Suppose you construct a set of parallel lines in $$ \mathbb {R}^2 $$. Now you mark regularly spaced points along the lines and map the points in adjacent lines to each other. Does it matter if different lines have different spacing? (yes it does, in $$ \mathbb {R}^2 $$ because integer arithmetic is based on the integers being separated by unit lengths).
Ok, so suppose you start with a square lattice of points in $$ \mathbb {R}^2 $$; How many ways can you construct sets of parallel lines, so you can map points to points between adjacent parallel lines?
Ok, so suppose you start with a square lattice of points in $$ \mathbb {R}^2 $$; How many ways can you construct sets of parallel lines, so you can map points to points between adjacent parallel lines?