STUDY #03 · 2026 · IN OBSERVATION

Chladni Figures

A visual study of standing waves drawn by sand.

MOVING IMAGE — ORBIT CUT drive point in slow orbit · Ω kicks · Faraday burst

WHAT IS THIS

Scatter sand on a metal plate and make it vibrate, and the grains flee the places that move — the antinodes — and gather where the plate stays still: the nodal lines. The plate's eigenmodes appear, drawn not by a formula but by matter organising itself. Ernst Chladni demonstrated this in 1787.

This study drives a plate model across its resonances and lets a cloud of simulated grains settle. Between clean resonances live nameless figures — blends of several modes — and the drive point, set off-centre, decides how symmetric the pattern becomes. The lines you see are simply where the grains stopped moving.

disc — eclipse disc · Ω 2.5 · γ 0.8 · p (0.36, 0.47)

Motif Plate-vibration eigenmodes / nodal lines / self-organisation of sand

Method A plate-vibration model was generated with AI assistance and ported to a real-time GPU (GLSL) renderer; simulated grains accumulate on the nodal lines. Figures were selected through a sweep of drive frequency and excitation point.

Observation Off-centre driving is the third creative axis: a centred drive excites only concentric rings, while eccentric driving turns the figures asymmetric and baroque. Discs give instrument-like mandalas; squares give architectural lattices.

Reference E. F. F. Chladni, "Entdeckungen über die Theorie des Klanges," Weidmanns Erben und Reich, Leipzig (1787).

Tools Python / NumPy / SciPy / three.js / GLSL / ffmpeg / AI coding assistant

Year 2026

This is not a scientific simulation result, but a visual interpretation of the phenomenon.

PARAMETERS EXPLORED

param meaning effect on the image

Ω drive frequency which modes resonate; on a resonance you get a textbook figure, between them a nameless blend

drive point excitation position off-centre driving breaks symmetry and excites degenerate mode pairs unequally

γ damping how sharply modes blend; ≈0.6–1.0 keeps the classical figure legible, higher dissolves it

drift grain lock-in how tightly grains settle to the nodes — from a soft dusty halo to hair-thin lines

Each image below records its exact parameter set.

THE MATHEMATICS the model behind the images

Behind the sand: the vibration eigenmodes of a thin plate (the biharmonic ∇⁴ eigenvalue problem). A drive frequency Ω blends the modes; the sand collects where the surface barely moves.

\varphi_{mn}(x,y) = \cos(m\pi x)\,\cos(n\pi y)

A square-plate eigenmode. The nodal lines, where φ = 0, are the still curves the sand settles onto.

W(x,y;\,\Omega,p) = \sum_k \frac{\varphi_k(p)}{\sqrt{(\omega_k^2 - \Omega^2)^2 + (\gamma\Omega)^2}}\;\varphi_k(x,y)

The plate’s response to a drive at frequency Ω applied at point p — a Lorentzian resonance blend of the modes. On resonance a textbook figure; between resonances, a figure with no name.

\mathbf{x}_i \;\leftarrow\; \mathbf{x}_i + \sigma\,\lvert W(\mathbf{x}_i)\rvert^{\alpha}\,\boldsymbol{\xi},\qquad \boldsymbol{\xi}\sim\mathcal{N}(0,1)^2

The sand itself: each grain jitters in proportion to the local amplitude |W|, drifting off the antinodes and stranding on the nodal lines.

Inspired by plate-vibration eigenmodes; the sand is a self-organising particle process, not an exact modal reconstruction.

SELECTED STILLS — 6

disc · nameless figure disc · Ω 13.5 · between resonances

disc · annular mandala disc · Ω 19 · γ 0.8

square · diamond lattice square · Ω 16 · γ 0.6

disc · walled cells disc · Ω 13.7 · γ 2.15 · edge drive

MOTION STUDIES

Chladni figures are made of movement — the sand only settles once the plate stops asking it to move. A few short studies of that settling.

settle — scattered grains find the nodal lines disc · Ω 19 · 780 steps

faraday burst — the powder rule inverted, then restored Ω 19 · Faraday 1831

breathing — a slow orbiting drive r 0.035 · Ω 2.5

PROCESS — PARAMETER SWEEPS

A tour of the drive frequency on an eccentric disc — the figure tightening from an off-centre eclipse to a ringed mandala as Ω rises.

A drive-frequency tour — eccentric disc Ω low→high · γ 0.8 · sand

COLOUR / FORM = REAL PHYSICS

Colour here is grounded the same way as the earlier studies — in the real materials. Classic Chladni is a black steel plate with white quartz sand; the contrast is the figure.

Swap the powder and the figure inverts. Fine, light lycopodium spores are carried by the plate's air currents to the antinodes instead — the same plate and tone yield the negative image (Faraday, 1831). The plate opposite is exactly that: brass with lycopodium, the pollen clouds glowing at the antinodes where quartz sand would leave darkness.

The hero palette — navy plate ⇄ gold sand, weaver — is the house colourway. All colours are artistic choices grounded in real plate-and-powder pairings, not measurements.

brass × lycopodium — Faraday inversion square · (2,5)⁻ pair · antinodal clouds

Same standing wave, different powder — nodal sand (quartz) vs antinodal dust (lycopodium).

REFERENCES

E. F. F. Chladni. "Entdeckungen über die Theorie des Klanges." Weidmanns Erben und Reich, Leipzig (1787).
W. Ritz. "Theorie der Transversalschwingungen einer quadratischen Platte mit freien Rändern." Annalen der Physik, vol.28, 737-786 (1909).

INTERACTIVE STUDY

A small window into the model behind this study — a deliberately simplified instrument, reduced in resolution, scope, and rendering. The finished works above are something else entirely: hundreds of thousands of simulated grains, settled and graded by hand. Here the standing wave answers instantly — sweep the frequency and watch the figure pass through nameless in-between states.

SIMPLIFIED INSTRUMENTPLATE MODES — DRIVE BLEND · SQUARE

This interactive study is not intended as a scientifically validated reproduction. It is a visual interpretation generated from an implemented model and curated parameter exploration — and it is a deliberately simplified instrument, separate from the full engine used to author the finished works.