Involving FCGR images in studying fractality and multifractality in human chromosome 22 and bacteria complete genome

The frequency chaos game representation (FCGR) is a simple yet powerful visualization method of DNA sequences. It provides the possibility of representing genomes by images, revealing in such a way different fractal structures. In this paper, we perform a fractal and multifractal analysis of Human chromosome 22 and some complete genomes based on the FGCR image. We used the fractal dimension (FD) and the multifractality degree (ΔDq) to characterize and distinguish genomes. First, we construct the FCGR image with different orders of human chromosome 22. Next, we calculate the fractal dimension, the general dimension spectrum and the multifractal spectrum of each FCGR image using the box-counting method. Then, we examine the FCGR image fractal and multifractal characteristics impact on highlighting the existence of repetitive DNA sequences in human chromosome 22. We also observe the relationship between fractality and multifractality. After that, we apply this study to bacteria completes genomes and C.elegans chromosome I. The obtained results show that the multifractal spectra of all organisms studied are multifractal-like and chromosome 22 strong multifractality proves its richness of repetitive sequences. Also, we observed that with the increasing the FCGR order value, the multifractality grows and the fractal dimension lessens. Finally, by assigning to each sequence a point in two-dimensional space (FD, ΔDq), we obtained three classes of genomes. We can easily distinguish the human chromosome 22 from other genomes and Bacteria are almost close in the spaces (FD, ΔDq).