Scientific applications of the tikzducks

Question

Are the tikzducks used to explain any scientific stuff?

I'm currently compiling a list of such applications for an upcoming talk, so even if you are not able to share your image, it would be helpful to hear examples of topics the tikzducks are used for.

Please note, that no ducks may be harmed in your answers

Answer 1

It is possible to form a grammatical English sentence of length n, using only the words "duck" and "ducks", for all values of n.

Using tikzducks perhaps makes the visualization of the structures easier.

\documentclass{article}
\usepackage[margin=1in]{geometry}
\usepackage{amsthm}
\newtheorem{theorem}{Theorem}
\usepackage{tikzducks}
\usepackage[linguistics]{forest}
\usepackage{multicol}
\newcommand{\Ducks}{\begin{tikzpicture}[scale=.2]\duck\begin{scope}[xshift=1.5cm]\duck\end{scope}\end{tikzpicture}}
\let\ducks\Ducks
\usepackage{gb4e}
\begin{document}
\begin{theorem}
For any $n$, there is a grammatical English sentence of length $n$ consisting only of some combination of the words \emph{duck} and \emph{ducks}.  
\end{theorem}
Here are the first $6$ (with very simplified trees).
\begin{multicols}{2}
\begin{exe}
\ex Duck!
\ex Ducks duck.
\ex Ducks duck ducks.
\ex Ducks ducks duck duck.
\ex Ducks ducks duck duck ducks.
\ex Ducks ducks ducks duck duck duck.
\end{exe}
\columnbreak\setcounter{exx}{0}
\begin{exe}
\ex Duck!
\ex \Ducks{} duck.
\ex \Ducks{} duck \ducks.
\ex \Ducks{} \ducks{} duck duck.
\ex \Ducks{} \ducks{} duck duck \ducks.
\ex \Ducks{} \ducks{} \ducks{} duck duck duck.
\end{exe}
\end{multicols}
\setcounter{exx}{0}
\begin{multicols}{2}
\begin{exe}
\ex\begin{forest}
[S [NP\\pro ] [VP [V\\duck ]]]
\end{forest}
\ex\begin{forest}
[S [NP\\\Ducks ] [VP [V\\duck]]]
\end{forest}
\ex\begin{forest}
[S [NP\\\Ducks ] [VP [V\\duck ] [NP\\\ducks ]]]
\end{forest}
\ex\begin{forest}
[S [NP [NP\\\Ducks ][S [NP\\\Ducks ] [VP [V\\duck]]]] [VP [V\\duck]]]
\end{forest}
\ex
\begin{forest}
[S [NP [NP\\\Ducks ][S [NP\\\Ducks ] [VP [V\\duck]]]] [VP [V\\duck ] [NP\\\ducks ]]]
\end{forest}
\ex
\begin{forest}
[S [NP [NP\\\Ducks ][S [NP [NP\\\Ducks ][S [NP\\\Ducks ] [VP [V\\duck]]]] [VP [V\\duck]]]][VP [V\\duck]]]
\end{forest}
\end{exe}
\end{multicols}
\end{document}

Answer 2

Using the wake of a duck to explain the opening angle of Cherenkov light

(See https://physics.stackexchange.com/a/9483 for more details about this analogy)

\documentclass{standalone}
\usepackage{tikzducks}
\begin{document}
\begin{tikzpicture}
  \begin{scope}[scale=0.5,xshift=-23,yshift=320] 
    \duck
  \end{scope}

  \draw[black] 
    (10,6) circle (4.45)
    (9,6) circle (4)

    (8,6) circle (3.55)
    (7,6) circle (3.1)

    (6,6) circle (2.68)
    (5,6) circle (2.24)

    (4,6) circle (1.8)
    (3,6) circle (1.35)

    (2,6) circle (0.9)

    (1,6) circle (0.47)

  ; 
  \draw[blue,thick] 
    (12,0) -- (0,6) -- (12,12)
    (0,6) -- (15,6)
    (8.15,1.96) -- (10,6) -- (8.15,10.04)
    (8.8,6)arc(180:120:1.345551)
  ;
  \draw[thick,rotate=26.5,blue,->]   (4,5.35) -- ++(0,0.8);
  \draw[thick,rotate=26.5,blue,->]   (6,5.35) -- ++(0,0.8);
  \draw[thick,rotate=26.5,blue,->]   (8,5.35) -- ++(0,0.8);
  \draw[thick,rotate=26.5,blue,->]   (10,5.35) -- ++(0,0.8);
  \draw[thick,rotate=26.5,blue,->]   (12,5.35) -- ++(0,0.8);
  \draw[thick,rotate=26.5,blue,->]   (14,5.35) -- ++(0,0.8);
  \draw[thick,rotate=-26.5,blue,<-]   (-1.4,4.55) -- ++(0,0.8);
  \draw[thick,rotate=-26.5,blue,<-]   (0.6,4.55) -- ++(0,0.8);
  \draw[thick,rotate=-26.5,blue,<-]   (2.6,4.55) -- ++(0,0.8);
  \draw[thick,rotate=-26.5,blue,<-]   (4.6,4.55) -- ++(0,0.8);
  \draw[thick,rotate=-26.5,blue,<-]   (6.6,4.55) -- ++(0,0.8);
  \draw[thick,rotate=-26.5,blue,<-]   (8.6,4.55) -- ++(0,0.8);

