How is the "distance estimator" derived?

[pauldoo]

Hi,
For my work in progress renderer I am using the distance estimation expression of "0.5 * |w| * log(|w|) / |δw|" which I found at the following link:

http://www.subblue.com/blog/2009/12/13/mandelbulb

This seems to work great, but I am very confused as to how this expression was derived.  Does anyone have pointers for that?

[David Makin]

This seems to work great, but I am very confused as to how this expression was derived.  Does anyone have pointers for that?

Not surprised you're having trouble finding it (at least here anyway) - the post is buried in "the thread" here (wait for it to locate):

http://www.fractalforums.com/3d-fractal-generation/true-3d-mandlebrot-type-fractal/msg8505/#msg8505

You may like to check out a number of the follow-up posts.