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A lattice is said to be oriented if there exists a rule which assigns a specified direction to any edge connecting arbitrary lattice points . In that way, an oriented lattice is intimately connected to an oriented graph.
Given a point lattice , one common such rule is the so-called north-east rule which orients each edge of in the direction of increasing coordinate-value. This type of ordered lattice is central in a number of fields, e.g.,in oriented percolation models within the field of discrete percolation theory.
Grimmett, G. Percolation, 2nd ed. Berlin: Springer-Verlag, 1999.
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