Is it possible to apply a ColorGradient to a string Style?

Question

After reading through the language reference on Style, ColorSchemes, ColorData and ColorFunction, I am at a loss as how to make a string appear with gradient colors. And now that I am curious, I am wondering what the easiest way to achieve this is under various scenarios, for instance:

1. apply gradient to each character independently
2. apply gradient to entire string as a whole
3. apply gradient such that each character is a solid color, but as a string it has a gradient mask applied

From reading elsewhere on stackExchange, I see I can apply a color to each character independently using Row (ex https://stackoverflow.com/questions/8956915/mathematica-how-to-have-text-in-multiple-colors). Programtically that seems rather tedious and impractical as a function.

At this point, I am not too concerned about the complexity of the gradient function - for right now, simple is better (ie, maybe a linear gradient?).

Thoughts?

Answer 1

Case 3: string with gradient, each character in a solid color (thanks to J.M. for improvements)

colorize[str_String, cf_] := "" <> MapThread[
      ToString[Style[#, cf@#2], StandardForm] &, {#, Subdivide[Length@# - 1]}] &@
   Characters@str;

colorize["Mathematica", ColorData["Rainbow"]]

Or even shorter with a bit different internal structure of the string

colorize2[str_String, cf_] := Row@MapThread[Style, 
      {#, cf /@ Subdivide[Length@# - 1]} &@Characters@str]~ToString~StandardForm;

colorize2["Mathematica", ColorData["Rainbow"]]