Fractal dimensionality of Brownian motion in two dimensions

Brownian trajectories, obtained from molecular dynamics simulations of twodimensional systems with inverse power-law potentials, exhibit fractal behaviour. The fractal dimensionality D goes to two asymptotically. The approach to the asymptotic value depends on the thermodynamic state of the system. Experiments are proposed to verify our predictions for the behaviour of D. © 1985 The Institute of Physics.