Cell[CellGroupData[{Cell[BoxData[ RowBox[{"Manipulate", "[", RowBox[{ RowBox[{"ParametricPlot3D", "[", " ", RowBox[{ RowBox[{"Evaluate", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"Cos", "[", "p", "]"}], RowBox[{"Sin", "[", "t", "]"}]}], ",", RowBox[{ RowBox[{"Sin", "[", "p", "]"}], RowBox[{"Sin", "[", "t", "]"}]}], ",", RowBox[{"Cos", "[", "t", "]"}]}], "}"}], RowBox[{"Abs", "[", RowBox[{"SphericalHarmonicY", "[", RowBox[{"l", ",", "m", ",", "t", ",", "p"}], "]"}], "]"}]}], "]"}], ",", " ", RowBox[{"{", RowBox[{"p", ",", RowBox[{"-", "Pi"}], ",", "Pi"}], "}"}], ",", RowBox[{"{", RowBox[{"t", ",", "0", ",", "Pi"}], "}"}], ",", RowBox[{"PlotRange", "->", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"-", ".5"}], ",", ".5"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", ".5"}], ",", ".5"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "1.1"}], ",", "1.1"}], "}"}]}], "}"}]}], ",", " ", RowBox[{"Mesh", "->", "False"}], ",", RowBox[{"PlotPoints", "->", RowBox[{"{", RowBox[{"36", ",", "18"}], "}"}]}], ",", RowBox[{"MaxRecursion", "->", RowBox[{"ControlActive", "[", RowBox[{"0", ",", "2"}], "]"}]}], ",", " ", RowBox[{"ViewAngle", "->", ".246"}], ",", RowBox[{"ImageSize", " ", "->", RowBox[{"{", RowBox[{"500", ",", "377"}], "}"}]}], ",", RowBox[{"Axes", "->", "False"}], ",", RowBox[{"SphericalRegion", "->", "True"}], ",", RowBox[{"Boxed", "->", "False"}], ",", RowBox[{"PlotLabel", "->", RowBox[{"Style", "[", RowBox[{ RowBox[{"With", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"l", "=", "l"}], ",", RowBox[{"m", "=", RowBox[{"Round", "@", "m"}]}]}], "}"}], ",", RowBox[{"TraditionalForm", "[", RowBox[{"HoldForm", "[", RowBox[{"r", "==", RowBox[{"SphericalHarmonicY", "[", RowBox[{"l", ",", "m", ",", "\[Theta]", ",", "\[Phi]"}], "]"}]}], "]"}], "]"}]}], "]"}], ",", "14"}], "]"}]}]}], "]"}], ",", " ", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"l", ",", "2", ",", "\"\\""}], "}"}], ",", "0", ",", "7", ",", "1", ",", RowBox[{"Appearance", "->", "\"\\""}]}], "}"}], ",", " ", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"m", ",", "0", ",", "\"\\""}], "}"}], ",", RowBox[{"-", "l"}], ",", "l", ",", "1", ",", RowBox[{"Appearance", "->", "\"\\""}]}], "}"}]}], "]"}]], "Input", CellGroupingRules->{"GroupTogetherGrouping", 10000.}, CellChangeTimes->{ 3.35264968450764*^9, {3.36327217342188*^9, 3.36327219760938*^9}, { 3.36327227621875*^9, 3.36327228157813*^9}, {3.37141684824303*^9, 3.37141685981645*^9}, 3.37141689716403*^9, {3.37141706864582*^9, 3.37141707447928*^9}, {3.37141717452415*^9, 3.37141718858686*^9}, { 3.3714174872445*^9, 3.37141763002204*^9}, {3.37141782291421*^9, 3.37141793644002*^9}, {3.37142816971687*^9, 3.37142818749846*^9}, { 3.3782287007540503`*^9, 3.378228720603299*^9}, { 3.378228874325667*^9, 3.3782288748639517`*^9}, { 3.378228987204692*^9, 3.378229044407482*^9}, {3.378229076322403*^9, 3.3782290814979258`*^9}, {3.378229146220326*^9, 3.3782292313122396`*^9}, {3.3782294512200203`*^9, 3.37822945435454*^9}, {3.378229637493128*^9, 3.378229670095272*^9}, {3.378643047314404*^9, 3.378643048482533*^9}, {3.378688934188416*^9, 3.378688957069816*^9}, {3.3786889964309464`*^9, 3.378688996992764*^9}, {3.37868903581819*^9, 