How to display a duck or marmot swallowed by a darkhole

Question

Following this question about representation of a darkhole, how could one represent a tikzduck or a tikzmarmot being swallowed by it.

No animal nor being should be harmed in the process.

I think this solution based on non-linear transforms or this one using transform canvas could help, but I don't know where to start really.

\documentclass[border=3.14pt]{standalone}
\usepackage{pgfplots}
\usepgfplotslibrary{colorbrewer}
\pgfplotsset{compat=newest}
\begin{document}
    \begin{tikzpicture}
        \begin{axis}[
            axis line style={draw=none},
            tick style={draw=none},
            colormap/Blues,
            data cs=polar,
            samples=50,
            domain=0:360,
            y domain=1:10,
            declare function={darkhole(\r)={-exp(-\r)};
                % added functions to calculate cartesian coordinates from polar coordinates
                pol2cartX(\angle,\radius) = \radius * cos(\angle);
                pol2cartY(\angle,\radius) = \radius * sin(\angle);
            },
            xtick={\empty},
            ytick={\empty},
            ztick={\empty},
        ]
            \addplot3 [surf,shader=flat,draw=black,z buffer=sort] {darkhole(y)};
        \end{axis}
    \end{tikzpicture}
\end{document}

Answer 1

A marmot would only fall in a black hole if it is a wormhole. Other than that, you need to draw the black hole in two stretches, first background, then the passenger(s), and then the foreground.

\documentclass[tikz,border=3.14pt]{standalone}
\usepackage{pgfplots}
\usepgfplotslibrary{colorbrewer}
\pgfplotsset{compat=1.16}
\usepackage{tikzmarmots}
\usepgfmodule{nonlineartransformations}
\makeatletter
\def\blackholetransformation{%
\pgf@xa=\pgf@x%
\pgf@ya=\pgf@y%
\pgfmathsetmacro{\myy}{\pgf@ya-40*exp(-0.04*abs(\the\pgf@xa))}%
\pgf@y=\myy pt}
\makeatother
\newsavebox\Back
\newsavebox\Front
\sbox\Back{\begin{tikzpicture}
        \begin{axis}[
            axis line style={draw=none},
            tick style={draw=none},
            colormap/Blues,
            data cs=polar,
            samples=25,
            y domain=1:10,
            declare function={darkhole(\r)={exp(-1)-exp(-\r)};
                % added functions to calculate cartesian coordinates from polar coordinates
                pol2cartX(\angle,\radius) = \radius * cos(\angle);
                pol2cartY(\angle,\radius) = \radius * sin(\angle);
            },
            xtick={\empty},
            ytick={\empty},
            ztick={\empty},
        ]
          \addplot3[surf,shader=flat,draw=black,z buffer=sort,
            domain=\pgfkeysvalueof{/pgfplots/view/az}:\pgfkeysvalueof{/pgfplots/view/az}+180] 
            {darkhole(y)};
          \addplot3[surf,shader=flat,draw=black,z buffer=sort,
            domain=\pgfkeysvalueof{/pgfplots/view/az}:\pgfkeysvalueof{/pgfplots/view/az}+180] 
            {-darkhole(y)}; 
         \addplot3[surf,shader=flat,draw=black,z buffer=sort,opacity=0,
            domain=\pgfkeysvalueof{/pgfplots/view/az}:\pgfkeysvalueof{/pgfplots/view/az}-180] 
            {darkhole(y)};  
         \addplot3[surf,shader=flat,draw=black,z buffer=sort,opacity=0,
            domain=\pgfkeysvalueof{/pgfplots/view/az}:\pgfkeysvalueof{/pgfplots/view/az}-180] 
            {-darkhole(y)}; 
        \end{axis}
    \end{tikzpicture}}
\sbox\Front{\begin{tikzpicture}
        \begin{axis}[
            axis line style={draw=none},
            tick style={draw=none},
            colormap/Blues,
            data cs=polar,
            samples=25,
            y domain=1:10,
            declare function={darkhole(\r)={exp(-1)-exp(-\r)};
                % added functions to calculate cartesian coordinates from polar coordinates
                pol2cartX(\angle,\radius) = \radius * cos(\angle);
                pol2cartY(\angle,\radius) = \radius * sin(\angle);
            },
            xtick={\empty},
            ytick={\empty},
            ztick={\empty},
        ]
          \addplot3[surf,shader=flat,draw=black,z buffer=sort,opacity=0,
            domain=\pgfkeysvalueof{/pgfplots/view/az}:\pgfkeysvalueof{/pgfplots/view/az}+180] 
            {darkhole(y)};
          \addplot3[surf,shader=flat,draw=black,z buffer=sort,opacity=0,
            domain=\pgfkeysvalueof{/pgfplots/view/az}:\pgfkeysvalueof{/pgfplots/view/az}+180] 
            {-darkhole(y)}; 
         \addplot3[surf,shader=flat,draw=black,z buffer=sort,
            domain=\pgfkeysvalueof{/pgfplots/view/az}:\pgfkeysvalueof{/pgfplots/view/az}-180] 
            {darkhole(y)};  
         \addplot3[surf,shader=flat,draw=black,z buffer=sort,
            domain=\pgfkeysvalueof{/pgfplots/view/az}:\pgfkeysvalueof{/pgfplots/view/az}-180] 
            {-darkhole(y)}; 
        \end{axis}
    \end{tikzpicture}}  
\begin{document}
\foreach \X in {-50,-48,...,-8,8,10,...,50}%{-50,-40,...,50}%
{\begin{tikzpicture}
\begin{scope}[local bounding box=nonlinear,transform shape
nonlinear=true]
 \pgftransformnonlinear{\blackholetransformation}
 \path[use as bounding box] (-5,-4) rectangle (5,5);
 \node[scale=2]{\usebox\Back};
 \begin{scope}[xshift={-1cm+\X*1mm},yshift={-1*tanh(\X/10)*4cm-1cm}]
  \marmot
 \end{scope}
 \node[scale=2]{\usebox\Front};
\end{scope} 
\end{tikzpicture}}
\end{document}

Another version with slower fall.

