Multifractal Analysis of Genomic Sequences CGR Images

To describe the fractal feature of chaos game representation (CGR) images of genomic sequences, a multifractal theory is presented in the analysis. With the probability set of CGR images, the general dimension spectrum and the multifractal spectrum are calculated and compared between two sample groups of gene thick sequences and gene black sequences. The experimental result shows that the probability set composed of the relative probability has the best scale-invariance performance. The scale invariance has different variance regions, which indicates genomic sequence segments with different lengths have different distribution rules. It is also shown that the sequences´ spectra for two groups are different, specially the attenuation index and value range of the general dimension spectrum, and the width of the multifractal spectrum. It is concluded that the mutifractal analysis and its parameters may be useful to analyze sequences´s statistic property and recognize gene sequence