This paper presents a new data hiding scheme under fractal image generation via Fourier filtering method for Computer Graphics (CG) applications. The data hiding operations are achieved in the frequency domain and a method similar to QAM used in digital communication is introduced for efficient embedding in order to explore both phase and amplitude components simultaneously. Consequently, this scheme enables us not only to generate a natural terrain surface without loss of fractalness analogous to the conventional scheme, but also to embed larger amounts of data into an image depending on the fractal dimension. This scheme ensures the correct decoding of the embedded data under lossy data compression such as JPEG by controlling the quantization exponent used in the embedding process.