Variations in the fractal dimension of earthquakes have been suggested to be a precursor of a large earthquake. However, the physical characteristics and seismicity are always different along a large fault system, and it is difficult to segment a large fault for further investigating. Therefore, the fractal dimension of earthquakes on a given fault only reflects the average seismic characteristics of the area and may be unrelated to precursory activity. In this paper, the evolution of the temporal generalized fractal dimension (D q) of a seismic cluster within a small fault system associated with the Chiayi earthquake (M L=6.4), Taiwan, is investigated. The earthquakes of this sequence are confined in small source volume and reflect the behavior of the local fault system.Our results show that the D q curve of the background stage is smooth with a low multifractal degree (0.36) and the seismicity is nearly monofractal in the Chiayi region. During the foreshock stage, the seismicity becomes active such that not only the D q curve exhibits greater variability especially for the steep slope of D q curve at q=0 but also the temporal fractal dimension changes from nearly monofractal to multifractal. In the aftershock stage, the fluctuation of D q is large and the multifractal degree is up to 1.0. The temporal multifractal property becomes more pronounced as well. Finally, when the seismicity returns to the background stage, the D q curve becomes smooth and nearly monofractal again. Therefore, the fluctuations in the D q spectrum of an earthquake cluster associated with a large earthquake not only give a clear picture of the temporal alterations in the seismogenic regimes but also illustrate their variability through time for a large earthquake. In addition, the variation of the slope of D q curve at q=0 in the foreshocks may be used as a precursor of a large earthquake.