Vrftjkry

I'd like to use Tikz to algorithmically generate some text that has a color value based on calculations. Take the following, for example:

  documentclass{standalone}

  usepackage{tikz}

  begin{document}

  begin{tikzpicture}

      foreach i in {0, 1, ..., 10} {

          draw (i, 0) node {textcolor[gray]{0.5}A};

      }

  end{tikzpicture}

  end{document}

This displays a row of "A"s in a gray:

How do I go about calculating the 0.5 value to, for example, display this set of "A"s in varying levels of gray, such as a black to white gradient? Could I use this same method to calculate arbitrary RGB values?

Yes, you can vary the gray levels, and the following can be used also to general non-gray colors.

documentclass{standalone}

  usepackage{tikz}

  begin{document}

  begin{tikzpicture}

      foreach i [evaluate=i as j using {int(i*10)}] in {0, 1, ..., 10} {

          draw (i, 0) node[text=gray!j!white] {A};

      }

  end{tikzpicture}

  end{document}

Just for fun, another foreach solution:

documentclass{standalone}

  usepackage{tikz}

  begin{document}

  begin{tikzpicture}

      foreach i [count=j] in {0, 10, ..., 100} {

          draw (j, 0) node[text=blue!i!red] {A};

      }

  end{tikzpicture}

  end{document}

You can evaluate a variable within the foreach loop itself (see page 904 of 3.0.1a manual).

Here since you want to go from black to white, you can do:

documentclass{standalone}

  usepackage{tikz}

  begin{document}

  begin{tikzpicture}

      foreach i [evaluate=i as gradient using 100-i*10] in {0, 1, ..., 10} {

          draw (i, 0) node[text=black!gradient] {A};

      }

  end{tikzpicture}

  end{document}

A slightly different syntax than what marmot proposed, but with the same effects

documentclass[tikz,border=3.14pt]{standalone}

  begin{document}

    begin{tikzpicture}

      draw foreach i [evaluate=i as j using {int(i*10)}] in {0, 1, ..., 10} {

          (i, 0) node[text=gray!j!white] {A}

      };

  end{tikzpicture}

  end{document}