Box-Counting Fractal Dimensions of Cranial Suture: Effects of Measurement Conditions and Model-Based Reproduction of Fractal-Like Patterns

1Cranial sutures are important structures associated with skull growth, and it is widely known that the cranial sutures have a fractal nature. However, the measurement conditions and analytical procedures have varied among studies, making direct comparison and interpretation difficult. In addition, the mechanisms by which such fractal-like patterns arise remain incompletely understood. In this study, we established and validated a standardized box-counting protocol for quantifying the fractal dimension (FD) of cranial sutures. Using this protocol, we quantified FD in 45 digitized images of human lambda sutures and in eight structure-formation model variants designed to generate fractal-like patterns via distinct kernel designs (step, Gaussian, Mexican-hat, and time-dependent/dual-stage), spatially inhomogeneous inhibition (Fbase), low-frequency noise, and different initial conditions (including sine-curve initialization). We show that FD estimates are strongly affected by preprocessing (including skeletonization) and the selected scale range, explaining discrepancies across previous studies. Crucially, under the matched preprocessing and scale-range criteria, three of the eight model variants reproduce the FD of real sutures within predefined equivalence margins, supporting the notion that appropriate dynamics can produce the observed fractal-like suture behavior and providing testable hypotheses for how such patterns may emerge.