What does 1px by 1px gaussian blurring mean in GIMP?

Question

So I was going through the options in Gaussian blur that are provided in GIMP, one of which is the ability to select the "Blur Radius". From my understanding, the Gaussian filter is created by sampling the Gaussian kernel function for the pixels inside the blurring radius. But that makes no sense if the blurring kernel is 1x1. Can anyone here explain what exactly happens when Gaussian blurring is done on GIMP?

Cheers.

PS: I have asked this question over on photo.stackexchange. However, I feel that that this is more of a software question than a photography question, so I'm asking it here.

Answer 1

The Gaussian kernel is based on the equation exp(-d²/2σ²) where d is the distance from the center point and σ the "radius". This is a fast decreasing function. The smaller σ, the smaller the weight of the surrounding pixels, but it is never zero and in theory the convolution is infinite.

One can estimate that for σ smaller than 0.3, the contribution of the immediate neightbors becomes smaller than 1/256, hence is completely invisible, but for σ=1, it is still 60%.