Interactive demo of using Newton's method in the complex plane with a cubic. Its a little slow, any ideas for improvements are welcome:
d.umn.edu/~mhampton/NewtCubicA

@hamptonio you could probably make it respond in realtime if you do the per-pixel calculations in a WebGL fragment shader running on a GPU instead of Javascript on a single core of a CPU

@hamptonio I made it roughly 2x faster (in Firefox 62 on Debian Buster) by avoiding memory allocation by [...] inside the loop: mathr.co.uk/tmp/Newton%27s%20m

here's one of my experiments from 2012 with GLSL fragment shader (using desktop OpenGL, not WebGL)
archive.org/details/ClaudiusMa 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..).

code.mathr.co.uk/fractaloids/b

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...).

code.mathr.co.uk/fractaloids for source/history browser

@mathr Ah that's awesome thanks!

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