Using the proposed distance metrics, we compared the trees before and after normalization and found that the topology of the trees is the same. Then we set , 4 = ρ 6, 8, 10 and found that we could get the trees with the same topology as the tree for 3 = ρ . As a result, there seems to be no noticeable effect by normalization of the distances and different values of 3 ≥ ρ . Figure 4 . The NJ tree of mitochondrial genomes based on the whole DNA sequences using the dynamical language approach with chord distance in the case K = 11. In this tree the birds and reptiles group together as Archosauria. Figure 5 . Phylogeny of 62 alpha-proteobacteria using the dynamical language approach with chord distance in the cases K = 5 and 6 based on all protein sequences. The topology of trees obtained by the dynamical language approach with pseudo-distance in [5] and piecewise distance in the cases K = 5 and 6 based on all protein sequences are the same as that in this figure.