Spherical Harmonics Yₗᵐ

Visualize components of complex spherical harmonics on the unit sphere; choose degree l and order m.

About this tool

The real and imaginary parts use the standard complex harmonic convention Yₗᵐ(θ, φ), with |m|≤l. Colour represents the selected signed component (or |Y|); the radial deformation always represents amplitude, so phase and size are not confused.

Y₀⁰ is constant and Y₁⁰ is proportional to cos θ. The seam at φ=±π and both poles represent the same directions.