If it was in a loaded area, it will walk to your location at its normal speed. When you pick up the jack handle, the game apparently alerts it to your exact position as if you shot some very loud weapon, and it will be around shortly. If you keep making noise, it will home in on you faster. Once you do, it starts to move fast to a relatively close area, then resumes normal speed and walks to the place you caused noise at. The patrol pattern is random as long as you do not shoot a non-silenced weapon. Imagine it moving at a 4× fast forward motion. If it is not patrolling the currently loaded area (essentially: the room you are standing in and all neighbouring rooms), then it moves at very high speeds and can teleport past unlocked doors but cannot go through locked ones. Once it is done looking around, it starts patrolling. Otherwise, it is only looking around once, walks a bit, looks around again, then enters patrol mode. The game seems to cheat a bit there as if you are in a neighbouring room, it seems to be searching for a good bit.
Once you break chase, it first goes into search mode in the vicinity. If the Tyrant is actively chasing you, it is following you at normal movement speed and tries to predict your movement, but for the most part, it just follows where it saw you the last.
