Ricci flow deforms a Riemannian metric proportionally to the Ricci curvature tensor: ∂gij/∂t = −2Rij.
Regions of positive curvature shrink while negatively-curved regions expand, smoothing the geometry.
Hamilton (1982) introduced the flow; Perelman (2003) used it with surgery to prove the Geometrization Conjecture (and Poincaré Conjecture).
This visualization shows a 2D cross-section profile evolving: the radial function r(θ,t) is updated by approximating mean curvature flow,
which in 2D is equivalent to Ricci flow on surfaces. Watch the irregular bumps smooth into a round circle.