  \node at (9.35,6.4) {\Large $\Theta_{c}$};
\end{tikzpicture}
\end{document}

---

Improved 3D version by @marmot

from https://chat.stackexchange.com/transcript/message/43703817#43703817

\documentclass{standalone}
\usepackage{tikzducks}
\usepackage{tikz-3dplot}
\begin{document}
\tdplotsetmaincoords{0}{0}
\begin{tikzpicture}
\begin{scope}[scale=0.5,xshift=-20,yshift=-20]
\duck
\end{scope}
\tdplotsetrotatedcoords{-30}{40}{45}
\begin{scope}[tdplot_rotated_coords]
\foreach \X in {1,...,10}
{
\draw[black] (0,0,\X) circle ({\X*0.45});
\draw[thick,blue,->] (0,{\X*0.45},\X) -- ++(0,0.32,{-0.3*0.45});
\draw[thick,blue,->] (0,{-\X*0.45},\X) -- ++(0,-0.32,{-0.3*0.45});
}
\draw[blue,thick]
(0,4.5,10) -- (0,0,0) -- (0,-4.5,10)
(0,0,0) -- (0,0,14.5) coordinate (P)
(0,4.5,10) -- (0,0,14.5) -- (0,-4.5,10);
\coordinate (M) at (0,0,10);
\end{scope}
\tdplotsetrotatedcoords{-120}{150}{0}
\begin{scope}[tdplot_rotated_coords,red]
\draw (M) arc (-90:-57:3) node[midway,right,yshift=-5]{\Large $\Theta_{c}$};
\end{scope}
\end{tikzpicture}
\end{document}

Answer 3

\documentclass{article}
\usepackage{tikzducks}
\begin{document}
\section*{Length contraction}
\begin{tabular}{ccc}
 $v=0$ & $v=0.5\cdot c$ & $v=0.9\cdot c$\\
 \begin{tikzpicture}
 \path[use as bounding box](0,0) rectangle (2.4,2.4);
 \duck
 \end{tikzpicture}
 &
 \begin{tikzpicture}
 \path[use as bounding box](-0.25,0) rectangle (2.15,2.4);
 \pgftransformcm{sqrt(1-0.5^2)}{0}{0}{1}{\pgfpoint{0cm}{0cm}} 
 \duck
 \end{tikzpicture}
 &
 \begin{tikzpicture}
 \path[use as bounding box](-0.5,0) rectangle (1.9,2.4);
 \pgftransformcm{sqrt(1-0.9^2)}{0}{0}{1}{\pgfpoint{0cm}{0cm}} 
 \duck
 \end{tikzpicture}
\end{tabular}\\
Don't worry, the ducks are fine!
\end{document}

Just for fun: rocket ducks.

\documentclass{article}
\addtolength{\textwidth}{2cm}
\usepackage{tikzducks}
\usetikzlibrary{shadings,fadings}
\newcommand{\RocketDuck}{ \duck
 \shade[ball color=blue,opacity=0.15] (1,1) circle (1.3);
 \fill [color=orange,path fading=east] (3.9,-0.75) 
 -- ++({3*cos(25)},{3*sin(25)}) arc (25:-25:3) 
 -- ++ ({-3*cos(25)},{3*sin(25)}) -- cycle;
 \shade[bottom color=red,top color=red!25!white] (4,0.25) arc (90:-90:0.25 and 1) -- (-2,-1.75) 
 arc (-90:90:0.25 and 1) -- cycle;
 \shade[bottom color=blue,top color=blue!25!white] (-2,-1.75) arc (-90:90:0.25 and 1) 
 -- (-3.2,-0.75) -- cycle;
}
\begin{document}
\section*{Length contraction (Don't worry, the ducks are fine!)}
 \begin{tikzpicture}
 \draw[ultra thick,-latex] (-1,1.8) -- (-3,1.8) node[midway,above]{$v=0$};
 \RocketDuck
 \begin{scope}[yshift=-5cm]
 \draw[ultra thick,-latex] (-1,1.8) -- (-3,1.8) node[pos=0.45,above]{$v=0.5\cdot c$};
 \pgftransformcm{sqrt(1-0.5^2)}{0}{0}{1}{\pgfpoint{0cm}{0cm}} 
 \RocketDuck
 \end{scope}
 \begin{scope}[yshift=-10cm]
 \draw[ultra thick,-latex] (-1,1.8) -- (-3,1.8) node[pos=0.45,above]{$v=0.9\cdot c$};
 \pgftransformcm{sqrt(1-0.9^2)}{0}{0}{1}{\pgfpoint{0cm}{0cm}} 
 \RocketDuck
 \end{scope}
 \end{tikzpicture}
\end{document}

