This is a Julia set colored by using the coloring method popularized by the Buddhabrot rendering scheme. It's a good way to demonstrate how much simpler the paths that Julia sets causes compared to the Mandelbrot set.
This coloring scheme is similar to a chaos game, in that points are chosen randomly to explore. While this causes the rendering to diverge initially, it tends to settle down based on the number of iterations specified.
Traditionally this rendering only counts the paths of points that escape, but you also render non-escaping points by checking the Non-Escaping box. Note that many Julia sets do not have any points, so attempting to rendering non-escaping points in those sets will be futile.