Hilbert curve · space-filling · slotting & picking

CLOSE IN THE LIST, CLOSE ON THE FLOOR

H(s) − H(t)‖  ≤  √6 · |st|½

One line visits every one of 4,096 slots and never crosses itself. It keeps a promise no row-by-row numbering can: two slots near each other in the list are near each other on the floor — never further apart than √6 times the square root of their distance in the list. Sort a pick list by that one number and the walk nearly plans itself. Across 600 random 25-pick orders it came within 20% of a 2-opt route. Walking aisle by aisle went 87% further.