Lattice Gauge Theory 2D: Wilson Loop Area Law

This is the same compact U(1) lattice gauge theory as the 3D plaquette explorer, rebuilt as a genuinely 2D-native diagram instead of a rendered 3D scene. Link phases and plaquette flux are drawn directly as a top-down vector field and heatmap, and instead of reading a single noisy Wilson loop snapshot, the simulator accumulates ensemble averages ⟨W(R)⟩ for every loop size up to R_max and fits ln W(R) against loop area R² live. The slope of that fit is the confinement string tension σ — in 2D the area law is exact, W(R,R) = (I₁(β)/I₀(β))^R², so you can watch the Monte Carlo estimate converge to the analytic answer sweep by sweep.