More than other art-forms, fractals tend to benefit most from decent anti-aliasing. What I've found out over the past couple of days is how much processor time is needed to obtain really smooth results. I used to double the width and height of each image and downsample to the proper resolution. This does indeed definitely help the image look more fluid than usual.

However, it turns out that sampling 8x8, 16x16 or even as much as 32x32 per pixel (i.e. 1024 times slower!!!) for many images will produce much crisper results. Few fractals demonstrate this better than this ultra-fine sponge texture (still from the standard Mandelbrot) which I have rendered versions of below for comparison.

Enjoy...

Here is the default 640*480 pixel image. It looks okay, but let's see what happens when we downsample...




Here we have the same image but downsampled from 1280*960 back to 640*480. Already, it's looking much better. But can you notice the noisy artifacts? Can we improve on this?




Downsampled from 2560*1920 back to 640*480. Again, even smoother than before. This could be easily mistaken to look as good as it could, but better is possible...




Getting near perfect, this is 64x times slower than before, but the results definitely show. A good compromise between detail and speed. (Downscaled from 5120*3840 to 640*480)




The longest I was willing to wait (and the maximum size my PC could handle is this whopping 10240*7680 resolution image downscaled to 640*480. All the details shine through, and noise is at its lowest.



Many eyes will probably see differences beyond even that level of detail, but I'm not sure how many would be willing to wait for the result

What downsampling scales do users here use for generating their fractal images out of interest?

Here are some images at bigger resolutions for wallpaper purposes:
1024*768
1280*960
1600*1200

excellent renders  is that level of zooming achievable with double precision floats?

there are some high-aa renders at a friend of mine's deviantart page: http://chaos5.deviantart.com (i taught him about monte carlo methods for getting good aa, as trifox mentioned those posts should still be stored in his previous journals and deviation comments...)

antialiasing and monte carlo methods are the closest thing i've found to a religion so far

I think so yes. It's 1.0e-7 per pixel for the 640*480 version, so for the massive 10,240 pixel version it's still only up to 6.0e-9 per pixel.

I'm guessing that whatever anti-alias method you use, the (initial) resolution will be a more significant factor in determining final image quality.

For the above images I used Irfanview's reducement alg. I've tried different ones from Irfanview such as Triangle, and B-spline, but they each come out looking *identical*. Maybe it only uses those for increasing res, rather than decreasing res. Hmm...