# Sonifold: Audio-Driven Nodal Surfaces on 3D Meshes

- Authors: Joonhyung Bae
- Venue: Journal of Mathematics and the Arts, Taylor & Francis, 2026
- Year: 2026 (Accepted)
- Type: Journal Paper
- DOI: https://doi.org/10.1080/17513472.2026.2702915
- Publisher page: https://www.tandfonline.com/doi/full/10.1080/17513472.2026.2702915
- Keywords: sonification, nodal surfaces, 3D meshes, audio-driven, mathematics and art
- Page: https://joonhyungbae.com/publication/sonifold-2026

## 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'.

클라드니 도형을 3D 메시 위로 확장해, 오디오 스펙트럼을 라플라스–벨트라미 고유함수에 대응시켜 소리의 마디면(nodal surface)을 그린다. 같은 소리도 형태가 다르면 다른 무늬가 나온다 — '형태 선택이 곧 필터 선택'.

## 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 / 클라드니 도형·사이매틱스(cymatics)를 디지털·3D로 재현하려 할 때
- You are applying spectral geometry (Laplace–Beltrami eigenfunctions) to audio visualization or sound art / 스펙트럴 지오메트리(라플라스–벨트라미 고유함수)를 오디오 시각화·사운드 아트에 쓰려 할 때
- You treat shape as a time-sequenceable generative parameter in audio-reactive graphics / 오디오 반응형 생성 그래픽에서 '형태'를 시간에 따라 바꾸는 생성 파라미터로 다루고 싶을 때
- You study how topology and eigenstructure relate to visual complexity in mathematical art / 수학과 예술의 접점(위상·고유구조와 시각적 복잡도의 관계)을 다룰 때

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

## How to 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

```bibtex
@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}
}
```