Applications
A contraction mapping may then be thought of as a way of approximating the final result of a computation (which can be guaranteed to exist by the Banach fixed point theorem). Similar ideas can be found in domain theory. P-adic analysis makes heavy use of the ultrametric nature of the p-adic metric.
Applications are also known in solid-state physics, namely in the treatment of spin glasses by the replica-theory of Giorgio Parisi and coworkers, and also in the theory of aperiodic solids.
Ultrametric distances are also utilized in taxonomy and phylogenetic tree construction using the UPGMA and WPGMA methods.
Read more about this topic: Ultrametric Space