I found this cool rendering somewhere on the net.
Apparently the author generated nice tendrils you'd have to follow if you want to escape. I wonder about the math behind this. I know how to calculate the derivatives (generating a single thread), but is there an easier way to compute the image than to track each point's path? And how did they arrive at the width and luminescence of these tendrils?
Looks like a variant of stripe average colouring, see:
One variation that is useful for this kind of image is to consider only the last $S$ iterations when computing the average, this makes the image contrast/detail almost independent of iteration count. Various ways of weighting the iterations are possible, but maintaining continuity is usually a priority, so as the pixel moves further from the boundary (iteration count at escape decreases), fade out later iterations and fade in earlier iterations into the stripe calculation.