Canvas JS - how to do random movement with acceleration

I am struggling with this particular task. I want to make animation of particles that are moving randomly (I know it can't be that much random) with kind of acceleration. I found one website that is using this effect and I am not able to replicate it myself and I spent quite a few hours researching solution, no success.

This site has the desired effect. I don't know how to do the movement and acceleration to be repeating over and over.

For a moment I thought I got a clue that it's made in pixijs, but I haven't managed to do it in pixi either. All I could do was just randomly generated circular movement, but it doesn't look that well.

I would really appreacite if someone could push me in right direction.