Answer 4

Here's my math joke about the formula calculating the volume of cylinder/disk which might be easier remembered by students/pupils:

The chef duck is perfectly suited for this:

\documentclass[10pt]{article}

\usepackage[most]{tcolorbox}
\usepackage{amsmath}
\usepackage{tikzducks}


\begin{document}
\boldmath
\begin{tcbraster}[raster columns=2,raster rows=2,height=15cm,raster equal height]
\begin{tcolorbox}[height=0.5\linewidth,valign=center,halign=center,width=0.5\linewidth,enhanced, fontupper={\large},colback=yellow!20!white, circular arc, drop shadow]

  What is the formula for the volume of a cylinder with

  \begin{itemize}
  \item radius $z$ 
  \item[]  and
  \item height $a$
  \end{itemize}


  ?
\end{tcolorbox} 
\begin{tcolorbox}[drop shadow,colback=yellow!20!white]
\begin{tikzpicture}[scale=2.5]
\duck[chef=white!95!yellow,
rollingpin=brown!80!black, think={$ V = pi \cdot z \cdot z \cdot a$}]
\end{tikzpicture}
\end{tcolorbox}
\end{tcbraster} 
\end{document}

No ducks were harmed → they are just the pizza chefs...

Answer 5

In order to add some chemistry to this list, here is a laboratory duck helping to explain the concept of chirality.

\documentclass{standalone}
\usepackage{tikzducks}
\usepackage{chemfig}
\usepackage{arydshln}
\begin{document}
\colorbox{black!20!white}{
\begin{tabular}{c:c}
\begin{tikzpicture}[xscale=-1,transform shape]
    \duck[glasses=gray,tshirt=black!10!white,jacket=white]
    \path[xshift=35,yshift=20,scale=0.2,rotate=-10,draw,clip] (-0.5,1.75) to[rounded corners=2pt]++(0,-1)to[rounded corners=2pt]++(-1,-2.5)to[rounded
corners=2pt, bend right=10pt]++(3,0) to[rounded corners=2pt]++(-1,2.5)--++(0,1)++(-0.5,0) circle [x radius=0.5, y radius=0.1];
\path[xshift=35,yshift=20,scale=0.2,rotate=-10,fill=green!90!black](-1.6,-2) rectangle (1.6,{1cm-2cm});
\path[xshift=35,yshift=20,scale=0.2,rotate=-10,fill=green!90!white] (0,1cm-2cm) circle [x radius=1.5cm-(1cm-0.25cm)*0.4 , y radius=0.1 cm];
\path[xshift=35,yshift=20,scale=0.2,rotate=-10,draw=black,  line width=0.2pt, fill=green!70!white] (0,0) circle (5pt);
\path[xshift=35,yshift=20,scale=0.2,rotate=-10,draw=black,  line width=0.2pt, fill=green!70!white] (-0.2,0.75) circle (3pt);
\path[xshift=35,yshift=20,scale=0.2,rotate=-10,draw=black,  line width=0.2pt, fill=green!70!white] (0.25,1.15) circle (2pt);
\path[xshift=35,yshift=20,scale=0.2,rotate=-10,draw=black,  line width=0.2pt, fill=green!70!white] (0,1.4) circle (4pt);
\path[xshift=35,yshift=20,scale=0.2,rotate=-10,draw=black,  line width=0.2pt, fill=green!70!white] (-0.25,-0.5) circle (3pt);
\path[xshift=35,yshift=20,scale=0.2,rotate=-10,draw=black,  line width=0.2pt, fill=green!70!white] (0.25,-1) circle (5pt);
\end{tikzpicture}
&
\begin{tikzpicture}
   \duck[glasses=gray,tshirt=black!10!white,jacket=white]
\path[xshift=35,yshift=20,scale=0.2,rotate=-10,draw,clip] (-0.5,1.75) to[rounded corners=2pt]++(0,-1)to[rounded corners=2pt]++(-1,-2.5)to[rounded
corners=2pt, bend right=10pt]++(3,0) to[rounded corners=2pt]++(-1,2.5)--++(0,1)++(-0.5,0) circle [x radius=0.5, y radius=0.1];
\path[xshift=35,yshift=20,scale=0.2,rotate=-10,fill=green!90!black](-1.6,-2) rectangle (1.6,{1cm-2cm});
\path[xshift=35,yshift=20,scale=0.2,rotate=-10,fill=green!90!white] (0,1cm-2cm) circle [x radius=1.5cm-(1cm-0.25cm)*0.4 , y radius=0.1 cm];
\path[xshift=35,yshift=20,scale=0.2,rotate=-10,draw=black,  line width=0.2pt, fill=green!70!white] (0,0) circle (5pt);
\path[xshift=35,yshift=20,scale=0.2,rotate=-10,draw=black,  line width=0.2pt, fill=green!70!white] (-0.2,0.75) circle (3pt);
\path[xshift=35,yshift=20,scale=0.2,rotate=-10,draw=black,  line width=0.2pt, fill=green!70!white] (0.25,1.15) circle (2pt);
\path[xshift=35,yshift=20,scale=0.2,rotate=-10,draw=black,  line width=0.2pt, fill=green!70!white] (0,1.4) circle (4pt);
\path[xshift=35,yshift=20,scale=0.2,rotate=-10,draw=black,  line width=0.2pt, fill=green!70!white] (-0.25,-0.5) circle (3pt);
\path[xshift=35,yshift=20,scale=0.2,rotate=-10,draw=black,  line width=0.2pt, fill=green!70!white] (0.25,-1) circle (5pt);
\end{tikzpicture}
\\[0.25cm]
\scalebox{0.6}{\chemfig{A-[:30](-[:90]B)(<:[:-10]C)(<[:-50]D)}}
&
\scalebox{.6}{\chemfig{A-[:150](-[:90]B)(<:[:190]C)(<[:230]D)}}
\end{tabular}
}

