Simulation based on the 2D wave equation. Note that the wave equation applies equally to fluids (Navier-Stokes), sound and light propagation, and to quantum mechanics.
Bottom graph is a projection of the accumulated square of the amplitude for the waves that reach the bottom line, which should approximate the energy density for a wave or the probability of finding a particle for the Schrödinger equation.
An offscreen buffer has been added to "taper off" any reflections on the walls, which sometimes leads to ghost echoes. To my surprise, there appear to be no easy alternatives that avoid reflections while only modifying countour conditions (i.e. those pesky pixels right near the border).