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GPGPU (General Purpose computing on Graphic Processing Unit) systems attract a great deal of attention, which are used for general-purpose computations like numerical calculations as well as graphic processing, but the peak power consumption of the GPU is relatively high. On the other hand, fractal image coding is one of the most prominent compression technologies. It can be also used for industrial applications like image indexing methods and image retrieval methods. In this paper, we implement parallel programs for the fractal image coding algorithms on GPGPU systems by using CUDA (Compute Unified Device Architecture) and discuss the power-aware evaluation of the application. We also consider the availability of the GPU from the point of view of the green computing.