Ohh I attempted to make one in PDF (it doesn't have any control flow so loops must be manually unrolled), but it turns out that most PDF readers doesn't actually follow the spec when displaying a PDF on a monitor (no you can't just throw the precision away internally just because the end result is going to be displayed with limited precision) - this includes Adobe Reader btw. I have been wanting to write a blog post about it for some time, but have never gotten around to get it done.
I'm sure I saw a way of doing it in Latex - I'm guessing that when you call pdftex (or whatever) then that's the point it calculates the output image, rather than letting the PDF reader do it?
PGF (LaTeX) indeed has a "Mandelbrot set" shading parameter[1]. Note: this is calculated by the PDF renderer. PDF has function shading and I think one can abuse it enough to render the Mandelbrot set. It certainly looks different in different viewers.
I did it in PDF by manually writing a custom tint transformation function. I used a 16x16 image with grayscale values from 0 to 255 and split the values in nibbles in the function code (which is a limited subset of postscript without things such as control flow). This worked fine, though a 16x16 Mandelbrot isn't very interesting.
So I tried with a 256x256 image instead with 16bpp, but it turns out that most viewers doesn't give a fuck and rounds the values down to 8 bits of precision before they are handed to the tint function.
Nice experiment. Some time ago I bumped into a similar problem when I experimented with SVGs lighting functions. SVG supports Phong shading based on a bump map. AFAIK you have to pass the bump map as the alpha channel of an image. Firefox only uses 8 bits for the alpha channel so the sphere I designed had steps on it.
Also Firefox used the sRGB non-linear colorspace for Phong shading producing incorrect results, but it was a different annoyance.
Apparently Chromium has the same problem as Firefox, however the image doesn't look like the same in the two browsers. The Firefox version is much darker mostly because of the usage of the incorrect colorspace for shading.
