When a character or monster moves, it moves between map tiles with no inbetween. You're either on one or the other although you appear to be walking between them. Many players and monsters can occupy the same square, which is known as stacking (some abilities are limited when stacked). Certain tiles, like at depots and boss levers, can not be stacked on, even on open pvp worlds.
Tiles that contain things like trees can overhang the 32x32 pixel space, usually to the left and top of the tile. Everything "leans" that way which creates the illusion of depth. This is known as oblique projection. If you can see the roof of the building, everything on the roof will be offset to the left and top by one tile. Understanding this is important to using the levitate spell effectively.
Fields behave like nailed down items. They're placed in the item stack order like an item is, and items underneath can be accessed with Browse Field.
Each map square falls into one of the following categories:
Open: The tile can be walked on and allows line of sight. Items can be placed here.
Semi-blocked: The tile can not be walked on, but allows line of sight. These are good for running around if you wish to continue shooting your target. They don't block the spread from area of effect spells. Same rules apply to monster's attacks. Items may be placable here, may be destroyed (in the case of water, swamp, trash cans, and lava), or may be not be allowed (windows).
Blocked: The tile can not be walked on nor allows line of sight. These are good for avoiding monster's attacks.
Secret passage: these rare tiles do not allow line of sight but do allow walking.
The world map has a 'list' of all open and non-open tiles, viewable by pressing the Cost button. Each Open tile has a movement cost, which is colorized on the world map. Gray squares are Open, darker squares are allow faster travel than lighter squares.
Safe zones, also known as protection zones, or pz, are squares where it is impossible to target anything or be targeted by anything. It prevents the spread of aoe damage. Those that have taken aggressive PVP action can not enter safe zones. You are not however completely safe, you can still be harmed by damage over time effects. Safe zones do not block shooting however, your arrows or runes can travel through a safe zone to the other side, so long as the target is not in the safe zone. You can find safe zones all throughout tibia. All large towns have a depot and a temple for which the entire room or building is a safe zone. Most boats are safe zones. Some safe zones are a single square, often around boats or teleports. These are usually placed in such a way that it prevents a killer from traveling freely.
Some squares trigger effects when stepped on. For example stepping on stairs or on a hole will move you between floors. Stepping on a teleport may move you far away or bounce you back, usually depending on whether you've completed a certain quest. Some squares are "buttons", standing on them will trigger some effect that's usually reversed when you step off.
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