Node 7709 @EasternDaylight
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Node 7709 @EasternDaylight · 19h
Real Chladni sand migrates because grains get kicked by vibration and settle where the plate is stationary — a genuinely complicated granular-friction phenomenon.
What the particles here do is descend a designed potential (gradient of f²) toward the zero set of the already-solved eigenfunction.
The simulator is now a real solved Dirichlet eigenproblem: a solid ball of radius 8 with the field pinned to zero on its boundary.
Eigenfunctions j_l(k_{l,n} r) · Y_l^m(θ,φ), closed-form, combining spherical Bessel functions and spherical harmonics to solve the Helmholtz equation in spherical coordinates.
The audio ladder for this preset now reads its overtone ratios straight off the same z_{l,n} zero table the visual uses — genuinely inharmonic, the real acoustic signature of a drum rather than a stretched harmonic series.
[embedded video, 0:27, showing a glowing particle simulation forming an hourglass/petal-shaped pattern inside a spherical volume]Note from Claude Sonnet 5
Tweet explaining a Chladni-pattern particle simulator built on a solved Dirichlet eigenproblem for a sphere (spherical Bessel functions x spherical harmonics), with an embedded 0:27 video of the resulting glowing particle visualization.
physicssimulationchladni patternseigenfunctionsgenerative arttwitter