\end{document}

PS: Thanks to appropriate personal protective equipment (safety glasses and a lab coat) no ducks were harmed during the experiments...

The code for the erlenmeyer flask is heavily inspired frome this question: tikz and \pgfdeclareshape why the text is not at the center anchor?

Answer 6

Moebius Duck's evocation

\documentclass[margin=1cm,tikz]{standalone}
\usepackage{luatex85,tikzducks,ifthen}
\usetikzlibrary{calc}

\begin{document}

\foreach \frame in {0,...,81} {%

\pgfmathtruncatemacro{\x}{mod(\frame,41)}

\ifthenelse{\x>64 \OR \x<4}{\def\Orient{-1}}{\def\Orient{1}}

\begin{tikzpicture}[x  = {(1cm,0cm)},
                    y  = {(45:.5cm)},
                    z  = {(0cm,1.5cm)},
                    scale=3]

\foreach \L [count=\z from -2, evaluate=\z as \y using \z/4 ] in {A,...,E} {%
    \foreach \x [count=\n from 0] in {0,9,...,360} {%
        \pgfmathsetmacro{\T}{1+0.5*\y*cos(\x/2)}
        \pgfmathsetmacro{\X}{\T*cos(\x)}
        \pgfmathsetmacro{\Y}{\T*sin(\x)}
        \pgfmathsetmacro{\Z}{0.5*\y*sin(\x/2)}
        \path (\X,\Y,\Z) coordinate (\L\n)
            ;
    }
}


    \ifthenelse{\frame=62 \OR \frame=63}{%
    \begin{scope}[x={(1cm,0cm)},
                    y={(0cm,1cm)},
                    shift={($(C\x)-(.05,.03)$)},
                    scale=.05]
    \duck
    \end{scope}}{}



\foreach \i  [evaluate=\i as \j using int(\i+1),
            evaluate=\i as \K using 80-30*cos(9*(\i-22.5))
            ] in {0,1,...,39} {%
    \ifthenelse{\frame=18 \AND \i>17 \AND \i<20}{%
    \begin{scope}[x={(1cm,0cm)},
                    y={(0cm,1cm)},
                    shift={($(C18)-(.05,.03)$)},
                    scale=.05]
    \duck
    \end{scope}}{}
    \draw[smooth,gray,fill=orange!25!white!\K!blue]
                (A\i) -- (E\i) -- (E\j) -- (A\j) -- cycle ;
    \draw[smooth,gray] (B\i) -- (B\j) (D\i) -- (D\j) ;
    \draw[smooth,thick] (C\i) -- (C\j) ;
}

    \ifthenelse{\frame<18 \OR \frame>63}{%
    \begin{scope}[x={(1cm,0cm)},
                    y={(0cm,1cm)},
                    shift={($(C\x)-(.05,.03)$)},
                    scale=.05]
    \duck
    \end{scope}}{}


