Thanks! (And thanks for the other replies as well)

This resource is the most interesting to me.

As I got a lot of answers about zooming and resampling, I'll try to restate my original question:

What I have is some mechanism to sample something as much and as detailed as I want. This is why I mentioned a fractal. I don't want to zoom or resample, just find the optimal way to sample the original data to construct, say, a 500x500 pixel image. Up until I read this article, I would just sample randomly in the [0.0, 0.0]-[1.0, 1.0] space and avergage out the value. If there's a better way, I'd love to learn it.

The best answer might just be "main metric of quality for them is how they look" from fsloth.

> Up until I read this article, I would just sample randomly in the [0.0, 0.0]-[1.0, 1.0] space and avergage out the value.

What does it mean to sample “random” points in a fractal? In practice you’re probably sampling in terms of numbers at some specific precision (e.g. the limit of your floating point type for the range in question). This is still going to be points in some particular discrete lattice. Depending on the way the fractal is constructed, this could bias your picture.

Again, I’m not sure that the color of an “area” is meaningful for a fractal. But yeah, I think fsloth has the right idea: if the purpose of the images is to be pretty, then do it in whichever way gets you results you prefer.

Techniques like the chaos game are used to sample according to the associated fractal measure, which addresses the issue of bias. Issues or floating point representations and the like are a separate problem, but you can address them also.