This was called frequency clamping in the book 'advanced renderman' which talks a lot about procedural textures.

A simple way to think about it is to imagine a pattern of thin black and white stripes. If you go far enough away from the pattern, there will be multiple black and white stripes in the same pixel. When they are smaller than a pixel the average color will be grey. Knowing this, you can fade to grey as the stripes get tiny instead of arriving at grey from heavy sampling.