Non-Euclidean Axioms for Digital Geometry

In digital geometry many of Euclid's axioms do not hold up.

Some other interesting consequences of digital geometry:

Intersections can contain more than one unit, and in some cases an intersection can contain multiple units that are not connected.

In digital geometry, Euclid's 5th axiom, the parallel postulate, does not hold up:

above, the blue and purple lines are parallel to the black line and both go through the red point, yet the two lines are not the same.