\end{tikzpicture}   }

\end{document}

Answer 7

Ducks preserve the amount of movement

\documentclass[tikz,margin=1cm]{standalone}
\usepackage{tikzducks,luatex85,ifthen}
\usetikzlibrary{calc,backgrounds}

\pgfdeclarelayer{background}
\pgfdeclarelayer{foreground}
\pgfsetlayers{background,main,foreground}


\newcommand{\Duck}[1]{%
\begin{scope}[scale=\scl,shift={(-1.05,-1.075)}]
\clip (.1,.1) rectangle (2.1,2.15) ;
\coordinate (dck) at (1.05,1.075) ;
\duck
\end{scope}
\begin{pgfonlayer}{background}
\draw[gray!25] (dck) -- (A#1) ;
\end{pgfonlayer}
}

\begin{document}

\def\pas{.434}
\def\scl{.22}

\foreach \x in {-9,...,9,8,7,...,-8} {%


\begin{tikzpicture}

\path[use as bounding box] (-2,0) rectangle (4,1.5) ;

\foreach \i [evaluate=\i as \j using (\i-1)*\pas] in {0,...,6} {%
\coordinate[] (A\i) at (\j,1.5) ;
\fill (A\i) circle (1pt) ;
}

\ifthenelse{\x<0}{%
    \pgfmathsetmacro{\L}{-90+60*sin(10*\x)}
    \gdef\R{-90}
    }{%
    \gdef\L{-90}
    \pgfmathsetmacro{\R}{-90+60*sin(10*\x)}
    }

\begin{scope}[shift=($(A6)+(\R:1.5)$)]
\Duck{6}
\end{scope}

\begin{scope}[shift=($(A0)+(\L:1.5)$)]
\Duck{0}
\end{scope}


\foreach \i in {1,...,5} {%
    \begin{scope}[xshift=\pas*\i cm -\pas cm]
    \Duck{\i}
    \end{scope}
}


\end{tikzpicture}}
\end{document}

Answer 8

I will admit that this was slightly inspired by this question, but here is a genuine worksheet that I used today.

Answer 9

The Doppler Duck's affect

\documentclass[margin=1cm,tikz]{standalone}
\usepackage{luatex85,tikzducks,ifthen}
\usetikzlibrary{calc,decorations.markings,backgrounds}

\pgfdeclarelayer{background}
\pgfdeclarelayer{foreground}
\pgfsetlayers{background,main,foreground}


\begin{document}

\foreach \i [count=\frame from 1] in {-12.5,...,12.5} {

\ifthenelse{\frame>14}{\def\K{blue}}{\def\K{red}}

\begin{tikzpicture}

\def\X{15}
\def\Y{2}

\filldraw[gray!50,transform canvas={xslant=2}] (-\X,-\Y) -- (\X,-\Y) -- (\X,\Y) -- (-\X,\Y) -- cycle ;


\draw[line width=5pt,
    white,
    transform canvas={xslant=2},
    dash pattern=on 20mm off 8mm] (-\X,0) -- (\X,0) ;

    \begin{pgfonlayer}{foreground}
    \begin{scope}[shift={(\i,-.9)},xscale=-1]
    \ifthenelse{\frame=14}{%
        \duck[speech={Coin !},bubblecolour=white!95!yellow]}{%
        \duck
        }
    \coordinate (LH) at (wing) ;
    \end{scope}
    \end{pgfonlayer}

    \begin{scope}[shift={(-\i,.6)}]
    \duck
    \coordinate (RH) at (wing) ;
    \end{scope}

    \path[decoration={%
    markings,% switch on markings
    mark=between positions .18 and .98 step 0.2 with {
        \draw[ultra thick,\K] (0,0)
            arc (0:15:\pgfkeysvalueof{/pgf/decoration/mark info/sequence number}) ;
        \draw[ultra thick,\K] (0,0)
            arc (0:-15:\pgfkeysvalueof{/pgf/decoration/mark info/sequence number}) ;
        }
    },
    postaction={decorate}] (LH) -- (RH) ;

\end{tikzpicture}
}
\end{document}

The redshift version :

\documentclass[margin=1cm,tikz]{standalone}
\usepackage{luatex85,tikzducks,ifthen}
\usetikzlibrary{calc,decorations.markings,backgrounds}

\pgfdeclarelayer{background}
\pgfdeclarelayer{foreground}
\pgfsetlayers{background,main,foreground}


\begin{document}

\foreach \i [count=\frame from 1] in {-12.5,...,12.5} {

\pgfmathsetmacro{\Koeff}{100*cos(\i/15*90)}

\ifthenelse{\frame<14}{%
    \def\K{yellow!\Koeff!blue}}{%
    \def\K{yellow!\Koeff!red}
}

\begin{tikzpicture}

\def\X{15}
\def\Y{2}

\filldraw[gray!50,transform canvas={xslant=2}] (-\X,-\Y) -- (\X,-\Y) -- (\X,\Y) -- (-\X,\Y) -- cycle ;


