This application visualizes the complex function - spherical harmonics:
\[ Y_{lm}(\theta, \phi) = \sqrt{\frac{2l+1}{4\pi} \frac{(l-m)!}{(l+m)!}} P_l^m(\cos{\theta}) e^{im\phi} \]where \( P_l^m \) is the associated Legendre function.
The function is plotted in spherical coordinates:
\[ \left\{ \begin{array}{l} r \leftarrow |Y_{lm}| \\ \theta \leftarrow \theta \\ \phi \leftarrow \phi \end{array} \right. \]The \(r\) component can only represent the modulus of a complex number. Its phase is represented by color.