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Abstract Across mammalia, brain morphology follows specific scaling patterns. Bigger bodies have bigger brains, with surface area outpacing volume growth, resulting in increased foldedness. We have recently studied scaling rules of cortical thickness, both local and global, finding that the cortical thickness difference between thick gyri and thin sulci also increases with brain size and foldedness. Here, we investigate early brain development in humans, using subjects from the Developing Human Connectome Project, scanned shortly after pre-term or full-term birth, yielding magnetic resonance images of the brain from 29 to 43 postmenstrual weeks. While the global cortical thickness does not change significantly during this development period, its distribution does, with sulci thinning, while gyri thickening. By comparing our results with our recent work on humans and 11 non-human primate species, we also compare the trajectories of primate evolution with human development, noticing that the 2 trends are distinct for volume, surface area, cortical thickness, and gyrification index. Finally, we introduce the global shape index as a proxy for gyrification index; while correlating very strongly with gyrification index, it offers the advantage of being calculated only from local quantities without generating a convex hull or alpha surface.