How to plot spherical harmonics using two primary colors?

Question

I did go through Density plot on the surface of sphere where great examples are provided. What I am very much interested is in plotting spherical harmonics (real/imaginary or lets say just the assoc. Legendre Polynomials) on a 2-sphere (of unit radius) but just using two primary colors, say blue and red. I would like to use red when the value of the function goes to zero and blue when it peaks (to whatever it peaks) and a nice combination of these two somewhere in the middle. Is that possible? Rainbow doesn't help at all in visualizing. Have spent a lot of time but with no results! Any help would be highly appreciated.
I used
SphericalPlot3D[1, {θ, 0, π}, {Φ, 0, 2 π}, 
     ColorFunction -> Function[{x, y, z, θ, Φ, r}, 
         ColorData["Rainbow"][Re@SphericalHarmonicY[1,0,θ,Φ]]], 
     ColorFunctionScaling -> False, Mesh -> False, Boxed -> False, Axes -> False]

Bob Hanlon · Answer

Clear["Global`*"] SphericalHarmonicY[1, 0 , θ, Φ] is real for real {θ, Φ} FunctionDomain[ SphericalHarmonicY[1, 0, θ, Φ], {θ, Φ}] (* True *) The min and max values are {min, max} = #[{Re@SphericalHarmonicY[1, 0, θ, Φ], 0 <= θ <= Pi, 0 <= Φ <= 2 Pi}, {θ, Φ}] & /@ {MinValue, MaxValue} (* {-(Sqrt[(3/π)]/2), Sqrt[3/π]/2} *) For Red for zero and Blue at both of the extremes: SphericalPlot3D[1, {θ, 0, π}, {Φ, 0, 2 π}, ColorFunction -> Function[{x, y, z, θ, Φ, r}, Blend[{Blue, Red, Blue}, Rescale[SphericalHarmonicY[1, 0, θ, Φ], {min, max}]]], PlotPoints -> 100, ColorFunctionScaling -> False, Mesh -> False, Boxed -> False, Axes -> False] For Blue at negative extreme, Red at zero, and Yellow at positive extreme: SphericalPlot3D[1, {θ, 0, π}, {Φ, 0, 2 π}, ColorFunction -> Function[{x, y, z, θ, Φ, r}, Blend[{Blue, Red, Yellow}, Rescale[SphericalHarmonicY[1, 0, θ, Φ], {min, max}]]], PlotPoints -> 100, ColorFunctionScaling -> False, Mesh -> False, Boxed -> False, Axes -> False] EDIT: For variable {l, m} in SphericalHarmonicY[l, m, θ, Φ] Manipulate[ Module[{min, max}, m = Min[m, l]; {min, max} = N[#[{Re@SphericalHarmonicY[l, m, θ, Φ], 0 <= θ <= Pi, 0 <= Φ <= 2 Pi}, {θ, Φ}, WorkingPrecision -> 15] & /@ {NMinValue, NMaxValue}]; Column[{ StringForm["min = ``, max = ``", Round[min, 0.01], Round[max, 0.01]], SphericalPlot3D[ 1, {θ, 0, π}, {Φ, 0, 2 π}, ColorFunction -> Function[{x, y, z, θ, Φ, r}, Blend[{Blue, Red, Blue}, Rescale[ Re@SphericalHarmonicY[l, m, θ, Φ], {min, max}]]], PlotPoints -> 100, ColorFunctionScaling -> False, Mesh -> {{0.}}, MeshFunctions -> {Function[{x, y, z, θ, Φ, r}, Re@SphericalHarmonicY[l, m, θ, Φ]]}, MeshStyle -> {Black, Thick}, Boxed -> False, Axes -> False, ImageSize -> Medium]}]], {{l, 1}, Range[5], ControlType -> SetterBar}, {{m, 0}, Range[0, l], ControlType -> SetterBar}]

How to plot spherical harmonics using two primary colors?

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