Due to their all-weather, all-time and penetration characteristics, synthetic aperture radar (SAR) images are frequently used to monitor ground targets. As a result, environmental changes via natural events or human activities can be observed by applying a change detection technique. Theoretically, SAR signals can be characterized as chaotic phenomena since the scattering of signals within a resolution cell can be summed coherently. Accordingly, an SAR signal can be represented by a spatial chaotic model (SCM) and characterized by its fractal dimension. In this study, two approaches for estimating fractal dimensions are conducted, which are estimated by the differential box-counting (DBC) and improved fractal dimension methods in the z-direction. Based on the spatial chaotic model, a simplified SAR image change detection procedure is proposed. This method first calculates the differences in fractal dimensions among multitemporal SAR images to detect the changes in building and grass-recovery areas. Both the constant false alarm rate (CFAR) and support vector machine (SVM) are applied to classify the changed and unchanged areas, respectively. The experimental results reveal that both the DBC and improved fractal dimension methods are similar for detecting changes in building areas. However, regarding the changes in grass recovery areas, the improved fractal dimension method outperforms the DBC method. The results also show that the SVM performs better than the CFAR for both building and grass areas.