\draw[line width=5pt,
    white,
    transform canvas={xslant=2},
    dash pattern=on 20mm off 8mm] (-\X,0) -- (\X,0) ;

    \begin{pgfonlayer}{foreground}
    \begin{scope}[shift={(\i,-.9)},xscale=-1]
    \ifthenelse{\frame=14}{%
        \duck[body=\K,speech={Coin !},bubblecolour=white!95!yellow]}{%
        \duck[body=\K]
        }
    \coordinate (LH) at (wing) ;
    \end{scope}
    \end{pgfonlayer}

    \begin{scope}[shift={(-\i,.6)}]
    \duck[body=\K]
    \coordinate (RH) at (wing) ;
    \end{scope}

\end{tikzpicture}
}
\end{document}

Answer 10

Visualization of a sinus function

\documentclass{article}
\usepackage[utf8]{inputenc} %probably not needed ...
\usepackage[T1]{fontenc}
\usepackage{geometry}
\geometry{papersize={128mm,96mm},margin=0.5cm} %\textwidth=11.8, \textheight=8.6
\usepackage[x11names]{xcolor}
\usepackage{tikzducks}
\usetikzlibrary{shapes.geometric}
\pagestyle{empty}
\parindent=0pt
\usepackage{eso-pic}
\usepackage{xfp}
\tikzstyle{witchstars}=[star, star points=5, star point ratio=2.25, draw,inner sep=1.3pt,anchor=outer point 3]



\begin{document}
\AddToShipoutPictureBG{%
 \AtPageLowerLeft{%
 \begin{tikzpicture}[overlay,remember picture]
 \fill[DeepSkyBlue3] (0,0) rectangle (\paperwidth,\paperheight);
 \pgfmathsetseed{2}
 \end{tikzpicture}}}

\newcommand\loopmax{30}

\foreach \z in {1,2,...,\loopmax}{%
\begin{tikzpicture}
\path (0,0) rectangle (\textwidth,\textheight);
\begin{scope}[scale=2]
%\draw[domain=0:10, black,smooth]   plot (\x,{sin(\x r)+0.5}) ;
\end{scope}
\begin{scope}[overlay,
              xshift=\fpeval{0.67-\z*(0.67/\loopmax)}\textwidth,
              yshift=\fpeval{sin(\z/\loopmax*2*pi)+0.5}cm ]
\begin{scope}[scale=2]

\duck[witch=black!50!gray,
longhair=red!80!black,
jacket=black!50!gray,
magicwand]
\fill[red] (0,0) node[witchstars,fill=red,inner sep=2.3pt]{};
\end{scope}
\end{scope}
\foreach \y in {1,2,...,\loopmax}{%
 \begin{scope}[overlay,
              xshift=\fpeval{0.67-\y*(0.67/\loopmax)}\textwidth,
              yshift=\fpeval{sin(\y/\loopmax*2*pi)+0.5}cm ]
 \fill[] (0,0) node[witchstars,fill=yellow,inner sep=1.3pt]{};
 \end{scope}
}

\end{tikzpicture}\newpage}

\end{document}

Answer 11

It can be used to illustrate Occam's razor, which could be argued to be the epitome of scientific guessing:

If it looks like a duck, floats like a duck, and bobs its head like a duck, then obviously it is a duck! (Even if it is just a toy duck.)

Answer 12

Here are some ducks illustrating the need for sidelobe supression in radar. (I may have been a little bit inspired by this question, but I used this in a real presentation.)

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{calc, positioning, shapes.arrows}
\usepackage{tikzducks}

%%% extract coordinate
\newdimen\XCoord
\newdimen\YCoord
\newcommand*{\ExtractCoordinate}[1]{\path (#1); \pgfgetlastxy{\XCoord}        
{\YCoord};}%

