# Mathematical Curves

**URL:** <https://forums.synfig.org/t/mathematical-curves/14377>\
**Category:** Assets & Templates\
**Created:** [September 3, 2023, 3:16am UTC](https://forums.synfig.org/t/mathematical-curves/14377 "2023-09-03T03:16:50Z")\
**Posts on this page:** 3\
**Page:** 1

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**Author:** ![Rhvy1](https://forums.synfig.org/letter_avatar_proxy/v4/letter/r/a587f6/32.png) [@Rhvy1](https://forums.synfig.org/u/Rhvy1)\
**Post date:** [September 3, 2023, 3:16am UTC](https://forums.synfig.org/t/mathematical-curves/14377/1 "2023-09-03T03:16:50Z")

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Hey!

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](https://en.m.wikipedia.org/wiki/Lemniscate_of_Bernoulli) (Focus on the parametric equations)

P.S. No keyframes was involved in this animation.  
[Lemniscate.sifz](https://forums.synfig.org/uploads/short-url/jjLa72kPNiVjFWFz1lUchX9zbXq.sifz) (4.0 KB)

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**Author:** ![Svarov](https://forums.synfig.org/user_avatar/forums.synfig.org/svarov/32/8167_2.png) [@Svarov](https://forums.synfig.org/u/Svarov)\
**Post date:** [September 3, 2023, 6:04am UTC](https://forums.synfig.org/t/mathematical-curves/14377/2 "2023-09-03T06:04:21Z")

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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](https://forums.synfig.org/uploads/short-url/pKQ3tW5rC2tL6pMuqsyCwNARPHK.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:  
 ![Lemniscate2](https://forums.synfig.org/uploads/default/original/2X/2/2dd5076050b4f2e593822b440d6a5566d97d85eb.gif)

Another thing you can do is to replace circle with something else. For example, here I replaced it with an outline and motion blur:  
 ![Lemniscate](https://forums.synfig.org/uploads/default/original/2X/4/4003db4d7b5c1c39888d7e2ce645d24671029ea8.gif)

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.

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<div class="post-metadata">

**Author:** ![Rhvy1](https://forums.synfig.org/letter_avatar_proxy/v4/letter/r/a587f6/32.png) [@Rhvy1](https://forums.synfig.org/u/Rhvy1)\
**Post date:** [September 3, 2023, 9:19pm UTC](https://forums.synfig.org/t/mathematical-curves/14377/3 "2023-09-03T21:19:16Z")

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

> [@Svarov](#):
>
> Another thing you can do is to replace circle with something else. For example, here I replaced it with an outline and motion blur

That application is rad!

Just trying to look for my next victim curve!