Heart Tube Looping (2D): Elastic-Rod Buckling & Bifurcation

This 2D companion renders embryonic cardiac looping through a genuinely distinct numerical route from its 3D sibling: instead of bending a tube mesh into a closed-form circular arc, it discretizes the heart tube as forty rigid links pinned to the fixed cavity chord and relaxes them, frame by frame, toward a minimum-bending-energy configuration via iterative position-based-dynamics constraints — the buckle emerges from the solver instead of being assigned to it. A second panel plots a live pitchfork bifurcation diagram of loop chirality against the Nodal/Pitx2 left-right bias, making explicit the stochastic symmetry-breaking that the 3D build only narrates: near-zero bias leaves the straight state mechanically unstable, forcing a coin-flip onto one of two stable D-loop/L-loop branches, exactly as real loss-of-function heterotaxy does.