movement activity can lead to Lévy flight patterns of movement, which produce efficient searches.