Fourier Series of Square Wave

square-wave.tex

% Fourier Series of Square Wave - illustrated and computed by TeX.
% Author : Seungwon Park (swpark.me)
% convert -delay 10 -loop 0 -density 400 -alpha remove square-wave.pdf square-wave.gif
\documentclass[tikz]{standalone}
\usepackage{tikz}
\usetikzlibrary{calc}
\usepackage{amsmath,amssymb}
\usepackage{centernot}
\begin{document}
	\foreach \angle in {0,4,...,360}{
		\begin{tikzpicture}
			\draw[white] (-4,-1.6) rectangle (6.5,5); % frame
			\node at (1.5,3.5) {\fbox{\parbox{6cm}{\centering
						Fourier Series of Square Wave \\
						~ \\
						$ \displaystyle f(x) = \frac{4}{\pi} \sum_{2\centernot\mid n}^{\infty}
						\frac{1}{n}\sin\left(\frac{n\pi x}{L}\right). $
			}}};
			\draw plot[smooth,samples=100,domain=\angle-360:\angle] (pi/180*\angle-pi/180*\x,{sin(\x)+1/3*sin(3*\x)+1/5*sin(5*\x)+1/7*sin(7*\x)});
			\draw (-2,0) circle [radius=1];
			\draw (-2,0) -- +(\angle:1);
			\draw (-2,0) +(\angle:1) circle [radius=1/3];
			\draw (-2,0) +($ (\angle:1) + (3*\angle:1/3) $) circle [radius=1/5];
			\draw (-2,0) +($ (\angle:1) + (3*\angle:1/3) + (5*\angle:1/5) $) circle [radius=1/7];
			\filldraw (-2,0) 
			+(\angle:1) circle (1pt) -- 
			+($ (\angle:1) + (3*\angle:1/3)  $) circle (1pt) -- 
			+($ (\angle:1) + (3*\angle:1/3) + (5*\angle:1/5) $) circle (1pt) --
			+($ (\angle:1) + (3*\angle:1/3) + (5*\angle:1/5) + (7*\angle:1/7) $) circle (1pt) -- (pi/180*\angle-pi/180*\angle,{sin(\angle)+1/3*sin(3*\angle)+1/5*sin(5*\angle)+1/7*sin(7*\angle)}) circle (1pt);
			\node at (-2,-1.3) {\footnotesize $ (n=1,3,5,7) $};
			\node at (2.8,-1.3) {\footnotesize by Seungwon Park, illustr. \& computed with \LaTeX.};
   		\end{tikzpicture}
	}
\end{document}

https://git.io/vHrAL

http://i.imgur.com/l3GFf15.gif

Nice gif!