Adding noise to sinusoidal plot

Question

I have the code which outputs a couple of sinusoidal functions

\documentclass[tikz,border=3.14mm]{standalone}
\usepackage{tikz-3dplot}
\usetikzlibrary{arrows.meta,bending}
\usepackage{xparse}
\usepackage{tikz}

\usetikzlibrary{3d}
\begin{document}
\tdplotsetmaincoords{70}{20}
\begin{tikzpicture}[tdplot_main_coords,
declare function={pX=2;}]
 \begin{scope}[canvas is yz plane at x=0]
 \draw (-pX,-pX) coordinate (bl1) -- (pX,-pX) coordinate (br1)
   -- (pX,pX) coordinate (tr1)  -- (-pX,pX) coordinate (tl1) -- cycle;
   \draw[stealth-stealth] (0,pX) node[below left]{$$}
   -- (0,0) --  (pX,0) node[below left]{$$};
   \pgflowlevelsynccm
 \end{scope}
 %\foreach \X in {bl,tl,br,tr}
 %{\draw[-latex] (\X1) -- ++ (1,0,0);}
 %
 %\draw (0,0,0) -- (4,0,0);
 % plane
  \fill[gray,fill opacity=0] (-1,-4,0) -- (7,-4,0) --
  (7,4,0) -- (-1,4,0) -- cycle;
 \begin{scope}[canvas is yz plane at x=4]
  \draw (-pX,-pX) coordinate (bl2) -- (pX,-pX) coordinate (br2)
   -- (pX,pX) coordinate (tr2)  -- (-pX,pX) coordinate (tl2) -- cycle;
   \draw[stealth-stealth];
 \end{scope}
 %\draw[-latex] (4,0,0) -- (5.5,0,0) node[below left]{$$};
  \begin{scope}[canvas is xy plane at z=0]
   \begin{scope}
      \clip (0,-2) rectangle (4,3);
      \draw[densely dashed] (0,-2) -- (0,2);
      \foreach \X in {0.25,0.75,...,5}
       {\pgfmathsetmacro{\myrnd}{rnd*360}
       \foreach \Y in {-1.75,-1.25,...,1.75}
        {
        \draw[-stealth] ({\X-0.2*cos(\myrnd)},{\Y-0.2*sin(\myrnd)}) --
        ({\X+0.2*cos(\myrnd)},{\Y+0.2*sin(\myrnd)});
        }
        \draw[densely dashed] (\X+.25,-2) -- (\X+0.25,2);}
   \end{scope} 
  \end{scope}
%
\begin{scope}[shift={($(-4,0,0)-(0,0,0)$)}]
 \begin{scope}[canvas is xy plane at z=0,dashed]
   \foreach \X in {2.1,2.3,...,4}
    {\begin{scope}
      \pgflowlevelsynccm
      \draw[-latex,thin] (1*\X,0) -- (1*\X,{-2*sin(\X*180)});
     \end{scope} 
    }
   \draw plot[smooth,domain=2:4,samples=41] (1*\x,{-2*sin(\x*180)});  
  \begin{scope}
   \pgflowlevelsynccm
   \draw[-latex,ultra thin,solid] (12.2,0) -- (12.8,0);
  \end{scope}
 \end{scope} 
 \begin{scope}[canvas is xz plane at y=0]
   \foreach \X in {2.1,2.3,...,4}
    {\begin{scope}
      \pgflowlevelsynccm
      \draw[-latex,thin] (1*\X,0) -- (1*\X,{2*sin(\X*180)});
     \end{scope} 
    }
   \draw plot[smooth,domain=2:4,samples=41] (1*\x,{2*sin(\x*180)});   
 \end{scope} 
 \node at (1*3.5,1.75,0) {$$};
 \node at (1*3.5,0,-1.25) {$$};
\end{scope} 

