3 deleted 174 characters in body edited Jul 25 '18 at 18:02 Henrik Schumacher 68.6k55 gold badges9898 silver badges191191 bronze badges The ColorFunction of a SphericalPlot3D has fivesix arguments, the first three being the $$x$$, $$y$$ , $$z$$ coodinates in $$\mathbb{R}^3$$. The last twofourth and fifth argument are the actual parameterization parameters of the surface and the last argument is the distance from the origin (the radius). # (Slot) and & (Function) together allow to define anonymous function. #4 and #5 refer to the fourth and fifth argument. Here is (essentially) equivalent rewrite with Function in long form: SphericalPlot3D[1, {θ, 0, π}, {ϕ, 0, 2 π}, ColorFunction -> Function[ {x, y, z, u, v}, ColorData["Rainbow"][Re[SphericalHarmonicY[5, 2, u, v]]] ], ColorFunctionScaling -> False ]  Compare this also toHere is the followingexample from the documentation: gGraphicsGrid[ =Partition[#, GraphicsRow[3] &@ Table[SphericalPlot3D[ Table[ SphericalPlot3D[1 1 + Sin[5 ϕ]/10, {θ, 0, πPi}, {ϕ, 0, 2 πPi}, PlotPoints -> 100, ColorFunction -> f ], {f, { Function[{x, y, z, u, v}, ColorData["Rainbow"][(1 + Sin[5 Pi x])/2]], Function[{x, y, zθ, uϕ, vr}, ColorData["Rainbow"][(1 + Sin[5 Pi y])/2]]Evaluate[f]],     Function[{x,PlotLabel y,-> zf, u,  v}, ColorData["Rainbow"][(1 + Sin[5Axes Pi-> z])/2]]None], Function[{xf, y{Hue[x], zHue[y], uHue[z], v}Hue[θ], ColorData["Rainbow"][(1 + Sin[5 Pi u])/2]], Function[{x, y, z, u, v}Hue[ϕ], ColorData["Rainbow"][(1 + Sin[5 Pi v])/2]] Hue[r]} } ],   ImageSize -> Full ]  The ColorFunction of a SphericalPlot3D has five arguments, the first three being the $$x$$, $$y$$ , $$z$$ coodinates in $$\mathbb{R}^3$$. The last two are the actual parameterization parameters of the surface. # (Slot) and & (Function) together allow to define anonymous function. #4 and #5 refer to the fourth and fifth argument. Here is (essentially) equivalent rewrite with Function in long form: SphericalPlot3D[1, {θ, 0, π}, {ϕ, 0, 2 π}, ColorFunction -> Function[ {x, y, z, u, v}, ColorData["Rainbow"][Re[SphericalHarmonicY[5, 2, u, v]]] ], ColorFunctionScaling -> False ]  Compare this also to the following: g = GraphicsRow[ Table[ SphericalPlot3D[1, {θ, 0, π}, {ϕ, 0, 2 π}, PlotPoints -> 100, ColorFunction -> f ], {f, { Function[{x, y, z, u, v}, ColorData["Rainbow"][(1 + Sin[5 Pi x])/2]], Function[{x, y, z, u, v}, ColorData["Rainbow"][(1 + Sin[5 Pi y])/2]],   Function[{x, y, z, u, v}, ColorData["Rainbow"][(1 + Sin[5 Pi z])/2]], Function[{x, y, z, u, v}, ColorData["Rainbow"][(1 + Sin[5 Pi u])/2]], Function[{x, y, z, u, v}, ColorData["Rainbow"][(1 + Sin[5 Pi v])/2]] } } ], ImageSize -> Full ]  The ColorFunction of a SphericalPlot3D has six arguments, the first three being the $$x$$, $$y$$ , $$z$$ coodinates in $$\mathbb{R}^3$$. The fourth and fifth argument are the actual parameterization parameters of the surface and the last argument is the distance from the origin (the radius). # (Slot) and & (Function) together allow to define anonymous function. #4 and #5 refer to the fourth and fifth argument. Here is (essentially) equivalent rewrite with Function in long form: SphericalPlot3D[1, {θ, 0, π}, {ϕ, 0, 2 π}, ColorFunction -> Function[ {x, y, z, u, v}, ColorData["Rainbow"][Re[SphericalHarmonicY[5, 2, u, v]]] ], ColorFunctionScaling -> False ]  Here is the example from the documentation: GraphicsGrid[ Partition[#, 3] &@ Table[SphericalPlot3D[ 1 + Sin[5 ϕ]/10, {θ, 0, Pi}, {ϕ, 0, 2 Pi}, PlotPoints -> 100, ColorFunction -> Function[{x, y, z, θ, ϕ, r}, Evaluate[f]],   PlotLabel -> f,   Axes -> None], {f, {Hue[x], Hue[y], Hue[z], Hue[θ], Hue[ϕ], Hue[r]}}],   ImageSize -> Full ]  2 added 786 characters in body edited Jul 25 '18 at 16:39 Henrik Schumacher 68.6k55 gold badges9898 silver badges191191 bronze badges The ColorFunction of a SphericalPlot3D has five arguments, the first three being the $$x$$, $$y$$ , $$z$$ coodinates in $$\mathbb{R}^3$$. The last two are the actual parameterization parameters of the surface. # (Slot) and & (Function) together allow to define anonymous function. #4 and #5 refer to the fourth and fifth argument. Here is (essentially) equivalent rewrite with Function in long form: SphericalPlot3D[1, {θ, 0, π}, {ϕ, 0, 2 π}, ColorFunction -> Function[ {x, y, z, u, v}, ColorData["Rainbow"][Re[SphericalHarmonicY[5, 2, u, v]]] ], ColorFunctionScaling -> False ]  Compare this also to the following: g = GraphicsRow[ Table[ SphericalPlot3D[1, {θ, 0, π}, {ϕ, 0, 2 π}, PlotPoints -> 100, ColorFunction -> f ], {f, { Function[{x, y, z, u, v}, ColorData["Rainbow"][(1 + Sin[5 Pi x])/2]], Function[{x, y, z, u, v}, ColorData["Rainbow"][(1 + Sin[5 Pi y])/2]], Function[{x, y, z, u, v}, ColorData["Rainbow"][(1 + Sin[5 Pi z])/2]], Function[{x, y, z, u, v}, ColorData["Rainbow"][(1 + Sin[5 Pi u])/2]], Function[{x, y, z, u, v}, ColorData["Rainbow"][(1 + Sin[5 Pi v])/2]] } } ], ImageSize -> Full ]  The ColorFunction of a SphericalPlot3D has five arguments, the first three being the $$x$$, $$y$$ , $$z$$ coodinates in $$\mathbb{R}^3$$. The last two are the actual parameterization parameters of the surface. # (Slot) and & (Function) together allow to define anonymous function. #4 and #5 refer to the fourth and fifth argument. Here is (essentially) equivalent rewrite with Function in long form: SphericalPlot3D[1, {θ, 0, π}, {ϕ, 0, 2 π}, ColorFunction -> Function[ {x, y, z, u, v}, ColorData["Rainbow"][Re[SphericalHarmonicY[5, 2, u, v]]] ], ColorFunctionScaling -> False ]  The ColorFunction of a SphericalPlot3D has five arguments, the first three being the $$x$$, $$y$$ , $$z$$ coodinates in $$\mathbb{R}^3$$. The last two are the actual parameterization parameters of the surface. # (Slot) and & (Function) together allow to define anonymous function. #4 and #5 refer to the fourth and fifth argument. Here is (essentially) equivalent rewrite with Function in long form: SphericalPlot3D[1, {θ, 0, π}, {ϕ, 0, 2 π}, ColorFunction -> Function[ {x, y, z, u, v}, ColorData["Rainbow"][Re[SphericalHarmonicY[5, 2, u, v]]] ], ColorFunctionScaling -> False ]  Compare this also to the following: g = GraphicsRow[ Table[ SphericalPlot3D[1, {θ, 0, π}, {ϕ, 0, 2 π}, PlotPoints -> 100, ColorFunction -> f ], {f, { Function[{x, y, z, u, v}, ColorData["Rainbow"][(1 + Sin[5 Pi x])/2]], Function[{x, y, z, u, v}, ColorData["Rainbow"][(1 + Sin[5 Pi y])/2]], Function[{x, y, z, u, v}, ColorData["Rainbow"][(1 + Sin[5 Pi z])/2]], Function[{x, y, z, u, v}, ColorData["Rainbow"][(1 + Sin[5 Pi u])/2]], Function[{x, y, z, u, v}, ColorData["Rainbow"][(1 + Sin[5 Pi v])/2]] } } ], ImageSize -> Full ]  1 answered Jul 25 '18 at 16:28 Henrik Schumacher 68.6k55 gold badges9898 silver badges191191 bronze badges The ColorFunction of a SphericalPlot3D has five arguments, the first three being the $$x$$, $$y$$ , $$z$$ coodinates in $$\mathbb{R}^3$$. The last two are the actual parameterization parameters of the surface. # (Slot) and & (Function) together allow to define anonymous function. #4 and #5 refer to the fourth and fifth argument. Here is (essentially) equivalent rewrite with Function in long form: SphericalPlot3D[1, {θ, 0, π}, {ϕ, 0, 2 π}, ColorFunction -> Function[ {x, y, z, u, v}, ColorData["Rainbow"][Re[SphericalHarmonicY[5, 2, u, v]]] ], ColorFunctionScaling -> False ]