In this study, we created metamaterials consisting of square unit cells—inspired by fractal geometry—and described the parametric equation necessary for their creation. The area and thus the volume (density) and mass of these metamaterials are constant regardless of the number of cells. They were created with two layout types; one consists solely of compressed rod elements (ordered layout), and in the other layout, due to a geometrical offset, certain regions are exposed to bending (offset layout). In addition to creating new metamaterial structures, our aim was to study their energy absorption and failure. Finite element analysis was performed on their expected behavior and deformation when subjected to compression. Specimens were printed from polyamide with additive technology in order to compare and validate the results of the FEM simulations with real compression tests. Based on these results, increasing the number of cells results in a more stable behavior and increased load-bearing capacity. Furthermore, by increasing the number of cells from 4 to 36, the energy absorption capability doubles; however, further increase does not significantly change this capability. As for the effect of layout, the offset structures are 27% softer, on average, but exhibit a more stable deformation behavior.