Manhattan distance (source code)

= Manhattan distance
{c}
{title2=$d_1(x,y)=\sum_i|x_i-y_i|$}

The <metric> induced by the <L1 norm> gives <taxicab geometry>. Each difference in <Cartesian coordinates> contributes its <absolute value> independently, so an axis-aligned route with no backtracking realizes the endpoint distance.