A search outward in growing square rings is not nearest-first

Fact

Searching a grid outward in square rings (every cell at Chebyshev distance r, then r + 1) is the usual way to find the nearest cell that qualifies. Returning the first match is not nearest-first, in two ways:

• Within a ring, the loop order decides. A corner of ring r is r√2 away and its edge midpoints only r, and a loop that starts at (-r, -r) meets the corner first.
• Across rings, ring r + 1 holds cells r + 1 away, which is nearer than ring r's corners once r ≥ 3, since r√2 > r + 1.

Why it matters

The answer is always close and always valid, so it looks right. It shows up as something placed a little to one side, such as a creature appearing at the far corner of a pool instead of at the edge that was tapped. That reads as a placement quirk, not as a search bug.

How to apply

• Keep the best match by true (Euclidean) distance, skip cells that cannot beat it, and stop only once the ring index is past the best distance found.
• Test with a target whose nearest qualifying cell is straight ahead on a ring's edge while the same ring also has qualifying corners.