  The presence of low dimensional chaos in the protein secondary structures,
using the binary coded $\alpha$-helices and $\beta$-sheet motifs, has been
investigated. In order to analyse symbolic DNA/RNA sequences the assignment,
based on the purine/pyrimidine and strong/wea k H - bond classification sheme,
of binary numbers to the nucleotides was made. We have found that this
assignment leads to different averaged fractal dimensions for $\alpha$-helices
and $\beta$-sheets. When embedded in the two dimensional phase space the binary
string structures show the attractor type behavior which depends on the value
of the time lag parameter.
