The design of the experiments was to explore the complexity of genome sequences by wavelet transform and fractal geometry theory. The mathematic model was set up by Fractional Brownian Motion (FBM) to study the self-similarity of the deoxyribonucleic acid (DNA) sequences. The DNA sequence was expressed as a numerical signal by the method of DNA walk at first. There were three kinds of representation for DNA sequences such as AG walk, AC walk and AT walk. The DNA sequence was investigated by continuous Mexican hat wavelet transform. Each scale of the transform was corresponding to a certain characteristics length of nucleotides. Then the fractal dimension can be calculated and used to describe the self-similarity in the DNA sequences. Three horizontal cuts about the wavelet coefficients were shown at three different scales a at a-1=2~3 , a-2 = 2~5 , a-3 = 2~7 , which correspond to looking at the fluctuations of the DNA walk over a characteristic length of the order of 32, 128 and 512 nucleotides respectively. The smaller scale can observe the details, and the bigger scale displays the approximate. This train of thoughts can be a choice for the forward research of gene's evolutional information that relative to the self-similar structure of the gene sequences.

Key words: DNA, SEQUENCE ANALYSIS, MATHEMATICAL MODELS