It's almost criminal to post things like that without any annotations. The first picture plots points where radius and angle (in polar coordinates) are uniform

It's almost criminal to post things like that without any annotations. The first picture plots points where radius and angle (in polar coordinates) are uniformly distributed. Of course, this is not uniform in the disc. I don't have the time right now, but if I do later, I'll type up the math behind what a uniform distribution in the disc looks like, and what's going on in other pictures.