An experimental study of the solid phase dynamics in a three-phase fluidized bed reactor using heavy and light particles is carried out. A radioactive particle tracking technique is employed to obtain extended time series of the tracer path. The tracer has the same properties as the rest of the particles in the bed. A rescaled range-analysis is applied to time series of the fluctuating velocities to investigate the features of solid phase turbulence. It is found that turbulence is anisotropic. In the axial direction, the correlations between the fluctuating velocities are persistent in time, indicating a superdispersive axial dispersion of the solids. Hence a constant axial dispersion coefficient, which is traditionally used in these reactors to represent the solid phase turbulence, only constitutes a lumped parameter hardly extrapolable to different operating conditions, different systems, and different geometries. The tracer path is also analyzed according to the theory of deterministic chaos. It is found that the solids motion is chaotic. An increase in the gas flow rate increases the values of the parameters that quantify the chaotic behavior of the solids motion. This analysis is found to constitute a promising tool to determine flow regime transitions.