Minecraft wiki entry for Taxicab_distance, associated text: This is a less accurate but more efficient calculation suitable for efficiently processing numerous or rapidly-repeating calculations in a short time. A consequence of this calculation is that a taxicab "circle" drawn with a constant taxicab radius appears as a diamond, in which the taxicab radius equals the Euclidean radius only in the four cardinal directions (north, south, east, west), and the radius is shorter in all other directions. Similarly, in three dimensions, a taxicab "sphere" appears as an octahedron.