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Orthogonal
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Orthogonal, or orthogonally, is a fancy word for "not diagonally". It's the technical word for "East-West, North-South" or "up or down or left or right".
Each of these lighter tile is orthogonal to the darker tile:
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These tiles are all connected orthogonally:
▓▓▓▓▓▓ ▓▓▓ ▓▓ ▓ ▓▓▓▓▓▓▓
These tiles are not, some are diagonal:
▓▓▓ ▓▓ ▓▓
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In Dwarf Fortress, this concept is important in many aspects of construction, fluid pressure, and pathing, among other areas. Especially in construction, where a tile above the ground and not connected orthogonally to something either cannot be built, or will collapse.