Spherical Harmonics

Y_l^m as Surface Deformations + Resonant Audio
Y_l^m deformed sphere (rotate drag)
|Y_l^m(θ,φ)| polar map
ℓ (degree)
2
m (order)
1
deform scale
0.40
rotation speed
0.01
Y₂¹(θ,φ) = −½√(15/2π) sin(θ)cos(θ)e^{iφ}
Spherical harmonics Y_ℓ^m(θ,φ) are eigenfunctions of the spherical Laplacian: ΔY = −ℓ(ℓ+1)Y.
They form an orthonormal basis for L²(S²). The deformed sphere shows r = 1 + s·|Y_ℓ^m|.
Audio tone: frequency ∝ √(ℓ(ℓ+1)), like quantum energy levels on a sphere.