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40d:Path
The term Path, or Pathing, is used in Fortress Mode to refer to the game process of determining how and where dwarfs and other creatures will get from one place to another, to fulfill their various personal tasks and priorities. The game code attempts to send them on the shortest, quickest route possible. If a dwarf needs to move down a hall, they "path" down that hall. If some other dwarfs are coming the other way, each one paths to avoid the other if possible. If the hall is too crowded, a dwarf might decide its faster (at that moment) to path down a different hall, and take a longer way around. If a large hall is very crowded, each creature in that hall constantly changes their pathing as the others do as well. An animal or dwarf may choose to path next to a magma pipe, with unfortunate results.
Pathing has a serious affect on framerate, or "frames per second" (fps), the speed at which the game advances. The more creatures on the map, the slower the framerate goes (tho' this may not be noticeable or a concern on more powerful computers).
Liquids (water or magma) also path, and although their rules for movement may seem more simple ("go downstream"), a body of liquid has a huge number of "individuals", different tiles that each do their own pathing to more accurately simulate the properties of that liquid as it flows and spreads. Waterfalls, especially, are known to hurt framerate. (If an underground river has a waterfall, as many do, fps has been observed to drop from the moment that river is first discovered and the waterfall exposed - more than if an identical river without the waterfall is discovered. Similarly when artificial waterfalls are first activated.)
If a dwarf refuses to fulfill a job, simply standing in place, often a lack of path is the problem. Forbidden doors, up-stairs that have been removed, or orders to construct bridges that are designated to operate from the far side of a chasm are all common pathing deal-breakers.
Pathing decisions in certain areas can be weighted by a player by designating high, low or restricted Traffic areas. Careful use of traffic areas has been known to improve framerate by reducing pathing load.