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The next step is smooth coloring. I've written a post explaining it here: https://csl.name/post/mandelbrot-rendering/

The js code can be tested on https://csl.name/mandelbrot

Did you forget renew a domain name? The demo link in your post's opening paragraph is now leading to some kind of Japanese Bra company.

Haha, thanks for spotting that! It should lead to the link in the above comment of course.