The response shall be where u found the gif. Guessing, I think it's made in CSS. Look at the CSS properties and implement them. I would say they are:
- interpolating size
- interpolating position
Given a specific time, u calculate the pos of the moving circle, and the size of 8 fixed circles. The size shall be a single ecuation, and for every circle u out of phase it with a constant time
I did not try any libs for this, but searching "SFML animation libs" seems to yield good results. U could go with specific libs for making true HTML / CSS interface, as SFML allows u to control the OpenGL, but maybe it's overkill