Physical Mathematics of Embryonic Push/Pull Morphogenesis: A Fractal and Mechanical Framework for Sexual Dimorphism via Ibaguner Fractal Operator (IFO)

The classical view of sexual differentiation emphasizes genetic and hormonal pathways. However, emerging evidence suggests that mechanical forces and fractal morphogenesis may contribute to subtle but measurable differences in tissue architecture between male and female embryos. We propose that: • Male-typical morphogenesis: “Pushing out” — expansive, space-filling growth withpositive mean curvature bias. • Female-typical morphogenesis: “Drawing in” — invaginating, folding growth withnegative mean curvature bias. These differences are not absolute but represent statistical biases in the morphogenetic field, amplified by mechanosensitive feedback loops. This document provides the complete mathematical formalism for detecting and quantifying these differences.