How to implement chaotic movement of an object around a point?

Question

C++ / C#

Actually a question. I want to do about the same receiving awards as shown in this video. I use DOTween.
I do not understand a couple of things:
1) How to make the movement so smooth? To select the smoothness function, or is it somehow achieved differently here?
2) How to make the movement seem or be chaotic, but at the same time the object does not leave the point at a distance greater than N;

Answer 1

Hypotrochoid
https://ru.wikipedia.org/wiki/Hypotrochoid
https://ru.wikipedia.org/wiki/Hypocycloid
+ 'element of chance +- from coordinates