d = 2
curse

Volume runs away from the center

blue ball: of the cube
red ÷ blue, volume:
red ÷ blue, reach along an axis:
curse

Distances become similar

nearest ÷ farthest:
consequence

The tree ends up measuring everything

filled = measured by the tree: of 4,096
the ball stays on its side of the first cutthe ball crosses cuts: ever more neighbouring boxes openedevery box opened: a plain scan does this without the queue; the ten nearest lie within of the question, the first cut is away
the way out

Angles become nearly perpendicular

pairs within 10° of 90°: