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and if you use de-based coloring, you don't need aa at all

Ehh... now after zooming in and taking a closer look at the results, I'm not too crazy about this method.

The problem is that it underestimates the distance around long, thin tendrils, and especially the big needle sticking out of the left of the main cardioid, and it overestimates the distance in the valleys, especially the elephant valley. This leads to jagged valleys, and over-blurring near the needle (right now, since I've implemented exterior DE only, features on the needle have a 'hairy tarantula' look about them). It works great on the other areas of the M-set, though.

Now, this is a long shot, but does anyone know of a more accurate DE formula? I'm using exactly the one found here: http://www.ozone3d.net/tutorials/mandelbrot_set_p6.php

Otherwise, if I could find some sort of metric to differentiate valley-like areas from tendril areas from 'normal' areas, then I could easily come up with an approximate correction term for the DE. Any ideas?

Yeah, my results look just like those images, but the accuracy is highly dependent on the area you're looking at. After thinking about it for a while, I don't think it's due to an inaccuracy with my DE formula. The problem is that distance is an imperfect metric for approximating pixel coverage in the first place. In areas with lots of thin tendrils, a pixel can have a very close distance to the M-set, yet have very little area coverage because the features are just so thin. In places with more compact geometry, like elephant valley, the opposite effect occurs.

It's a shame, because when this method works, it works really well. I tried to come up with a kludgy solution to correct for this inaccuracy, but it was slow and not worth a damn. So I guess the only solution is to adjust the distance threshold manually to best suit the area you're viewing. A slight inconvenience, which, in my opinion, is well worth the savings in rendering speed.

Once I finish implementing interior DE, I'll post some comparison pics.