I’ve just realized that I’ve been using this very basic option all wrong. The filter radius setting in Apophysis applies a small blur to each individual pixel, helping smooth out jaggy edges and noisy areas (in some cases). But one fundamental thing I had failed to understand until now is that this setting needs to be directly proportional to your render size, regardless of how much you think the particular fractal you’re working on needs it.
The reasoning is simple: In a large image, typically used for a print, there are just too many levels of self similarity, too many little distractions everywhere, taking away from the whole rather than adding to it. These details reside at the sub-pixel level in normal render sizes, and so don’t get proper attention. But they do distract from the lines, texture and sense of direction in your piece. The opposite happens for thumbnails and smaller images, which tend to lose focus and crispness. Supersampling helps there, but it can’t work properly if you’re just blurring over it.
The rounding errors introduced by small buffer sizes tend to naturally blur the image. Counteract this effect (or lack thereof) according to your render dimensions.