I think I know such a function for the Mandelbrot set: http://iquilezles.org/www/articles/distancefractals/distancefractals.htm http://iquilezles.org/www/articl

I think I know such a function for the Mandelbrot set: http://iquilezles.org/www/articles/distancefractals/distancefractals.htm http://iquilezles.org/www/articles/distancefractals/distance... (Well, the function that this one converges to.) Not sure about it's differentiability, though.