A spherical harmonic , , is a single-valued, continuous, bounded, complex function of the angular coordinates and . They play an important role in quantum mechanics as the eigenfunctions of the angular momentum operators and . Alternatively, the spherical harmonics are a complete basis for the irreducible representations of the infinite rotations group .
Depicting the complex functions would require four dimensions. We can represent, however, the real combinations of spherical harmonics defined as:
The images have been created using tessel , a program that reads in the analytical expressions that define a parametric surface and produces a quadrilateral or triangular mesh of it. The rendering of the surfaces has been done with POV-Ray 2.2.