Customize ColorData function

Question

I am trying to customize the color data

ColorData["AvocadoColors"]

I want to make color data function of the gradient starting from the green to the white instead of the green to the yellow. So I want the output such that,

ColorData["MyColorFunction"]

Any suggestions?

Answer 1

If you inspect the InputForm of the "ColorFunction" property for "AvocadoColors" you see that it uses Blend with a list of colors:

ColorData["AvocadoColors", "ColorFunction"] // InputForm

ColorDataFunction["AvocadoColors", "Gradients", {0, 1}, Blend["AvocadoColors", #1] &]

Similarly, for "Rainbow" and other gradient color schemes:

ColorData["Rainbow", "ColorFunction"] // InputForm

 ColorDataFunction["Rainbow", "Gradients", {0, 1}, Blend["Rainbow", #1] & ] 

The function DataPaclets`ColorData`GetBlendArgument gives the list of colors used in Blend:

clist = DataPaclets`ColorData`GetBlendArgument["AvocadoColors"]

Now you can replace the last color with White and use with Blend:

mycolorFunc = Blend[Append[Most[clist], White], #] &;

This function retains the yellow tones in the middle of the list. Alternatively, you can have White play the role of Yellow in your new color scheme using blends of the second color with White to construct an alternative list of blending colors:

myclist  = Prepend[FoldList[Blend[{#, White},#2]&, clist[[2]], {1, 2, 3}/3] , clist[[1]]]

mycolorFunc2 = Blend[myclist, #]&;

Examples:

Row[Plot3D[Sin[x y], {x, 0, 3}, {y, 0, 3}, ColorFunction -> #, ImageSize -> Medium]& /@
  {"AvocadoColors", mycolorFunc[#3] &, mycolorFunc2[#3] &}]

Style[Row[LinearGradientImage/@{"AvocadoColors", mycolorFunc, mycolorFunc2}, 
 Spacer[10]], ImageSizeMultipliers->{1,1}]

To add your custom color function to the existing color schemes you can use this answer by Mr. Wizard:

ColorData[1];
new = {{"myColorFunction", "", {}}, {"Gradients"}, 1, {0, 1}, myclist, ""};
AppendTo[DataPaclets`ColorDataDump`colorSchemes,  new];
AppendTo[DataPaclets`ColorDataDump`colorSchemeNames,  "myColorFunction"];
ColorData["myColorFunction"]

Examples:

BarLegend["myColorFunction", LegendLayout -> "Row", LegendMarkerSize -> {400, 100}]

PieChart[Range[10], ColorFunction -> "myColorFunction"]