Ricci Flow and Curvature from Christoffel Symbols

This visualization gives a geometric feel for the Ricci flow equation $\partial_t g_{ij} = -2 R_{ij}$. We interpret a 2D surface whose metric is encoded by a deforming grid. The Christoffel symbols $\Gamma^k_{ij}$ twist and bend the grid lines; their combinations determine the Ricci tensor $R_{ij}$. The flow $-2 R_{ij}$ drives the metric to smooth out curvature: regions of positive curvature contract, and negatively curved directions stretch. Use the controls to adjust how strongly curvature acts, how much time has passed, and how we visualize the connection-like twisting of the grid.