Which spherical harmonic function will correspond to such a representation?

Question

On Wiki there's a figure displaying "visual representations of the first few spherical harmonics."

I was wondering exactly which spherical harmonic function will generate a representation like this (red means positive, green means negative; I don't have sufficient reputation for posting images, sorry for the inconvenience :P).

Thanks!

Answer 1

The rotating images from the same page indicate the values $l=3$ and $m=2$. In Maple notation it would be SphericalY(3,2,.,.) where the dots are angle variables (the usage of letters $\theta$ and $\phi$ for spherical coordinates is not consistent). The following Maple code produces a vastly improved version of your image.

r:=Re(SphericalY(3,2,phi,theta));
with(plots):
S1:=plot3d([r*cos(theta)*sin(phi), r*sin(theta)*sin(phi), r*cos(phi)], theta=0..2*Pi, phi=0..Pi, color=red, grid=[100,100]);
S2:=plot3d([-r*cos(theta)*sin(phi), -r*sin(theta)*sin(phi),-r*cos(phi)], theta=0..2*Pi, phi=0..Pi, color=green, grid=[100,100]);
display([S1,S2]);