Mathematical Curves


I have been working for a while on a way to generate mathematical curves in synfig using converters for an animation . I have been quite successful and thought that while I prep a tutorial, I could share the file here because of my schedule.

The curve generated is a lemniscate of Bernoulli. Find out more here Lemniscate of Bernoulli - Wikipedia (Focus on the parametric equations)

P.S. No keyframes was involved in this animation.
Lemniscate.sifz (4.0 KB)


Great work! I experimented with it for a couple of hours, made some small adjustments:

  • Made step as ‘Translate’ layer, now it’s possible to construct a particle from whatever layers you want
  • Exported color to library with its sub-parameters for ease of control
  • Add scale parameter to control movement

The modified source:
Lemniscate2.sifz (4.8 KB)

I noticed that if we reduce the step of the duplicate layer we can get a smooth line, although it’s taxing on performance. Also, you can animate “SCALE” parameter to make the line gradually disappear. Here’s how it looks:

Another thing you can do is to replace circle with something else. For example, here I replaced it with an outline and motion blur:

Doesn’t look that good, but I didn’t spend much time adjusting. Some cool effects sure can be made.

Overall, awesome stuff! It was fun playing with it.


I ws quite afraid that I wouldn’t be understood.

That application is rad!

Just trying to look for my next victim curve!