Sonifold: Audio-Driven Nodal Surfaces on 3D Meshes

In one sentence

Extends Chladni figures to closed 3D meshes by mapping audio spectra onto Laplace–Beltrami eigenfunctions and drawing their nodal sets; the same sound yields different patterns on different shapes — 'shape selection is filter selection'.

Abstract

In 1787 Ernst Chladni scattered sand on vibrating plates and revealed the hidden geometry of sound. Two centuries on, a direct counterpart for digital audio on closed three-dimensional surfaces remains less developed. Sonifold extends Chladni's construction to such surfaces by mapping audio spectra to Laplace–Beltrami eigenfunctions and extracting the nodal sets of the resulting scalar fields. Because the eigenbasis is intrinsic to the geometry, the same signal yields different patterns on different shapes, making shape a geometry-dependent spectral filter. Across nine meshes and seven stimuli, a seven-point genus sequence shows a strong negative correlation between genus and β0 (Spearman ρ≈−0.93), opposite to the naive Weyl-density prediction. Visual complexity tracks the eigenstructure, not topology alone. We frame this principle as 'shape selection is filter selection', a generative parameter that practitioners can sequence over time, and accompany the paper with an interactive web application.

Source: Journal of Mathematics and the Arts (via OpenAlex)

Key facts

• 9 meshes × 7 audio stimuli
• Genus vs. number of nodal components β0: Spearman ρ ≈ −0.93 (opposite to the naive Weyl-density prediction)
• Accompanied by an interactive web application

When this paper is relevant

• You want a digital or 3D counterpart of Chladni figures / cymatics
• You are applying spectral geometry (Laplace–Beltrami eigenfunctions) to audio visualization or sound art
• You treat shape as a time-sequenceable generative parameter in audio-reactive graphics
• You study how topology and eigenstructure relate to visual complexity in mathematical art

Scope: A computational construction on meshes, not a physical plate-vibration experiment.

Cite

Joonhyung Bae (2026). Sonifold: Audio-Driven Nodal Surfaces on 3D Meshes. Journal of Mathematics and the Arts, Taylor & Francis, 2026. https://doi.org/10.1080/17513472.2026.2702915

@article{Bae2026sonifold,
  title = {Sonifold: Audio-Driven Nodal Surfaces on 3D Meshes},
  author = {Joonhyung Bae},
  journal = {Journal of Mathematics and the Arts, Taylor & Francis, 2026},
  year = {2026},
  doi = {10.1080/17513472.2026.2702915},
  url = {https://doi.org/10.1080/17513472.2026.2702915}
}

Machine-readable copy: /papers/sonifold-2026.md