END OF AN ERA, FRACTALFORUMS.COM IS CONTINUED ON FRACTALFORUMS.ORG

If no image above then look here:

http://makinmagic.deviantart.com/art/Distance-Estimators-Comparison-141327379

These images give a direct comparison between the analytical distance estimator and the "delta" distance estimator as applied to the z^2+c quaternionic Mandelbrot.

All 4 renders where done @3840*2880 pixels.
The analytical DE renders took 9mins 17 secs and 12mins 5secs.
The delta DE renders took 13mins 36secs and 19mins 52secs.

As expected the delta method is somewhat less than twice as slow as the analytical one (the difference in speed being primarily due to the delta method requiring 2 iteration loops per ray-step rather than just one). Note that for a more complicated iterative formula then the delta method wil be closer to twice as slow.