Chladni Constellation — Chladni Figures mathematical physical art

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Chladni Constellation

Chladni Figures

Sand forming star-like constellations on a vibrating plate. Each grain finds its place in the geometry of sound.

Price

$29.00

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Format Art Print
Size 18 × 24 in
Material Enhanced matte paper · 200gsm · archival · unframed
Resolution 300 DPI · rendered at 5400 × 7200 px
Production Professional print-on-demand · ships from nearest facility
Shipping Most countries · calculated at checkout
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The mathematics

About this system

Chladni figures are the nodal patterns of a vibrating plate, first demonstrated by Ernst Chladni in 1787 by drawing a violin bow across a brass plate covered with sand. The sand migrates to the nodes — the lines where the plate isn't moving — revealing the underlying eigenmode of vibration. Mathematically: Z(x,y) = sin(mπx)·sin(nπy) + sin(nπx)·sin(mπy) for integer mode numbers m, n. This image is the literal level-set rendering of one such eigenmode sum.

In the Chladni Figures collection

When a thin plate is set into vibration at one of its resonant frequencies, sand scattered on its surface migrates to the nodal lines where the plate isn't moving — revealing the underlying vibration mode as a geometric pattern. Ernst Chladni first demonstrated this in 1787 with a violin bow on a brass plate, and the resulting figures helped found the field of acoustics. The mathematics is a sum of trigonometric eigenmodes: Z(x, y) = sin(mπx)·sin(nπy) + sin(nπx)·sin(mπy), where m and n are mode numbers. Each combination produces a distinct mandala. Every image in this collection is a high-resolution evaluation of these eigenmode sums, rendered as continuous fields rather than discrete sand grains.

Z(x,y) = sin(mπx)sin(nπy) + sin(nπx)sin(mπy)