The Fog increases during the in-game night (approximately 11 PM) and decreases at dawn (approximately 9 AM).
The Fog is also believed to be heavier in certain areas, This has been confirmed true, as the maze becomes very foggy and almost impossible to navigate at night.
The Fog changed throughout the stages ALPHA & BETA, and in ALPHA the Fog was very little and believed to be only seen 6,000 studs away from a player, yet there is no photo evidence to prove that. According to the 2016 Halloween Update, Fog has been increased a lot throughout October at Night time.
In BETA the fog increased throughout Lumberland, possibly only 1,000 studs from a players sight, and was a slightly lighter shade of purple than it is now.
Later in the BETA stage, the Fog decreased to 300 studs away from a player and has been set like that ever since. It's now a firmed property of the game and will possibly either decrease/increase in the future.