The turbulent motion of particles in gas-liquid-solid systems has been characterized by the fractal analysis of particle trajectories obtained from direct visualization using a two-dimensional column. It is shown that the particle motion depends strongly upon large-scale turbulent eddies in the bubble wake structure. The fractal dimension of particle trajectories is found to be a maximum at a gas flow rate corresponding to the transition of bubble flow from homogeneous bubbly to churn-turbulent flow regimes.