A type of metric which satisfies a much stronger form of the triangle inequality: For all points x,y,z,

d(x,z) ≤ *max*(d(x,y),d(y,z))

Distances in an ultrametric "look like this":

,--y
/
x---<
\
`--z

rather than "like this":

_,-y
_,-' |
x< |
~ |
`-._ |
`-z

Examples include distances on a tree and the distance defined by the p-adic norm.