%
\begin{scope}[shift={($(4,0,0)-(0,0,0)$)}]
 \begin{scope}[canvas is xy plane at z=0,dashed]
   \foreach \X in {0.4,0.6,...,3}
    {\begin{scope}
      \pgflowlevelsynccm
      \draw[-latex,thin] (1*\X,0) -- (1*\X,{-3*exp(-\X)*sin(\X*180)});
     \end{scope} 
    }
   \draw plot[smooth,domain=0:4,samples=41] (1*\x,{-3*exp(-\x)*sin(\x*180)});  
  \begin{scope}
   \pgflowlevelsynccm
   \draw[-latex,ultra thin,solid] (12.2,0) -- (12.8,0);
  \end{scope}
 \end{scope} 
 \begin{scope}[canvas is xz plane at y=0]
   \foreach \X in {0.4,0.6,...,3}
    {\begin{scope}
      \pgflowlevelsynccm
      \draw[-latex,thin] (1*\X,0) -- (1*\X,{3*exp(-\X)*sin(\X*180)});
     \end{scope} 
    }
   \draw plot[smooth,domain=0:4,samples=41] (1*\x,{3*exp(-\x)*sin(\x*180)});   
 \end{scope} 
 \node at (1*3.5,1.75,0) {$$};
 \node at (1*3.5,0,-1.25) {$$};
\end{scope} 

\end{tikzpicture}






\end{document}

which outputs

where I want the wave on the right of the image, to have a random amplitude. So it looks random, and decays. How can I achieve this in tikz?

Answer 1

Here is a proposal. It is slightly nontrivial because rnd always gets evaluated new, so we need to store the coordinates where the arrows end and draw smooth curves through them. This is somewhat more efforts when one uses \pgflowlevelsynccm.

\documentclass[tikz,border=3.14mm]{standalone}
\usepackage{tikz-3dplot}
\begin{document}
\tdplotsetmaincoords{70}{20}
\begin{tikzpicture}[tdplot_main_coords,
declare function={pX=2;}]
 \begin{scope}[canvas is yz plane at x=0]
 \draw (-pX,-pX) coordinate (bl1) -- (pX,-pX) coordinate (br1)
   -- (pX,pX) coordinate (tr1)  -- (-pX,pX) coordinate (tl1) -- cycle;
   \draw[stealth-stealth] (0,pX) node[below left]{$$}
   -- (0,0) --  (pX,0) node[below left]{$$};
   \pgflowlevelsynccm
 \end{scope}
 %\foreach \X in {bl,tl,br,tr}
 %{\draw[-latex] (\X1) -- ++ (1,0,0);}
 %
 %\draw (0,0,0) -- (4,0,0);
 % plane
  \fill[gray,fill opacity=0] (-1,-4,0) -- (7,-4,0) --
  (7,4,0) -- (-1,4,0) -- cycle;
 \begin{scope}[canvas is yz plane at x=4]
  \draw (-pX,-pX) coordinate (bl2) -- (pX,-pX) coordinate (br2)
   -- (pX,pX) coordinate (tr2)  -- (-pX,pX) coordinate (tl2) -- cycle;
   \draw[stealth-stealth];
 \end{scope}
 %\draw[-latex] (4,0,0) -- (5.5,0,0) node[below left]{$$};
  \begin{scope}[canvas is xy plane at z=0]
   \begin{scope}
      \clip (0,-2) rectangle (4,3);
      \draw[densely dashed] (0,-2) -- (0,2);
      \foreach \X in {0.25,0.75,...,5}
       {\pgfmathsetmacro{\myrnd}{rnd*360}
       \foreach \Y in {-1.75,-1.25,...,1.75}
        {
        \draw[-stealth] ({\X-0.2*cos(\myrnd)},{\Y-0.2*sin(\myrnd)}) --
        ({\X+0.2*cos(\myrnd)},{\Y+0.2*sin(\myrnd)});
        }
        \draw[densely dashed] (\X+.25,-2) -- (\X+0.25,2);}
   \end{scope} 
  \end{scope}
%
\begin{scope}[shift={($(-4,0,0)-(0,0,0)$)}]
 \begin{scope}[canvas is xy plane at z=0,dashed]
   \foreach \X in {2.1,2.3,...,4}
    {\begin{scope}
      \pgflowlevelsynccm
      \draw[-latex,thin] (1*\X,0) -- (1*\X,{-2*sin(\X*180)});
     \end{scope} 
    }
   \draw plot[smooth,domain=2:4,samples=41] (1*\x,{-2*sin(\x*180)});  
  \begin{scope}
   \pgflowlevelsynccm
   \draw[-latex,ultra thin,solid] (12.2,0) -- (12.8,0);
  \end{scope}
 \end{scope} 
 \begin{scope}[canvas is xz plane at y=0]
   \foreach \X in {2.1,2.3,...,4}
    {\begin{scope}
      \pgflowlevelsynccm
      \draw[-latex,thin] (1*\X,0) -- (1*\X,{2*sin(\X*180)});
     \end{scope} 
    }
   \draw plot[smooth,domain=2:4,samples=41] (1*\x,{2*sin(\x*180)});   
 \end{scope} 
 \node at (1*3.5,1.75,0) {$$};
 \node at (1*3.5,0,-1.25) {$$};
\end{scope} 

