Just search for videos, stuff like this:

https://www.youtube.com/watch?v=eEwZeY51mT0

You can make similar kinds of videos for all 3 of them. That video shows a divergence free field since number of particles aren't changing, I easily see that since I know the intuitive explanation for divergence, it is useful to have intuition for those things.

Gradient is just the equivalent of slope but for higher than 1 dimension.

Edit: Or no, that field has divergence, I'm dumb I didn't watch the start, many particles accumulate at a few points, that is due to divergence. Divergence is essentially areas that attracts or repels particles in that simulation.

Found the divergence video, in case it is hard to understand what I said above: https://www.youtube.com/watch?v=c0MR-vWiUPU

Note: This series (Multivariate calc on Kahn Academy) is done by Grant Sanderson of 3Bl1Brown. It's outstanding, and goes over the concepts related to how the article here describes the fields.