Computer reconstruction of digital images is an important problem in many areas such as image processing, computer vision, medical imaging, sensor systems, robotics, and many others. A very popular approach in that regard is the use of different kernels for various morphological image processing operations such as dilation, erosion, blurring, sharpening, and so on. In this paper, we extend this idea to the reconstruction of digital fractal images. Our proposal is based on a new affine kernel particularly tailored for fractal images. The kernel computes the difference between the source and the reconstructed fractal images, leading to a difficult nonlinear constrained continuous optimization problem, solved by using a powerful nature-inspired metaheuristics for global optimization called the bat algorithm. An illustrative example is used to analyze the performance of this approach. Our experiments show that the method performs quite well but there is also room for further improvement. We conclude that this approach is promising and that it could be a very useful technique for efficient fractal image reconstruction.