If you want the fog to be cut away as the player passes you could use a blob image and play pingpong with the render targets while updating the blobs position accordingly.
Imagine a completely black image and stamping your blob image on it, but because we would loose the last position of the "stamped" blob you need to capture the last result before stamping the new position on it.
And because you don't want to create new images over and over again you just reuse the previous one, thats what we mean when we talk about playing pingpong with render targets
I think you don't even need a high resolution image for the pinpong if you apply a clever blur or something to it afterwards, not sure if that makes sense performance wise
@GaborD: You mean the same ? (not explaining the pinpong part) but instead of using an image you want to calculate the blob in the shader right ?