Laplace Equation Solver

Draw boundary conditions — watch ∇²φ = 0 relax to solution

The Laplace equation ∇²φ = 0 describes electrostatic potential, steady-state heat flow, and incompressible fluid streamlines. With Dirichlet boundary conditions (fixed values on the boundary), Gauss-Seidel iteration updates each interior point as the average of its four neighbors: φ(i,j) = ¼[φ(i±1,j)+φ(i,j±1)]. The solution is the unique harmonic function interpolating the boundary data.