Orthogonal

In the domain of Dwarf Fortress, orthogonal, or orthogonally, is a fancy word used to mean "not diagonally". It's shorthand for "East-West, North-South" or "up or down or left or right".

This concept is important in many aspects of construction, fluid pressure, and other areas. Especially in above-ground construction, where a tile not connected orthogonally to something either cannot be built, or will collapse.

   Diagram 1:

    xox
    oCo
    xox

• The center tile, C, is orthogonal to the four o tiles.
  
• Each o tile is orthogonal to the center C tile, plus two x tiles.
  
• The x tiles are all orthogonal to two o tiles.
  
• No x tiles are orthogonal to each other, nor are any o tiles orthogonal to each other.

These X's are all connected orthogonally:

XXXXXX   XXX
   X     X
   XXXXXXX

These X's are not--some connections are diagonal:

XXX XX    XX
  XX     X
    XXXXXX