\documentclass[tikz,border=3.14pt]{standalone}
\usepackage{pgfplots}
\usepgfplotslibrary{colorbrewer}
\pgfplotsset{compat=1.16}
\usepackage{tikzmarmots}
\usepgfmodule{nonlineartransformations}
\makeatletter
\def\blackholetransformation{%
\pgf@xa=\pgf@x%
\pgf@ya=\pgf@y%
\pgfmathsetmacro{\myy}{\pgf@ya-60*exp(-0.06*abs(\the\pgf@xa))}%
\pgf@y=\myy pt}
\makeatother
\newsavebox\Back
\newsavebox\Front
\sbox\Back{\begin{tikzpicture}
        \begin{axis}[
            axis line style={draw=none},
            tick style={draw=none},
            colormap/Blues,
            data cs=polar,
            samples=25,
            y domain=1:10,
            declare function={darkhole(\r)={exp(-1)-exp(-\r)};
                % added functions to calculate cartesian coordinates from polar coordinates
                pol2cartX(\angle,\radius) = \radius * cos(\angle);
                pol2cartY(\angle,\radius) = \radius * sin(\angle);
            },
            xtick={\empty},
            ytick={\empty},
            ztick={\empty},
        ]
          \addplot3[surf,shader=flat,draw=black,z buffer=sort,
            domain=\pgfkeysvalueof{/pgfplots/view/az}:\pgfkeysvalueof{/pgfplots/view/az}+180] 
            {darkhole(y)};
          \addplot3[surf,shader=flat,draw=black,z buffer=sort,
            domain=\pgfkeysvalueof{/pgfplots/view/az}:\pgfkeysvalueof{/pgfplots/view/az}+180] 
            {-darkhole(y)}; 
         \addplot3[surf,shader=flat,draw=black,z buffer=sort,opacity=0,
            domain=\pgfkeysvalueof{/pgfplots/view/az}:\pgfkeysvalueof{/pgfplots/view/az}-180] 
            {darkhole(y)};  
         \addplot3[surf,shader=flat,draw=black,z buffer=sort,opacity=0,
            domain=\pgfkeysvalueof{/pgfplots/view/az}:\pgfkeysvalueof{/pgfplots/view/az}-180] 
            {-darkhole(y)}; 
        \end{axis}
    \end{tikzpicture}}
\sbox\Front{\begin{tikzpicture}
        \begin{axis}[
            axis line style={draw=none},
            tick style={draw=none},
            colormap/Blues,
            data cs=polar,
            samples=25,
            y domain=1:10,
            declare function={darkhole(\r)={exp(-1)-exp(-\r)};
                % added functions to calculate cartesian coordinates from polar coordinates
                pol2cartX(\angle,\radius) = \radius * cos(\angle);
                pol2cartY(\angle,\radius) = \radius * sin(\angle);
            },
            xtick={\empty},
            ytick={\empty},
            ztick={\empty},
        ]
          \addplot3[surf,shader=flat,draw=black,z buffer=sort,opacity=0,
            domain=\pgfkeysvalueof{/pgfplots/view/az}:\pgfkeysvalueof{/pgfplots/view/az}+180] 
            {darkhole(y)};
          \addplot3[surf,shader=flat,draw=black,z buffer=sort,opacity=0,
            domain=\pgfkeysvalueof{/pgfplots/view/az}:\pgfkeysvalueof{/pgfplots/view/az}+180] 
            {-darkhole(y)}; 
         \addplot3[surf,shader=flat,draw=black,z buffer=sort,
            domain=\pgfkeysvalueof{/pgfplots/view/az}:\pgfkeysvalueof{/pgfplots/view/az}-180] 
            {darkhole(y)};  
         \addplot3[surf,shader=flat,draw=black,z buffer=sort,
            domain=\pgfkeysvalueof{/pgfplots/view/az}:\pgfkeysvalueof{/pgfplots/view/az}-180] 
            {-darkhole(y)}; 
        \end{axis}
    \end{tikzpicture}}  
\begin{document}
\foreach \X in {-50,-48,...,50}
{\begin{tikzpicture}[declare function={darkhole(\r)=exp(-2.5)-exp(-\r);}]
 \path[use as bounding box] (-5,-6) rectangle (5,7);
 \node[scale=2]{\usebox\Back};
 \begin{scope}
  \clip (-5,6) -- plot[domain=-5:-0.5] ({\x},{25*darkhole(abs(5*\x))})
  -- plot[domain=-0.5:-5] ({\x},{-25*darkhole(abs(5*\x))})
  |- (5,-7)
  -- plot[domain=5:0.5] ({\x},{-25*darkhole(abs(5*\x))}) 
  -- plot[domain=0.5:5] ({\x},{25*darkhole(abs(5*\x))}) |-cycle;
  \begin{scope}[local bounding box=nonlinear,transform shape
  nonlinear=true]
   \pgftransformnonlinear{\blackholetransformation}
   \begin{scope}[xshift={-1cm+\X*1mm},yshift={-1*tanh(\X/10)*4cm-1cm}]
    \marmot
   \end{scope}
  \end{scope}
 \end{scope}  
 \node[scale=2]{\usebox\Front};
\end{tikzpicture}}
\end{document}