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coincidence effect.tex
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coincidence effect.tex
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\documentclass[border={1cm 0.5cm 1cm -1.25cm}]{standalone} %E,S,W,N
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{tikz}
%“The coincidence effect,” from Taylor, Rupert. (1970). Noise. New York: Penguin, fig. 41
%Note: this takes a long time to compile, because of all of the random dots
%increasing the density would make it look nicer, but who's got that kind of time?
\begin{document}
\begin{tikzpicture}
%RANDOM DOTS (total: 2800)
%based on https://tex.stackexchange.com/questions/145969
\draw[domain=-7.25:0,only marks,mark=*,samples=300,mark size=1] plot (\x,{0.5*6+0.5*9.125+0.5*\x + 0.5*rand*-1.75}); %large dots, upper band
\draw[domain=-7.25:0,only marks,mark=*,samples=300,mark size=1] plot (\x,{0.5*6+0.5*3+0.5*\x+0.5*rand*-1.5}); %large dots, lower band
%% \draw[domain=-7.25:0,only marks,mark=*,samples=300,mark size=1] plot (\x,{0.5*3.125+0.5*9.125+0.5*\x + 0.5*rand*-4.5}); %large dots
\draw[domain=-7.25:0,only marks,mark=*,samples=300,mark size=0.875] plot (\x,{0.5*3.125+0.5*9.125+0.5*\x + 0.5*rand*-3.5}); %big dots
\draw[domain=-7.25:0,only marks,mark=*,samples=500,mark size=0.875] plot (\x,{0.5*3.125+0.5*9.125+0.5*\x + 0.5*rand*-2.5}); %medum dots
\draw[domain=-7.25:0,only marks,mark=*,samples=300,mark size=0.75] plot (\x,{0.5*3.125+0.5*9.125+0.5*\x + 0.5*rand*-1.25}); %small dots
\draw[domain=-7.25:0,only marks,mark=*,samples=300,mark size=0.75] plot (\x,{0.5*3.125+0.5*9.125+0.5*\x + 0.5*rand*-0.5}); %small dots
% \draw[green, thick, domain=-7.25:-1] plot (\x, {9.125+0.5*\x}); %imaginary upper line
% \draw[blue, thick, domain=-7.25:-1] plot (\x, {6+0.5*\x});
% \draw[very thick,gray] (-7.25,2.375)--(0,6);
% \draw[green, thick, domain=-7.25:-1] plot (\x, {3.125+0.5*\x}); %middle line
% \draw[very thick,gray] (-7.25,-3.625)--(0,0);
% \draw[blue, thick, domain=-7.25:-1] plot (\x, {1.5625+0.5*\x});
% \draw[blue, thick, domain=-7.25:-1] plot (\x, {0+0.5*\x});
% \draw[green, thick, domain=-7.25:-1] plot (\x, {-2.875+0.5*\x}); %lower line
\draw[domain=-7.25:0,only marks,mark=*,samples=300,mark size=1] plot (\x,{0.5*3.125+0.5*\x+0.5*rand*-1.75}); %large dots, upper band
\draw[domain=-7.25:0,only marks,mark=*,samples=300,mark size=1] plot (\x,{-0.5*3.125+0.5*\x+0.5*rand*1.5}); %large dots, lower band
%% \draw[domain=-7.25:0,only marks,mark=*,samples=300,mark size=1] plot (\x,{0.5*3.125-0.5*2.875+0.5*\x + 0.5*rand*-4.5}); %large dots
\draw[domain=-7.25:0,only marks,mark=*,samples=300,mark size=0.875] plot (\x,{0.5*3.125-0.5*2.875+0.5*\x + 0.5*rand*-3.5}); %big dots
\draw[domain=-7.25:0,only marks,mark=*,samples=500,mark size=0.875] plot (\x,{0.5*3.125-0.5*2.875+0.5*\x + 0.5*rand*-2.5}); %medium dots
\draw[domain=-7.25:0,only marks,mark=*,samples=300,mark size=0.75] plot (\x,{0.5*3.125-0.5*2.875+0.5*\x + 0.5*rand*-1.25}); %small dots
\draw[domain=-7.25:0,only marks,mark=*,samples=300,mark size=0.75] plot (\x,{0.5*3.125-0.5*2.875+0.5*\x + 0.5*rand*-0.5}); %tiny dots
%COVERUP
\fill[white] (0,6) to[out=90,in=145] (-1,9) to[bend left] cycle;
\fill[white,rotate around={30:(0,7)}] (0,7) rectangle (2,9);
\fill[white] (0,0) to[out=90,in=145] (-1,3) to[out=85,in=45] (0,6) to[bend left] cycle;
\fill[white] (0,0) to[out=45,in=85] (-1,-3) to[out=145,in=90] (0,-6) to[bend right] cycle;
%WAVY LINE
\draw[ultra thick,domain=0:15,samples=100,rotate=270] plot (-7.5+\x,{-.5+.5*sin(12.5/12*\x r)});
% \fill[red] (0,0) circle (3pt); \fill[red] (0,6) circle (3pt); %peaks
% \fill[blue] (-1,3) circle (3pt);\fill[blue] (-1,-3) circle (3pt); %troughs
%DIAGONAL LINES
\draw[very thick] (0,6)--(4,8); %top, diagonal
\draw[very thick] (0,6)--(7.5,6); %top, horizontal
% \draw[very thick] (-7.25,-0.125)--(4,5.5); %mid (through trough)
\draw[very thick] (-7.25,-0.5)--(4,5.125); %mid
\draw[very thick] (0,0)--(6,3); %from origin, diagonal
\draw[very thick] (0,0)--(7.5,0); %from origin, horizontal
% \draw[very thick] (-7.25,-6.125)--(4,-0.5); %bottom (through trough)
\draw[very thick] (-7.25,-6.5)--(4,-0.875); %bottom
%LABELS
\draw[thick] (1.2,0) arc (0:27:1.2cm); \node at (0.9,0.21) {\large $\theta$}; %angle
%
\fill[white] (4,6) circle (6pt);
\node at (4.4,5.25) {\rotatebox{-62}{\Large $\lambda$ = sound wavelength}};
\draw[ultra thick,<->,>=stealth] (5,2.6)--(2.6,7.15);
%
\node at (7.25,3) {\rotatebox{-90}{\Large$\lambda_\text{\scriptsize B}\!=$ bending wavelength}};
\draw[ultra thick,<->,>=stealth] (6.8,0.1)--(6.8,5.9);
%
\node[align=left,right] at (2.5,-4.6) {\LARGE $\lambda_\text{\scriptsize B} = \frac{\lambda}{\sin\theta}$};
\node[align=left,right] at (2.5,-5.5) {\large when $\lambda=\lambda_\text{\tiny B}$,};
\node[align=left,right] at (2.5,-6.0) {\large $f=$ `critical frequency'};
%
\node at (-2,-7.5) {\large vibrating panel};
\end{tikzpicture}
%Note: if the middle & bottom diagonal lines go through the trough of the sine curve,
% the diagonal rectangle is split into uneven halves. That's why they're fudged.
\end{document}