Chaos Game Representation of Genomes and their Simulation by Recurrent Iterated Function Systems

Chaos game representation (CGR) of DNA sequences and linked protein sequences from genomes was proposed by Jeffrey (Nucleic Acid Research 18 (1990) 2163-2170) and Yu et al. (J. Theor. Biol, 226 (2004) 341-348), respectively. In this paper, we consider the CGR of three kinds of sequences from complete genomes: whole genome DNA sequences, linked coding DNA sequences and linked protein sequences. Some fractal patterns are found in these CGRs. A recurrent iterated function systems (RIFS) model is proposed to simulate the CGRs of these sequences from genomes and their induced measures. Numerical results on 50 genomes show that the RIFS model can simulate very well the CGRs and their induced measures . The parameters estimated in the RIFS model reflect information on species classification .