Vibrating Plate Resonance: Chladni Patterns (2D)

This 2D companion computes the same rectangular-plate modal physics as the 3D version through a plain top-down canvas: every eigenmode up to order 7×7 is driven simultaneously as a damped forced oscillator at the chosen frequency, summed into a true complex-amplitude field, and rendered both as a live displacement heatmap and as sand grains that gradient-descend the field's stationary-node envelope — the actual locus where a real Chladni plate's sand would settle. Frequency, plate aspect ratio, material stiffness and damping are all independently adjustable and each visibly reshapes which mode dominates and how sharp its nodal lines are.