Manhattan Distance

Manhattan Distance is the distance between two points when you can only travel along axes at right angles. It's the sum of the absolute differences of their coordinates:

$d(\mathbf{p}, \mathbf{q}) = \sum\limits_{i=1}^{n} |p_i - q_i|$

It's named after the grid layout of streets in Manhattan, where you can't cut diagonally through the blocks. It's also called taxicab distance or L1 distance.

See L1 Norm. Compare with Euclidean Distance.