Image compression has seen much advancement over the years, with new algorithms and techniques being developed to make image files smaller and easier to transmit and store using both lossy compression methods as well as lossless compression techniques. This paper proposes a lossy fractal image compression method using hexagonal partitioning and domain classification on the quantized image pixels to alleviate the image compression technique's processing complexity. Fractal image compression is a technique for compressing digital images that uses the idea of self-similarity, which is the concept that a pattern can repeat itself at different scales. Our proposed method consists of transforming the spatial domain to frequency domain using discrete cosine transform with quantization and then applying hexagonal partitioning on the square image pixels. A range block is compared with every other classified domain block and the domain block having the least root mean squared (RMS) error is mapped to the range block and replaced with it, storing the original contrast and brightness settings. In this manner, an encoding file is created which stores information of all the mappings, and then the original image is decoded iteratively until the output resembles the original image. To evaluate the performance of the suggested algorithm, numerous simulations are performed.