For example, consider the green line. What is its length? In $L_2$, the answer is $1$, in $L_1$, the answer is $1$ as well. Now, for the same line, let's rotate it $45^\circ$ counterclockwise. What is the length again? In $L_2$, its length remains to be $1$. However, in $L_1$, using Manhattan distance, it's length is now $\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{...


Actually this is the Manhattan / $L_1$ / Norm 1 distance, if you just multiply the row by $8$ (or $N$). The $L_1$ distance between $[24, 2]$ and $[32, 5]$ is what you are looking for.

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