Significant progress has been made in understanding the interaction between mineral precursors and organic components leading to material formation and structuring in biomineralizing systems. The mesostructure of biological materials, such as the outer calcitic shell of molluscs, is characterized by many parameters and the question arises as to what extent they all are, or need to be, controlled biologically. Here, we analyse the three-dimensional structure of the calcite-based prismatic layer of Pinna nobilis, the giant Mediterranean fan mussel, using high-resolution synchrotron-based microtomography. We show that the evolution of the layer is statistically self-similar and, remarkably, its morphology and mesostructure can be fully predicted using classical materials science theories for normal grain growth. These findings are a fundamental step in understanding the constraints that dictate the shape of these biogenic minerals and shed light on how biological organisms make use of thermodynamics to generate complex morphologies.