Ultrametricity also appears in the theory of aperiodic solids. In taxonomy and phylogenetic tree construction, ultrametric distances are also utilized by the UPGMA and WPGMA methods. These algorithms require a constant-rate assumption and produce trees in which the distances from the root to every branch tip are equal. When DNA, RNA and protein data are analyzed, the ultrametricity assumption is called the molecular clock. Models of intermittency in three dimensional turbulence of fluids make use of so-called cascades, and in discrete models of dyadic cascades, which have an ultrametric structure. In geography and landscape ecology, ultrametric distances have been applied to measure landscape complexity and to assess the extent to which one landscape function is more important than another. References Bibliography Further reading . Metric geometry Metric spaces