Fractals and Hidden Symmetries in DNA

Abstract

This paper deals with the digital complex representation of a DNA sequence and the analysis of existing correlations by wavelets. The symbolic DNA sequence is mapped into a nonlinear time series. By studying this time series the existence of fractal shapes and symmetries will be shown. At first step, the indicator matrix enables us to recognize some typical patterns of nucleotide distribution. The DNA sequence, of the influenza virus A (H1N1), is investigated by using the complex representation, together with the corresponding walks on DNA; in particular, it is shown that DNA walks are fractals. Finally, by using the wavelet analysis, the existence of symmetries is proven.