This image contains 76000000 of roots, calculated in more o less 5 minutes. The matplotlib rendering is a bit more slow than the calculations. But there are faster way for rendering in caso of more than 100000000 of dots.
Thanks. I've got this project, "variograph", which similarly renders a lot of dots from input parameters. I just put a function to find roots of one of your posts' polynomials. I guess it's very broken so far but it runs in less than 1 second on GPU to make this. It stops at 8 newton method steps.
I can't send images in DMs. I got this with 150994944 dots/particles, 12 Newton method steps, and work on random Newton method seeds positions. It takes less than a second to render.