All metric spaces obey the triangle inequality which is, for three points $a,b,c$, that
$$d(a,c) \le d(a,b) + d(b,c)$$
One interesting special case of a metric space is one endowed with an ultrametric structure, in which case the triangle inequality is replaced by the stronger inequality
$$ d(a,c) \le \text{max} \{ d(a,b), d(b,c) \} \,. $$
Ultrametric spaces occur in many fields of study, and naturally describe spaces with a tree-like structure.
I have been working on a project involving spin-glasses, and one of the interesting mathematical properties of the spin-glass phase is that the space of states is ultrametric. I am wondering if there are any other examples from computer science, where ultrametricity shows up. I am particularly interested when the space of states are $n$-bit binary strings, $\{0,1\}^n$, and the distance measure $d(\cdot, \cdot)$ is the Hamming distance. Clearly $n$-bit binary strings are not ultrametric on their own, but perhaps there are situations where the $n$-bit strings are naturally restricted in such a way that over the constrained space of bit strings the ultrametric property is satisfied.