Spherical Harmonics

Manipulate[ParametricPlot3D[
Evaluate[{Cos[p]Sin[t],Sin[p]Sin[t],Cos[t]}Abs[SphericalHarmonicY[l,m,t,p]]],
{p,0,2Pi},{t,0,Pi},PlotRange->{{-.5,.5},{-.5,.5},{-1.1,1.1}},
Mesh->False,PlotPoints->{90,90},MaxRecursion->ControlActive[0,2],
ViewAngle->.246,ImageSize ->{800,600},Axes->False,SphericalRegion->True,Boxed->False,PlotLabel->Style[With[{l=l,m=Round@m},TraditionalForm[HoldForm[r==SphericalHarmonicY[l,m,θ,ϕ]]]],14]],
{{l,2,"degree l"},0,7,1,Appearance->"Labeled"},
{{m,0,"order m"},-l,l,1,Appearance->"Labeled"}]

THIS NOTEBOOK IS THE SOURCE CODE FROM

"Spherical Harmonics" from The Wolfram Demonstrations Project
 http://demonstrations.wolfram.com/SphericalHarmonics/

Contributed by: Stephen Wolfram

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