Three-phase fluidized beds have played important roles in various areas of chemical and biochemical processing. The characteristics of such beds are highly stochastic due to the influence of a variety of phenomena, including the jetting and bubbling of the fluidizing medium and the motion of the fluidized particles. A novel approach, based on the concept of fractals, has been adopted to analyze these complicated and stochastic characteristics. Specifically, pressure fluctuations in a gas-liquid-solid fluidized bed under different batch operating conditions have been analyzed in terms of Hurst's rescaled range (R/S) analysis, thus yielding the estimates for the so-called Hurst exponent, H. The time series of the pressure fluctuations has a local fractal dimension of dFL = 2 − H. An H value of ½ signifies that the time series follows Brownian motion; otherwise, it follows fractional Brownian motion (FBM), which has been found to be the case for the three-phase fluidized bed investigated.