dense image

[youhn]

Oh, and thanks for sharing the link to mathoverflow. The second answers is indeed very good. Did not know there was a name for it ... The hairiness theorem (source: http://mathoverflow.net/questions/187842/is-there-an-almost-dense-set-of-quadratic-polynomials-which-is-not-in-the-inte )

[Adam Majewski]

https://www.math.univ-toulouse.fr/~cheritat/wiki-draw/index.php/Mandelbrot_set
see downsacling with gamma correction

[claude]

Nice link, some formulas there are new to me (Henriksen's boundary detection method, distance estimator normal map).

Typically images are in non-linear sRGB colour space.  To downscale correctly, you need to do that in linear colour space:

input sRGB image -> convert to linear RGB image -> downscale (= low pass filter -> decimate) -> convert back to sRGB image -> output sRGB image

the formulas for sRGB conversion are on wikipedia:  https://en.wikipedia.org/wiki/SRGB#Specification_of_the_transformation

[Tglad]

There was a discussion on this a few years back: http://www.fractalforums.com/sterlingware/to-anti-alias-or-not-to-anti-alias-hit-the-button-or-leave-it-alone/

A nice answer is to use the local fractal dimension of the set to control the antialiasing. The local fractal dimension doesn't mean 2 for the Mandelbrot set, it is what the set looks like at a particular point and zoom depth... so is local in position and scale.

In the pic below the left image shows how supersampling makes tendrils fade out, the right image shows that if you give every point in the set a half-pixel width, then the result is too thick. The middle image shows the new local-fractal-dimension based method.

I published a paper on this: http://ieeexplore.ieee.org/document/7138673/ (paywalled unfortunately), and a short blog post: http://tglad.blogspot.com.au/2012/12/dimension-aware-rasterising.html