3.378689039427528*^9}, {3.378689070506419*^9, 3.378689139206118*^9}, 3.378689169616585*^9, { 3.3786892541021137`*^9, 3.378689274401804*^9}, { 3.378689445531608*^9, 3.3786894490396*^9}, {3.378689517244156*^9, 3.3786896265577993`*^9}, {3.378689731488573*^9, 3.3786897366706247`*^9}, {3.378689789242156*^9, 3.378689815932637*^9}, {3.378689895666855*^9, 3.3786898981105137`*^9}, {3.3786899289552183`*^9, 3.37868995730921*^9}, {3.380893671374487*^9, 3.380893672218237*^9}, {3.380893977436987*^9, 3.380893981265112*^9}, {3.3815258719538937`*^9, 3.3815258917829847`*^9}, {3.381525958747656*^9, 3.381525985916768*^9}, {3.381526051671184*^9, 3.381526090936517*^9}, {3.3815261784671993`*^9, 3.381526180336578*^9}, {3.381526211866322*^9, 3.3815262215224743`*^9}, {3.38152625664355*^9, 3.381526287012438*^9}, 3.7608047019632273`*^9}, CellID->1496021318], Cell[BoxData[ TagBox[ StyleBox[ DynamicModuleBox[{$CellContext`l$$ = 2, $CellContext`m$$ = 0, Typeset`show$$ = True, Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = "\"untitled\"", Typeset`specs$$ = {{{ Hold[$CellContext`l$$], 2, "degree l"}, 0, 7, 1}, {{ Hold[$CellContext`m$$], 0, "order m"}, Dynamic[-$CellContext`l$$], Dynamic[$CellContext`l$$], 1}}, Typeset`size$$ = { 500., {186., 191.}}, Typeset`update$$ = 0, Typeset`initDone$$, Typeset`skipInitDone$$ = True, $CellContext`l$221967$$ = 0, $CellContext`m$221968$$ = 0}, DynamicBox[Manipulate`ManipulateBoxes[ 1, StandardForm, "Variables" :> {$CellContext`l$$ = 2, $CellContext`m$$ = 0}, "ControllerVariables" :> { Hold[$CellContext`l$$, $CellContext`l$221967$$, 0], Hold[$CellContext`m$$, $CellContext`m$221968$$, 0]}, "OtherVariables" :> { Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, Typeset`skipInitDone$$}, "Body" :> ParametricPlot3D[ Evaluate[{ Cos[$CellContext`p] Sin[$CellContext`t], Sin[$CellContext`p] Sin[$CellContext`t], Cos[$CellContext`t]} Abs[ SphericalHarmonicY[$CellContext`l$$, $CellContext`m$$, \ $CellContext`t, $CellContext`p]]], {$CellContext`p, -Pi, Pi}, {$CellContext`t, 0, Pi}, PlotRange -> {{-0.5, 0.5}, {-0.5, 0.5}, {-1.1, 1.1}}, Mesh -> False, PlotPoints -> {36, 18}, MaxRecursion -> ControlActive[0, 2], ViewAngle -> 0.246, ImageSize -> {500, 377}, Axes -> False, SphericalRegion -> True, Boxed -> False, PlotLabel -> Style[ With[{$CellContext`l = $CellContext`l$$, $CellContext`m = Round[$CellContext`m$$]}, TraditionalForm[ HoldForm[$CellContext`r == SphericalHarmonicY[$CellContext`l, $CellContext`m, \ $CellContext`\[Theta], $CellContext`\[Phi]]]]], 14]], "Specifications" :> {{{$CellContext`l$$, 2, "degree l"}, 0, 7, 1, Appearance -> "Labeled"}, {{$CellContext`m$$, 0, "order m"}, Dynamic[-$CellContext`l$$], Dynamic[$CellContext`l$$], 1, Appearance -> "Labeled"}}, "Options" :> {}, "DefaultOptions" :> {ControllerLinking -> True}], ImageSizeCache->{545., {245., 251.}}, SingleEvaluation->True], Deinitialization:>None, DynamicModuleValues:>{}, SynchronousInitialization->True, UnsavedVariables:>{Typeset`initDone$$}, UntrackedVariables:>{Typeset`size$$}], "Manipulate", Deployed->True, StripOnInput->False], Manipulate`InterpretManipulate[1]]], "Output", CellGroupingRules->{"GroupTogetherGrouping", 10000.}, CellChangeTimes->{3.760804701963492*^9}, CellID->10334116] }, {2}]]