Interosseous sutures exhibit highly variable patterns of interdigitation and corrugation. Recent research has identified fundamental molecular mechanisms of suture formation, and computer models have been used to simulate suture morphogenesis. However, the role of bone strain in the development of complex sutures is largely unknown, and measuring suture morphologies beyond the evaluation of fractal dimensions remains a challenge. Here we propose a morphogenetic model of suture formation, which is based on the paradigm of Laplacian interface growth. Computer simulations of suture morphogenesis under various boundary conditions generate a wide variety of synthetic sutural forms. Their morphologies are quantified with a combination of Fourier analysis and principal components analysis, and compared with natural morphological variation in an ontogenetic sample of human interparietal suture lines. Morphometric analyses indicate that natural sutural shapes exhibit a complex distribution in morphospace. The distribution of synthetic sutures closely matches the natural distribution. In both natural and synthetic systems, sutural complexity increases during morphogenesis. Exploration of the parameter space of the simulation system indicates that variation in strain and/or morphogen sensitivity and viscosity of sutural tissue may be key factors in generating the large variability of natural suture complexity.