Crystal Lattice Phonons (2D)

This 2D companion swaps the 3D version's orbiting camera for a plan view built to make the underlying physics legible: every atom on this grid is a real point mass numerically coupled to its four nearest neighbours by identical springs, integrated frame by frame rather than driven by a canned sine wave. The panel exposes spring stiffness, driving frequency, drive amplitude and damping directly, and a live readout solves the lattice's dispersion relation in real time — reporting the current wavenumber, wavelength, phase velocity and group velocity when the drive frequency sits below the lattice's cutoff, and flagging the wave as evanescent (decaying rather than propagating) the moment you push the frequency slider past that cutoff. A "point pulse" source mode lets you click anywhere on the lattice to launch a radial pulse and watch how the discrete grid's own anisotropy bends a circular wavefront toward a square one as it spreads.