How to Make Animated Math GIFs: LaTeX + TikZ

The first animated GIF that I ever made was made with the LaTeX package TikZ and the command line utility ImageMagick. In this post, I’ll give a quick example of how to make a simple GIF that works by layering images with transparent backgrounds on top of each other repeatedly.

TikZ code

In our first step toward making the above GIF, we’ll make a PDF where each frame contains one of the above circles on a transparent background. In this case, each circle is placed uniformly at random with its center in a \(10 \times 10\) box, with a radius in \([0,1]\), and whose color gets progressively more red and less green with a random amount of blue at each step.

\documentclass[tikz]{standalone}
\usepackage{tikz}

\begin{document}
\foreach \red[evaluate=\red as \green using {255 - \red}] in {0,1,...,255} {
  \begin{tikzpicture}
    \useasboundingbox (0,0) rectangle (10,10);
    \pgfmathrandominteger{\blue}{0}{255}
    \definecolor{myColor}{RGB}{\red,\green,\blue}
    \fill[myColor] ({10*random()},{10*random()}) circle ({1+random()});
  \end{tikzpicture}
}
\end{document}

Starting with \documentclass[tikz]{standalone} says to make each tikzpicture its own page in the resulting PDF.

Next we loop through values of \red from 0 to 255, each time setting \green to be equal to 255 - \red so that with each step the amount of red goes up and the amount of green goes down.

The command \useasboundingbox (0,0) rectangle (10,10); gives each frame a \(10 \times 10\) bounding box so that all of the frames are the same size and positioned the same way.

The command \pgfmathrandominteger{\blue}{0}{255} chooses a random blue values between 0 and 255.

The command \fill[myColor] ({10*random()},{10*random()}) circle ({1+random()}); places a circle with its center randomly chosen in the \(10 \times 10\) box and with a radius between \(1\) and \(2\).

ImageMagick

When we compile this code, we get a PDF with one circle on each page. In order do turn this PDF into an animated GIF, we convert the PDF using ImageMagick, a powerful command-line utility for handling images. If we named our PDF bubbles.pdf then running the following code will give us an animated GIF called bubbles.gif.

convert -density 300 -delay 8 -loop 0 -background white bubbles.pdf bubbles.gif

I hope that you use this blog post as a jumping off point for making animated GIFs of your own! If you do, please reach out to share them with me!