The heat/diffusion equation ∂u/∂t = D ∇²u has a fundamental solution G(x,t) = (4πDt)^(-1/2) exp(-x²/4Dt) — a Gaussian that spreads as σ = √(2Dt). The width grows as t^(1/2), the peak falls as t^(-1/2), and the total integral is conserved (probability). Multiple initial conditions are shown simultaneously.