¿Cómo crear animaciones matemáticas usando LaTeX?

En este video explico cómo realizar una animación a partir de imágenes, de un archivo en pdf y utilizando solamente código.

\documentclass{article}
\usepackage{animate}
\usepackage{graphicx}
\usepackage{ifthen}
\usepackage{tikz}
\newcounter{a}
\setcounter{a}{-6}
\newcounter{grado}
\setcounter{grado}{0}
\begin{document}
  \textbf{Animación a partir de varias imágenes c1.png, c2.png,..., c6.png}   
  \begin{center}
    \animategraphics[controls,loop,width=0.5\linewidth]{3}{c}{1}{9}
  \end{center}
  
  \newpage
  \textbf{Animación a partir de varias páginas del archivo un tparabolico.pdf}
  
  \begin{center}
    \begin{figure}
      \animategraphics[controls]{1}{tparabolico}{}{}
    \end{figure}
  \end{center}
  
  \newpage
  \textbf{Animación utilizando un buche While}
  
  \begin{center}
    \begin{animateinline}[loop, poster = first, controls]{2}  
      \whiledo{\thea<7}{
        \begin{tikzpicture}
          \draw[thick,->,blue] (-3,0)--(3,0) node[below] {$x$}; % x axis
          \draw[thick,->,blue] (0,-3)--(0,3) node[left] {$y$}; % y axis
          \draw[ultra thick,cyan] (0,0) -- (0.5*\thea,0.5*\thea); 
        \end{tikzpicture}
        \stepcounter{a}
        
        \ifthenelse{\thea<7}{
          \newframe
        }{
        \end{animateinline}
      }
    } 
  \end{center}
  
  
  
  
  
  \newpage
  \textbf{Animación utilizando un buche While}
  \begin{center}
    \begin{animateinline}[loop, poster = first, controls]{30} 
      \whiledo{\thegrado<359}{
        \begin{tikzpicture}
          \draw[thick,->,blue] (-3,0)--(3,0) node[below] {$x$}; % x axis
          \draw[thick,->,blue] (0,-3)--(0,3) node[left] {$y$}; % y axis
          \draw[ultra thick,red,->] (0,0) -- (\thegrado:2.5cm);
          \draw[dashed,cyan,-] (0,0) |- (\thegrado:2.5cm);
          \draw[dashed,cyan,-] (0,0) -| (\thegrado:2.5cm);
        \end{tikzpicture}
        \stepcounter{grado}
        
        \ifthenelse{\thegrado<359}{
          \newframe
        }{
        \end{animateinline}
      }
    } 
  \end{center}  
\end{document}

        

\documentclass{article}
\usepackage[papersize={12cm,6.8cm},top=1mm,left=1mm,right=1mm,]{geometry}
\usepackage{graphicx}
\usepackage{tikz}
\begin{document}
  \foreach \i in {0,1,2,...,10}{
    \begin{tikzpicture}
    \draw[thick,->,blue] (0,0)--(10,0) node[below] {$x$}; % x axis
    \draw[thick,->,blue] (0,0)--(0,5) node[left] {$y$}; % y axis
    \node[red] at (\i,2.0*\i-0.20*\i*\i){$\bullet$};
    \draw[domain=0:\i, smooth, variable=\x, cyan] plot ({\x}, {2.0*\x-0.20*\x*\x});
    \node at (5,-0.3){$0.2x(10-x)$};
  \end{tikzpicture}

}

\end{document}