Sierpinski Gasket — Harmonic Analysis

Eigenfunctions of the Laplacian on a fractal
Level 5
Mode 1
Colormap
λ = —
The Laplacian on the Sierpinski gasket has a self-similar spectrum. Eigenvalues cluster in bands with Weyl law N(λ) ~ λds/2, where ds = log5/log3 ≈ 1.465 is the spectral dimension — distinct from the Hausdorff dimension dH = log3/log2 ≈ 1.585.