Spatial particle density distribution images in a pipe cross section have been evaluated by means of state transition matrix, which is a parameter indicating the dominant particle density transition patterns among time series images consisting or CT 2-D space and 1-D time. State transition characterizes the transition patterns for positions in a cross section as monotonous transitions, sudden transitions, and extreme value transitions. In a simulation, the real part of the state transition matrix is negative and the imaginary part is zero in the case of monotonous transition. The real part is positive and the imaginary part is zero in the case of extreme value transition. The imaginary part is nonzero in the case of sudden transition. In free-fall particles in a vertical pipe, high, sudden, and extreme value transitions do riot occur because the particle flow rate tit this position is loin, and therefore the probability or collision among particles is also loin. High, sudden, and extreme value transitions occur near the pipe center when the particle flow rate is high, because the probability or collision among particles is high.