Heat Equation
Draw a temperature profile (click/drag), then watch it diffuse. u_t = α u_xx
Heat Equation: ∂u/∂t = α ∂²u/∂x²
Any initial profile decomposes into Fourier modes: u(x,t) = Σ aₙ sin(nπx/L) e^(−α(nπ/L)²t). High-frequency modes decay fastest (rate ~ n²) — the equation is a "low-pass filter" in space. The bar chart shows the Fourier coefficients of the current profile.