This is the source code to some animations illustrating some numbers wiggling around on the complex plane.
These animations were part of a video in a series circulated to first-year maths students at Imperial College London. Each video reviewed a topic in maths that the students were expected to be familiar with; this was the second video on complex numbers. They were part of a StudentShapers project.
At the time of the project (August 2019), I knew my way around a few ways of getting a computer to make pretty images that moved. These included:
- Flash.
- javascript/GLSL was my go-to for maths-y visualisation-y things, but I got stuck trying to find a nice straightforward way of exporting canvas output a video format like
mp4. - Blender is amazing, but also overkill.
Most importantly, because this was maths, I wanted to have nice typography for the funny symbols and stuff, but the best solutions I could find for incorporating material typeset in LaTeX into any of my animation options was pulling some svg shenanigans and then working with each piece of text as an image.
All of this was pain.
In the absence of something that would let me put LaTeX into animations, I ended up deciding that I would just do my animations in LaTeX instead.
I spent a weekend throwing together some macros that interpolated between numbers, and a few more that multiplied and divided some dimensions so the resolution and framerate would work out. I also grepped the pgf manual and learnt how to do stuff with pgfkeys so that those macros are kind of sort of readable (tween[start=0, duration=0.2]{0}{1}!)
Now I was writing down the parametrisation of a scene, and compiling a tex file to get a dvi with one page for each frame of the animation. Temporarily setting the framerate to something like 8 frames per second, I could compile up to a few seconds of animation reasonably quickly, and scrub through the resulting file in a doc-view window to see how it looked.
Eventually the source would be compiled at a full 24fps, turned into a sequence of frames with gs, then piped into ffmpeg to be stitched together into an actual mp4. Ta-da, maths animations with nice LaTeX typesetting for the text!
All of this was still pain, but it is now my fault. Delightful.
This code is mostly being left here for personal / historical interest. An effort is tentatively being made to put the reusable parts of the code into presentable shape.