%
\pgfmathsetseed{42}
\begin{scope}[shift={($(4,0,0)-(0,0,0)$)},
    declare function={amp(\x)=3*exp(-\x)*(0.6+0.8*rnd)*sin(\x*180);}]
 \path (0,0,0) coordinate (B0) coordinate (E0); 
 \begin{scope}[canvas is xy plane at z=0,dashed]
   \foreach \X [count=\Y] in {0.2,0.4,...,3}
    {\begin{scope}
      \pgfmathsetmacro\myamp{-amp(\X)}
      \path (1*\X,\myamp) coordinate(B\Y);
      \pgflowlevelsynccm
      \draw[-latex,thin] (1*\X,0) -- (1*\X,\myamp);
      \xdef\Ymax{\Y}
     \end{scope} 
    }
   \draw plot[smooth,samples at={0,...,\Ymax}] (B\x);  
  \begin{scope}
   \pgflowlevelsynccm
   \draw[-latex,ultra thin,solid] (12.2,0) -- (12.8,0);
  \end{scope}
 \end{scope} 
 \begin{scope}[canvas is xz plane at y=0]
   \foreach \X [count=\Y] in {0.2,0.4,...,3}
    {\begin{scope}
      \pgfmathsetmacro\myamp{amp(\X)}
      \path (1*\X,\myamp) coordinate(E\Y);
      \pgflowlevelsynccm
      \draw[-latex,thin] (1*\X,0) -- (1*\X,\myamp);
      \xdef\Ymax{\Y}
     \end{scope} 
    }
   \draw plot[smooth,samples at={0,...,\Ymax}] (E\x);   
 \end{scope} 
\end{scope} 

\end{tikzpicture}
\end{document}

You may alter the appearance by changing the random function, i.e. change

declare function={amp(\x)=3*exp(-\x)*(0.6+0.8*rnd)*sin(\x*180);}

and change the argument of

\pgfmathsetseed{42}

One may also suppress too short arrows. (In principle, tips=on proper draw could do the job, but with all the \pgflowlevelsynccm it is easier to do it "manually".)

