The bubble column hydrodynamics are complex and the macroscopic flow structure is different in the column core and annulus due to both the bubble coalescence and breakup phenomena as well as the gross liquid circulation. In this work, for the first time the local Kolmogorov entropy (KE) minima at different superficial gas velocities U_g were identified. It was found that there is an agreement between the local KE minima (occurring around r/R = 0.63) and the inversion point (dimensionless radius = 0.7) for the axial liquid velocity reported by both Chen et al. (1994) and Wu and Al-Dahhan (2001). The KE radial profiles were also used to prove the existence of chaotic similarities between the flow patterns in the bubble bed at three different U_g values (0.089, 0.134 and 0.146 m/s) belonging to the heterogeneous regime. This finding implies that the flow patterns and the degrees of turbulence at these U_g values are also identical. The same similarity was also found between the KE profiles at U_g = 0.056 and 0.067 m/s, which belong to the transition flow regime. These results imply that the flow patterns in the bubble bed repeat (especially at different U_g values falling into the same flow regime). Based on the KE profiles as a function of U_g, the effect of the dimensionless radial position on the various transition velocities was studied. It was found that the end of the gas maldistribution regime is shifted to slightly higher U_g value in column core and annulus. In most of the cases, the onset of the churn-turbulent regime occurs at U_g = 0.101 m/s.