Serpentine-shaped plots on the x and y axes

Question

I would like to know how to create serpentine curves in the 'tikzpicture' and 'axis' environments on the x and y axes.

I used the 'tikzpicture' and 'axis' environments to build the uncolored part of the figure below following user Torbjørn T.'s directions in this answer here. As you can see I added the design of four curves in the shape of a serpentine in red, green, orange and blue

I need the serpentine-shaped curves to satisfy the following requirements:

1. That they are transparent and that I can control the level of transparency.
2. That I can choose to place hollow circles or filled circles at the beginning and end of the ends of the serpentine curves.
3. that I can place them both vertically and horizontally.
4. that I can control their colors
5. Control the length of the serpentine curve.
6. if possible, control the width of the space occupied by the serpentine curve.

Thanks.

UPDATE after comment of user @Qrrbrbirlbel

The serpentine curve = similar to sin wave. Circles be centered at the start/end. The connection of the serpentine to the border should be at the border of the circle (on the left when it is the final circle and on the right when it is the initial circle) and at the height of the circle center.

Answer 1

You can use the built-in coil decoration (requires the decorations.pathmorphing library. The resulting style can be applied to any path, even curves.

You can adjust pre length, post length and line thickness in the tikzset. You can also adjust the size of the circles by adjusting filled and open (but also change shorten to half the length). The other aspects can be adjusted using the syntax

\draw[serp=<amplitude>, <color>, segment length=<length>, opacity=<percent>, <tip>-<tip>]

where <tip> can be open or filled. Default amplitude is set to 1mm.

\documentclass{article}

\usepackage{tikz}
\usetikzlibrary{decorations.pathmorphing, arrows.meta}

\tikzset{serp/.style={thick, decorate, decoration={coil, aspect=0, pre length=1mm, post length=1mm, amplitude=#1}, shorten <=-1.5pt, shorten >=-1.5pt},
    serp/.default=1mm,
    filled/.tip={Circle[length=3pt]},
    open/.tip={Circle[open, length=3pt]}
}

\begin{document}

\begin{tikzpicture}
\draw(0,0)grid(3,2);
\draw[serp=1.5mm, blue, segment length=1mm, opacity=.3, open-filled](0,0)--(3,2);
\end{tikzpicture}

\end{document}

Answer 2

If I well understand I have a new, more complete solution (where You can choose the opacity, the space occupied, the colors, see comments added):

\documentclass[tikz,margin=20pt]{standalone}
\pgfmathsetmacro{\op}{.5} %<-- set the opacity of the picture
\pgfmathsetmacro{\h}{.3} % <-- set the space occupied by serpentine
\begin{document}
    \begin{tikzpicture}
        \draw[cyan!15,step=.5] (-6.7,-6.7) grid (6.7,6.7);
        \draw[-latex] (-6.7,0)--(7,0) node[right] () {$x$};
        \draw[-latex] (0,-6.7)--(0,7) node[right] () {$y$}; 
        % it is possible to change to colours (\c) of the 4 serpentines
        \foreach \ang/\c in {0/red,90/blue,180/violet,270/green}
            {
            \draw[\c,line width=2pt,rotate=\ang,opacity=\op] (1,0) circle(\h);
            \draw[\c,line width=2pt,opacity=\op] plot[domain=1:6.3,smooth,rotate=\ang] (\x,{\h*sin(6*\x r)});
            \fill[\c,line width=2pt,rotate=\ang,opacity=\op] (6.3,0) circle(\h);
            }
    \end{tikzpicture}
\end{document}

Output:

LAST VERSION:

\documentclass[tikz,margin=20pt]{standalone}
\pgfmathsetmacro{\op}{.3} %<-- set the opacity of the picture
\pgfmathsetmacro{\h}{.5} % <-- set the space occupied by serpentine
\begin{document}
    \begin{tikzpicture}
        \draw[cyan!15,step=.5] (-7.5,-7.5) grid (7.5,7.5);
        \draw[-latex,line width=.5pt] (-7.7,0)--(7.7,0) node[right] () {$x$};
        \draw[-latex,line width=.5pt] (0,-7.7)--(0,7.7) node[right] () {$y$}; 
        % it is possible to change to colours (\c) of the 4 serpentines
        \foreach \ang/\c in {0/red,90/blue,180/violet,270/green}
        {
            \draw[\c,line width=4pt,rotate=\ang,opacity=\op] (1,0) circle(\h) ({1+\h},0)--(2.05,0);
            \draw[\c,line width=4pt,opacity=\op] plot[domain=2:5.8,smooth,rotate=\ang] (\x,{\h*sin(15*pi*\x r)});
            \draw[\c,line width=4pt,rotate=\ang,opacity=\op];
            \filldraw[\c,line width=4pt,rotate=\ang,opacity=\op](5.75,0)--({6.3},0);
            \shade[ball color=\c,rotate=\ang,opacity=\op] ({6.3+\h},0) circle(\h) ;
        }
    \end{tikzpicture}
\end{document}

OUTPUT:

Note: My preference is to view the graph without grid and axis (for this comment the first 3 lines inside tikzpicture environment).

Answer 3

Like this (it is not clear if You want point/circle at start/end points):

Code:

\documentclass[tikz,margin=20pt]{standalone}
\begin{document}
    \begin{tikzpicture}
        \draw[cyan!15,step=.5] (-6.7,-6.7) grid (6.7,6.7);
        \draw[-latex] (-6.7,0)--(6.7,0) node[right] () {$x$};
        \draw[-latex] (0,-6.7)--(0,6.7) node[right] () {$y$};
        \draw[red,line width=2pt] plot[domain=-6.5:-1,smooth] (\x,{.2*sin(6*\x r)});
        \draw[blue,line width=2pt] plot[domain=1:6.5,smooth] (\x,{.2*sin(6*\x r)});
        \draw[violet,line width=2pt] plot[domain=1:6.5,smooth] ({.2*sin(6*\x r)},\x);
        \draw[green,line width=2pt] plot[domain=-6.5:-1,smooth] ({.2*sin(6*\x r)},\x);
    \end{tikzpicture}

\end{document}