\documentclass[tikz,border=3.14mm]{standalone}
\usepackage{tikz-3dplot}
\begin{document}
\tdplotsetmaincoords{70}{20}
\begin{tikzpicture}[tdplot_main_coords,
declare function={pX=2;}]
 \begin{scope}[canvas is yz plane at x=0]
 \draw (-pX,-pX) coordinate (bl1) -- (pX,-pX) coordinate (br1)
   -- (pX,pX) coordinate (tr1)  -- (-pX,pX) coordinate (tl1) -- cycle;
   \draw[stealth-stealth] (0,pX) node[below left]{$$}
   -- (0,0) --  (pX,0) node[below left]{$$};
   \pgflowlevelsynccm
 \end{scope}
 %\foreach \X in {bl,tl,br,tr}
 %{\draw[-latex] (\X1) -- ++ (1,0,0);}
 %
 %\draw (0,0,0) -- (4,0,0);
 % plane
  \fill[gray,fill opacity=0] (-1,-4,0) -- (7,-4,0) --
  (7,4,0) -- (-1,4,0) -- cycle;
 \begin{scope}[canvas is yz plane at x=4]
  \draw (-pX,-pX) coordinate (bl2) -- (pX,-pX) coordinate (br2)
   -- (pX,pX) coordinate (tr2)  -- (-pX,pX) coordinate (tl2) -- cycle;
   \draw[stealth-stealth];
 \end{scope}
 %\draw[-latex] (4,0,0) -- (5.5,0,0) node[below left]{$$};
  \begin{scope}[canvas is xy plane at z=0]
   \begin{scope}
      \clip (0,-2) rectangle (4,3);
      \draw[densely dashed] (0,-2) -- (0,2);
      \foreach \X in {0.25,0.75,...,5}
       {\pgfmathsetmacro{\myrnd}{rnd*360}
       \foreach \Y in {-1.75,-1.25,...,1.75}
        {
        \draw[-stealth] ({\X-0.2*cos(\myrnd)},{\Y-0.2*sin(\myrnd)}) --
        ({\X+0.2*cos(\myrnd)},{\Y+0.2*sin(\myrnd)});
        }
        \draw[densely dashed] (\X+.25,-2) -- (\X+0.25,2);}
   \end{scope} 
  \end{scope}
%
\begin{scope}[shift={($(-4,0,0)-(0,0,0)$)}]
 \begin{scope}[canvas is xy plane at z=0,dashed]
   \foreach \X in {2.1,2.3,...,4}
    {\begin{scope}
      \pgflowlevelsynccm
      \draw[-latex,thin] (1*\X,0) -- (1*\X,{-2*sin(\X*180)});
     \end{scope} 
    }
   \draw plot[smooth,domain=2:4,samples=41] (1*\x,{-2*sin(\x*180)});  
  \begin{scope}
   \pgflowlevelsynccm
   \draw[-latex,ultra thin,solid] (12.2,0) -- (12.8,0);
  \end{scope}
 \end{scope} 
 \begin{scope}[canvas is xz plane at y=0]
   \foreach \X in {2.1,2.3,...,4}
    {\begin{scope}
      \pgflowlevelsynccm
      \draw[-latex,thin] (1*\X,0) -- (1*\X,{2*sin(\X*180)});
     \end{scope} 
    }
   \draw plot[smooth,domain=2:4,samples=41] (1*\x,{2*sin(\x*180)});   
 \end{scope} 
 \node at (1*3.5,1.75,0) {$$};
 \node at (1*3.5,0,-1.25) {$$};
\end{scope} 
%
\pgfmathsetseed{42}
\begin{scope}[shift={($(4,0,0)-(0,0,0)$)},
    declare function={amp(\x)=3*exp(-\x)*(0.6+0.8*rnd)*sin(\x*180);}]
 \path (0,0,0) coordinate (B0) coordinate (E0); 
 \begin{scope}[canvas is xy plane at z=0,dashed]
   \foreach \X [count=\Y] in {0.2,0.4,...,3}
    {\begin{scope}
      \pgfmathsetmacro\myamp{-amp(\X)}
      \path (1*\X,\myamp) coordinate(B\Y);
      \pgfmathtruncatemacro{\itest}{ifthenelse(abs(\myamp)>0.075,1,0)}
      \ifnum\itest=1
        \pgflowlevelsynccm
        \draw[-latex,thin] (1*\X,0) -- (1*\X,\myamp);
      \fi 
      \xdef\Ymax{\Y}
     \end{scope} 
    }
   \draw plot[smooth,samples at={0,...,\Ymax}] (B\x);  
  \begin{scope}
   \path (4.8,0);
   \pgflowlevelsynccm
   \draw[-latex,ultra thin,solid] (4.2,0) -- (4.8,0);
  \end{scope}
 \end{scope} 
 \begin{scope}[canvas is xz plane at y=0]
   \foreach \X [count=\Y] in {0.2,0.4,...,3}
    {\begin{scope}
      \pgfmathsetmacro\myamp{amp(\X)}
      \path (1*\X,\myamp) coordinate(E\Y);
      \pgfmathtruncatemacro{\itest}{ifthenelse(abs(\myamp)>0.075,1,0)}
      \ifnum\itest=1
        \pgflowlevelsynccm
        \draw[-latex,thin] (1*\X,0) -- (1*\X,\myamp);
      \fi
      \xdef\Ymax{\Y}
     \end{scope} 
    }
   \draw plot[smooth,samples at={0,...,\Ymax}] (E\x);   
 \end{scope} 
\end{scope} 
\end{tikzpicture}
\end{document}