%%% Waves, source: https://tex.stackexchange.com/questions/423489/concentric-circle-segments-between-two-points-in-tikz/423567#423567 
%#1=Number of waves
%#2 ans #3 point A and B
%#4 Angle of first wave
%#5 Colour of waves
\def\NumSignalsFromToAngle#1#2#3#4#5{%
    \def\NumberSignals{#1}
    \ExtractCoordinate{#2}
    \xdef\Xa{\XCoord}
    \xdef\Ya{\YCoord}
    \ExtractCoordinate{#3}
    \xdef\Xb{\XCoord}
    \xdef\Yb{\YCoord}
    \def\lw {2} %line width
    \pgfmathsetmacro\dist{10*sqrt((\Xb/10-\Xa/10)^2+(\Yb/10-\Ya/10)^2)}
    \pgfmathsetmacro\step{\dist/\NumberSignals}
    \def\offset{0.02*\dist}
    \pgfmathsetmacro\AngleFromAToB{\ifdim\Xb>\Xa atan((\Yb/10-\Ya/10)/(\Xb/10 -\Xa/10))\else \ifdim \Xb<\Xa 180+atan((\Yb/10-\Ya/10)/(\Xb/10 -\Xa/10))\else\ifdim\Ya>\Yb -90\else90\fi\fi\fi}
    \foreach \i in {1,...,\NumberSignals}
        {%
        \coordinate(Point) at ($(#2)+({((\step pt)*(2*\i-1)/2-\offset)*cos(\AngleFromAToB) },{(((\step pt)*(2*\i-1)/2-\offset)*sin(\AngleFromAToB)})$);
        \pgfmathsetmacro\r{\step/2*(2*\i-1)}
        %\l_1=\l_i => \angle_i=\angle_1/(2i-1)
        \pgfmathsetmacro\angle{#4/(2*\i-1)}
        \draw[line width = \lw, #5]  (Point) arc (\AngleFromAToB:    {\AngleFromAToB+\angle/2}:\r pt);
        \draw[line width = \lw, #5]  (Point) arc (\AngleFromAToB:{\AngleFromAToB-\angle/2}:\r pt);
    }
}

\begin{document}

\begin{tikzpicture}
    %%% radar
    \def\h{2} %height
    \def\xd{0.5} %x-depth
    \def\yd{0.12} %y-depth
    \def\xw{1.2}   %x-width
    \def\yw{1} %y-width
    \coordinate (A) at (0,0);
    \coordinate (B) at ($(A) + (\xd,\yd) $);
    \coordinate (C) at ($(B) + (0,\h)$);
    \coordinate (D) at ($(A) + (0,\h)$);
    \coordinate (E) at ($(A) + (-\xw, \yw)$);
    \coordinate (F) at ($(E) + (0, \h)$);
    \coordinate (G) at ($(F) + (\xd,\yd)$);

    \shade[bottom color=gray!90, top color=black!30](A) -- (B) -- (C) -- (D) -- (A);
    \shade[bottom color=gray!80, top color=black!10](A) -- (D) -- (F) -- (E) -- (A);
    \shade[bottom color=gray!80, top color=black!10] (D) -- (C) -- (G) -- (F) -- (D);

    \coordinate (radar) at ($ (A) !0.5! (F)$);

    %%% graduate duck
    \coordinate (T) at ($ (radar) + (-5,0) $);
    \begin{scope}[shift = {($(T) + (-1,-0.4)$)}, scale = 0.5]
        \duck[book=\scalebox{0.6}{$\beta$},
            bookcolour=blue!60!red!70!white,graduate=gray!20!black,
            tassel=red!70!black];
    \end{scope}
    \NumSignalsFromToAngle{6}{radar}{T}{130}{blue!70}
    \NumSignalsFromToAngle{6}{T}{radar}{130}{red!70}
    \coordinate (midpos) at ($(radar) !0.5! (T) $);
    \node[single arrow,fill=red!50, above = of midpos]  {\scriptsize reflected};
    \node[single arrow,fill=blue!50, below = of midpos, shape border rotate = 180]  {\scriptsize emitted};

    %%% kulturman duck 
    \coordinate (T) at ($ (radar) + (-2,2) $);
    \coordinate (R) at ($ (radar) + (0,\h/3) $);
    \begin{scope}[shift = {($(T) + (+0.2,-0.3)$)}, yscale=.5,xscale=-.5]
        \duck[crazyhair, wine=red!70!black];
    \end{scope}
    \NumSignalsFromToAngle{3}{T}{R}{130}{red!70}

    %%% mirror duck
    \coordinate (T) at ($ (radar) + (-0.5,-1.5) $);
    \coordinate (R) at ($ (radar) + (0,-\h/3) $);
    \begin{scope}[shift = {($(T) + (-1,-1)$)}, scale = 0.5]
        \duck[beret=red!40!blue!90!white, signpost, signback=white!80!brown];
    \end{scope}
    \NumSignalsFromToAngle{2}{R}{T}{130}{blue!50}
    \NumSignalsFromToAngle{2}{T}{R}{130}{red!70}

    %%% mystery duck
    \coordinate (T) at ($ (radar) + (-6,-2) $);
    \coordinate (R) at (radar);%($ (radar) + (\xw/2,-\h/3) $);
    \begin{scope}[shift = {($(T) + (0,-0.5)$)}, yscale=.5,xscale=-.5]
        \duck[mask=black,cape=black];
    \end{scope}
    \NumSignalsFromToAngle{7}{T}{R}{130}{red!70}
\end{tikzpicture}

\end{document}

Answer 13

Dispersion of water waves

This answer can be seen as an extension to the answer for the Cherenkov effect. The effect is observed in the real world (just search for it or look into the relevant Wikipedia articles), when ducks (or boats, or anthing else) swim.

