  It is shown that metric representation of DNA sequences is one-to-one. By
using the metric representation method, suppression of nucleotide strings in
the DNA sequences is determined. For a DNA sequence, an optimal string length
to display genomic signature in chaos game representation is obtained by
eliminating effects of the finite sequence. The optical string length is
further shown as a self- similarity limit in computing information dimension.
By using the method, self-similarity limits of bacteria complete genomic
signatures are further determined.
