SetDirectory[$HomeDirectory<>"/Documents/handouts/math467/VibratingSphere"]

Vibrating Sphere

v[ϕ_,θ_,t_]:=(Cos[Sqrt[6]t]LegendreP[2,2,Cos[ϕ]]/168+Cos[2Sqrt[5]t]LegendreP[4,2,Cos[ϕ]]/420)Sin[2θ]

SphericalPlot3D[1+v[ϕ,θ,π/(3Sqrt[6])],{ϕ,0,π},{θ,-π,π},ColorFunction->Function[{x,y,z,θ,ϕ,ρ},GrayLevel[ρ]],MeshFunctions->{Function[{x,y,z,θ,ϕ,ρ},ρ]},Mesh->{Range[0.9850975165992307+0.0024837472334615497,1.0149024834007694-0.0024837472334615497,0.0024837472334615497]},PlotPoints->250,AxesLabel->{"\!\(\*TemplateBox[<|"boxes" -> FormBox[
StyleBox["x", "TI"], TraditionalForm], "errors" -> {}, "input" -> "x", "state" -> "Boxes"|>,"TeXAssistantTemplate"]\)","\!\(\*TemplateBox[<|"boxes" -> FormBox[
StyleBox["y", "TI"], TraditionalForm], "errors" -> {}, "input" -> "y", "state" -> "Boxes"|>,"TeXAssistantTemplate"]\)","\!\(\*TemplateBox[<|"boxes" -> FormBox[
StyleBox["z", "TI"], TraditionalForm], "errors" -> {}, "input" -> "z", "state" -> "Boxes"|>,"TeXAssistantTemplate"]\)"},BaseStyle->FontSize->12,MeshStyle->Thick]

Export["vibsphere.pdf",%,"PDF"]

Export["vibsphere.eps",%%,"EPS"]