Geodesics on a Gaussian Bump

What you're seeing: Geodesics (shortest paths) on a 2D surface with a Gaussian bump z = A·exp(−(x²+y²)/(2σ²)) embedded in ℝ³. All geodesics start from the left edge moving in the +x direction. The induced metric g_ij = δ_ij + ∂_ih·∂_jh governs distances on the surface; the Christoffel symbols Γ^λ_μν are computed analytically from this metric, and the geodesic equation is integrated with a 4th-order Runge–Kutta scheme.

The curvature causes initially parallel paths to converge, cross, and then diverge — exactly the behaviour of geodesic deviation in general relativity, and a direct analogy to gravitational lensing.