I was just informed
in this thread that diagonal travel cost is not well-characterized, or at least not with any definite proof. I am a little surprised that this result -- or lack of result -- isn't better understood. I searched the forums for "manhattan" and "Chebyshev" and did not see any rigorous answer to the question. Unfortunately, I can't figure out how to definitively
pose the question using DF.
So far, the test case I envision goes something like this: a dwarf is caged or locked into a 1x1 cell behind a floodgate. Two single-tile-wide tunnels are dug: one extends 21 tiles orthogonally; one runs 21 tiles diagonally. A single tile of food storage is placed at the end of each tunnel and a plump helmet is placed on each stockpile. The Enrichment Center is sealed off from the rest of the fortress. When the dwarf indicates hunger, the lever is pulled and the dwarf is released, presumably to seek out the nearest food.
The experiment results may be documented and repeated by moving either of the stockpiles closer to the origin; for example, if a true Pythagorean distance is implemented, we'd expect 10 diagonal tiles to be roughly equidistant with 14 orthogonal tiles.
Has anyone already tried this? Is my core assumption (dwarves always seek the nearest food) correct, or is there a better thing for a dwarf to seek?