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Functional Analysis: 3D Eigenfunction Spectrum

3D spectral decomposition: watch a plucked string's initial shape resolve into eigenfunction modes of a self-adjoint operator, each oscillating at its own eigenfrequency, stacked in depth to show the full spectrum at once.

Mathematics3DEasy60 FPS📱 Mobile-adapted⇄ 2D version

Self-adjoint operators are central to functional analysis because their eigenfunctions form an orthogonal basis and their spectral theory governs how systems evolve in time. This simulator decomposes a plucked-string initial shape into the eigenfunctions of −d²/dx², renders each eigenmode as its own ribbon stacked back in depth by frequency index, and evolves every mode forward at its own eigenfrequency n before summing them into the resultant curve at the front. Unlike a flat waveform chart, the depth axis here is the spectrum itself — you can see the whole decomposition and its time evolution simultaneously from any angle.

⚙ Under the hood

Visualize time-evolution of eigenfunctions sin(nx) as oscillating ribbons along a frequency-index depth axis, representing -d^2/dx^2's spectral modes.

functional-analysisspectral theoryeigenfunctions

3D · Three.js / WebGL renderer · 60 FPS target · runs fully client-side, no install