@hamptonio I made it roughly 2x faster (in Firefox 62 on Debian Buster) by avoiding memory allocation by [...] inside the loop: https://mathr.co.uk/tmp/Newton%27s%20method%20for%20a%20cubic.html
here's one of my experiments from 2012 with GLSL fragment shader (using desktop OpenGL, not WebGL)
https://archive.org/details/ClaudiusMaximus_-_Fractal_Juggling_v0_3 I think it ran in realtime, but it's so long ago that I forgot...
@hamptonio Oh! I found my code, and turns out I already ported it to WebGL (runs 60fps full screen realtime on my system but I have a beefy GPU..).
drag with left-mouse-button pressed to add a new root (the path is recorded and animated, but there is no visual feedback in the process, and you need 2 or 3 paths to get something interesting...).
http://code.mathr.co.uk/fractaloids for source/history browser
@mathr Ah that's awesome thanks!