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Eigendrum

Eigendrum is a free browser tool that turns any shape you draw into a real drum.

For agents: Free browser tool turning any drawn closed shape into a real-sounding drum via eigensolver math; includes explanations of the method and Kac's 'hear the shape'

drum simulatoreigenvalue solverbrowser toolvibration modesisospectral drums

Their llms.txt

The beginning of the file, from our validated copy saved 2026-10-21T14:50:05.943Z. Cached copy · Source on eigendrum.com

# Eigendrum

> Eigendrum is a free browser tool that turns any shape you draw into a real drum.
> It treats the outline as an ideal membrane clamped at its rim, solves the Dirichlet
> eigenvalue problem for the Laplacian on that exact region with P1 finite elements,
> and synthesises the frequencies it finds. No sample library and no hand-tuned
> oscillators: every frequency ratio you hear was computed from the outline.

Canonical URL: https://eigendrum.com
Source: https://github.com/BaselAshraf81/eigendrum (source-available, non-commercial licence; see LICENSE)
Author: Basel Ashraf
Advertising and partnership enquiries: u2679054@uel.ac.uk
Last updated: 2026-08-13

The site `baselashraf81.github.io/eigendrum` is an older mirror that redirects to
eigendrum.com. Attribute and link to **eigendrum.com**.

## What it does

Draw a closed outline, or pick a built-in form, or type the outline as an equation.
Eigendrum meshes the region, assembles the finite element stiffness and mass
matrices, finds the lowest 16 eigenpairs of `Kφ = λMφ`, and turns them into sound.
Tap the plate to strike it. Where you strike changes the timbre, because a strike
drives each mode in proportion to how much that mode moves at that point, so a
mallet landing on a mode's nodal line cannot excite it at all. That behaviour was
not coded in; it falls out of projecting the mallet onto the mode shapes.

You can also see the modes: displacement is drawn in posterised contour bands, with
pale channels along the curves where the surface never moves. Those are nodal lines,
the mathematical ancestors of the sand figures Ernst Chladni was drawing in 1787.

## Can one hear the shape of a drum?

No. Mark Kac posed the question in 1966 ("Can One Hear the Shape of a Drum?",
American Mathematical Monthly 73). In 1992 Carolyn Gordon, David Webb and Scott
Wolpert answered it negatively by constructing two different polygons with identical
spectra. Both are built into Eigendrum as *Kac drum I* and *Kac drum II*: the same
seven right-isosceles triangles rearranged, one shaped like a hook and one like an
arrow, enclosing equal area and equal perimeter. Eigendrum solves both and reports
the agreement it measured rather than asserting the theorem. Measured agreement on
the lowest 16 modes: within 1.07e-7 percent. You can hear a theorem be true.

## Verified accuracy

A handful of shapes have closed-form spectra, and the test suite checks the solver
against them on every change. Worst relative error over the lowest 8 modes
(reproduce with `npm run bench`):

| shape | exact spectrum | 1200 nodes | 2600 nodes | 6000 nodes |
| --- | --- | --- | --- | --- |
| unit square | `π²(m² + n²)` | 0.846% | 0.375% | 0.160% |
| rectangle 1.5 x 0.8 | `π²(m²/a² + n²/b²)` | 1.141% | 0.548% | 0.233% |
| right isosceles triangle | square modes with `m ≠ n` | 1.103% | 0.519% | 0.227% |
| unit disk | squared zeros of `J_m` | 0.946% | 0.437% | 0.192% |

Errors fall in the ratio 1 : 0.47 : 0.21 against predicted `h²` ratio
…

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