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Render time on the Mandelbrot fractal does not directly depend on pixel resolution or number of iterations. The chosen location in the set has a far greater effect on render time. The answer can stretch as far as 1 minute to more than an hour. Density of the intertwined shapes makes the difference.


This one was rendered in about 5 minutes on a laptop (Intel Core 2 Duo CPU T9600 @ 2.80 Ghz):



This one is on the same depth and took only 90 seconds:

You know that perturbation and series approximation now turns all estimations on rendering time up side down? An e15 and an e599 location can take about the same time if they have the same number of iterations and the same amount of iterations can be skipped, but if rendered traditionally with full precision the deeper location would take enormous much longer time
I would like to say that supersampling and image resizing is the same thing. Averaging iterations in a pixel can give a very noisy result, much worse than without antialias at all. Because the average will point to palette indexes chaotically. You must combine the resulting colors if you want a good result, which is the same as resizing.
(Which is of no use if you want to do a color cycling animation...)

BTW, it is possible to decide the number of samples by using distance estimate:
- Use more samples if the disc's size -which is given by the DE- is smaller than a pixel.
- If the disc covers multiple pixels one can use interpolation and save computations.

One can also use prefiltered palette and use the DE to choose the right filtering amount (useful when using a palette with lot of variation in color)

It happens that the derivative of the continuous coloring formula is: dr/(r*log(r)) which is the inverse -up to 0.5 factor- of the DE.

See attached fragmentarium shader.