If a duck just sits in the water and wobbles up and down, we can observe circles of water waves. (the code for this duck is easily found in the manual)

But when the duck swims with a (constant) velocity and naturally continues to wobble/continues to excite waves, these circles all have different origins. We would expect something like in the answer for the Cherenkov effect: Only in two direction for each wabe circle, there is a positive interference and two wavefronts should appear. The opening angle of the depends on the speed of the duck and the propagation speed of the water wave.

But this is not what is observed in reality! Water waves have a frequency-dependent speed of propagation (aka dispersion), and each emitted pulse (here denoted in time steps $\delta t$) has a group velocity and a different phase velocity. The angle where the constructive interference happens is determined by the groupd velocity because this one determines where the pulse is currently travelling, but inside this pulse, the phase velocity determines how the wavefront is oriented.

Overall, this leads to a picture like the following one.

The angles are not correct because I am too lazy (I think, they are quite fixed due to physics.) Also the wavefront shape is probably not perfect.

Code for the first part

\documentclass{standalone}
\usepackage{tikz}
\usetikzlibrary{ducks}

\begin{document}

\begin{tikzpicture}
  \begin{scope}[rotate=30,] 
  \draw[gray] 
    (8,6) circle (3.55)
    (6,6) circle (2.68) 
    (4,6) circle (1.8) 
    (2,6) circle (0.9)     
  ;
  \draw [<->,very thick,gray] (2,6) -- (4,6) node[midway,above,rotate=30] {$v_\mathrm{duck}\Delta t$} ;
  \draw [<->,very thick,gray] (4,6) -- (6,6) node[midway,above,rotate=30] {$v_\mathrm{duck}\Delta t$} ;
  \draw [<->,very thick,gray] (6,6) -- (8,6) node[midway,above,rotate=30] {$v_\mathrm{duck}\Delta t$} ;
  \draw [ ->,very thick] (2,6) -- ({2-0.90*sin(28)},{6-0.90*cos(28)}) node[midway,right,rotate=00] {$v_\mathrm{wave}\Delta t$};
  \draw [ ->,very thick] (4,6) -- ({4-1.80*sin(28)},{6-1.80*cos(28)}) node[midway,above,rotate=-90] {$2v_\mathrm{wave}\Delta t$};
  \draw [ ->,very thick] (6,6) -- ({6-2.68*sin(28)},{6-2.68*cos(28)}) node[midway,above,rotate=-90] {$3v_\mathrm{wave}\Delta t$};
  \draw [ ->,very thick] (8,6) -- ({8-3.55*sin(28)},{6-3.55*cos(28)}) node[midway,above,rotate=-90] {$4v_\mathrm{wave}\Delta t$};
  \draw[blue,thick] (12,0) -- (0,6) -- (12,12);
  \draw[gray,dashed]  (0,6) -- (15,6);
  \draw (-.5,6) pic[scale=0.75] {duck};
  \end{scope}  


\end{tikzpicture}

\end{document}

Similar Code for the second part

\documentclass{standalone}
\usepackage{tikz}
\usetikzlibrary{ducks}

\begin{document}

\begin{tikzpicture}
  \begin{scope}[rotate=30,] 
  \draw[gray] 
    (8,6) circle (3.55)
    (6,6) circle (2.68) 
    (4,6) circle (1.8) 
    (2,6) circle (0.9)     
  ;
  \begin{scope}
  \clip (0,6) -- (1,7) -- (11,12) -- (11,11) -- (1,6) -- cycle;
  \foreach \x in {0.7,1.4,...,5}{
  \draw[ultra thick,blue] (\x,6) -- (\x+7,6+7);
  }
  \end{scope}
  \begin{scope}
  \clip (0,6) -- (1,5) -- (11,0) -- (11,1) -- (1,6) -- cycle;
  \foreach \x in {0.7,1.4,...,5}{
  \draw[ultra thick,blue] (\x,6) -- (\x+7,6-7);
  }
  \end{scope}
  \draw[blue!50!gray,semithick] (12,0) -- (0,6) -- (12,12);
  \draw[gray,dashed]  (0,6) -- (15,6);
  \draw (-.5,6) pic[scale=0.75] {duck};
  \end{scope}  


\end{tikzpicture}

\end{document}