Manhattan distance

The manhattan distance is a different way of measuring distance. It is named after the grid shape of streets in Manhattan. If there are two points, formula_1 and formula_2, the manhattan distance between the two points is formula_3.
This distance can be imagined as the length needed to move between two points in a grid where you can only move up, down, left or right.
Extension.
This definition can be used for three and higher dimensions too.
If there are two vectors, formula_4 and formula_5, then the manhattan distance between the two points is the absolute value of the difference between all numbers in the vector. Or, in notation:
formula_6