In the present study, nonlinear hydrodynamic behavior of bubbles and particles in a gas-liquid-solid three-phase reactor is characterized by deterministic chaos analysis in terms of correlation dimension. The embedding method is used to determine correlation dimension from the series of the time intervals between successive optical signals triggered by bubbles or particles. The axial and radial distributions of correlation dimensions are examined and the effect of superficial gas velocity on correlation dimensions for gas and solid phases is investigated. In the bubbly flow regime, with increasing axial position the correlation dimensions for the gas phase increase to reach a maximum and slightly drop at the center of the column. On the other hand, in the churn-turbulent flow regime, the correlation dimension of the gas phase has a minimum at the middle of the column. The correlation dimensions of solid phase are 1-2 lower than those of gas phase, and decrease with axial positions. Uniform radial distributions of both gas and solid phases are observed except near the wall.