XOR ultrametric vs 2-adic metric clustering of 4-bit integers 0–15: the two metrics partition the same numbers into completely different groups.

XOR ultrametric — groups by shared prefix (MSB)
{0–3} d≤2 {0–7} d≤4 {0–15} d≤8
0371115
hover a number to see its XOR distance from 0
2-adic metric — groups by shared suffix (LSB)
odd d=1 ≡2 mod 4, d=0.5 ≡4 mod 8, d=0.25 ≡8 mod 16, d=0.125
0371115
hover a number to see its 2-adic distance from 0
1000 (= 8) sits at maximum XOR distance from 0 (d=8, leading bit flipped) but minimum 2-adic distance (d=0.125, three trailing zeros). The two metrics are completely orthogonal — the extreme of one is the tight core of the other.