Irrational directions
The integer orchard
If trees sit at every whole-number coordinate, which directions let you walk forever without exactly hitting a point-tree?
Irrational directions
Can you walk through an infinite orchard without hitting a tree?
Imagine an idealised orchard with one point-like tree at every whole-number coordinate: `(0, 0)`, `(1, 0)`, `(0, 1)`, `(1, 1)` and so on. If you walk from the origin in a straight line with rational slope, you eventually hit another lattice point. With irrational slope, you never pass exactly through another point tree.
Why this belongs here
This is the same kind of idea as the seed rotation tool. Simple fractions make alignment. Irrational numbers resist exact repetition, which can help explain why the golden-ratio turn spreads points so well.