How to create a new symbol (with adjustable colors) in tikz

Question

I have a naive question --- How to create a new symbol like the figure below (with adjustable colors) in the tikz?

I believe that it is doable with tikzpicture. For example, using tikzpicture, are we able to switch its black color to another color like the brown color?

Here is a working MWE template:

\documentclass{article}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}
\coordinate 

\fill[black]
\end{tikzpicture}
\end{document}

Answer 1

I consider that you need a mathematical symbol. I built it as a \newcommand that invokes \mathchoice for a good scaling if it happens to be used as an index, for example. It depends on an optional argument that gives the color.

The code

\documentclass[12pt]{article}
\usepackage{tikz}
\usepackage{ifthen}

\newcommand*{\tmp}[2]{%
  \mathrel{%
    \begin{tikzpicture}[color=#2, x={(#1 ex, 0)}, y={(0, #1 ex)}, xscale=1.2]
      \path[use as bounding box] (-.2, .05) rectangle ++(1.7, 2.1);
      \draw (.1, 2.2) -- ++(10: 1.)
      to[out=10, in=0] ++(0, -.9) --++(190: 1.1);
      \draw (.05, 1.75) -- ++(10: .55)
      to[out=10, in=80] ++(0, -.8) coordinate (M)
      to[out=260, in=90] (0, -.25);
      \draw (M) -- ++(10: .5)
      to[out=0, in=80] ++(-.05, -.5)
      to[out=260, in=110]
      (1.25, -.25); 
    \end{tikzpicture}%
  }%
}
\newcommand*{\funnysymbol}[1][]{%
  \ifthenelse{\equal{#1}{}}{\colorlet{rgb}{.}}{\colorlet{rgb}{#1}}
  \mathchoice{\tmp{.8}{rgb}}{\tmp{.8}{rgb}}{\tmp{.6}{rgb}}{\tmp{.5}{rgb}}
}

\begin{document}

$X \funnysymbol Y$ \quad $X_{a\funnysymbol b}$ \qquad
$X \funnysymbol[red!60!black] Y$ \quad $X_{a\funnysymbol[blue] b}$

$X \mathbin{R} Y$ \quad $X_{a\mathbin{R}b}$
\end{document}

Answer 2

Well, your MWE is not exactly an MWE (not even an MNWE), but is this what you are looking for? You can define pics with arguments (even more than one if needed):

\documentclass[border=10pt]{standalone}
\usepackage{tikz}
\tikzset{blurb/.pic={
     \draw[line cap=round, line width=4pt, #1] (0,0) to[out=10, in=10, looseness=4] (0,-1)
         plot [smooth, tension=1.2] coordinates{(0,-0.5) (0.3,-0.4) (1,-1) (0.5,-2) (0,-3)}
         plot [smooth, tension=1.2] coordinates{(1,-1) (1.4, -1.4) (1,-2) (2,-3)};}
}
\begin{document}
\begin{tikzpicture}
    \pic[scale=0.5] (a) at (0,0) {blurb=blue};
    \pic[scale=0.5] (b) at (1,0) {blurb={red, opacity=0.5}};
\end{tikzpicture}
\end{document}

I built the shape with the method of "let's try this". But you can draw the symbol as a frame line in xfig or inkscape and get the coordinates from there.