Simulation for chaos game representation of genomes by recurrent iterated function systems

some pattern (information) in the DNA sequence Chaos game representation (CGR) of DNA (Goldman 1993). Goldman (1993) interpreted the sequences and linked protein sequences CGRs in a biologically meaningful way. All points from genomes was proposed by Jeffrey (1990) plotted within a quadrant must corresponding to suban d Yu et al. (2004), respectively. In this sequences of the DNA sequence that end with the paper, we consider the CGR of three kinds of base labelling the corner of that quadrant. He also prosequences from complete genomes: whole posed a discrete time Markov Chain model to simugenome DNA sequences, linked coding DNA late the CGR of DNA sequences and use the sequences and linked protein sequences. sequence's dinucleotide and trinucleotide frequenSome fractal patterns are found in these cies to calculate the probabilities in these models. CGRs. A recurrent iterated function systems Goldman's Markov model can be calculated directly (RIFS) model is proposed to simulate the and easily from the raw DNA sequences, without refCGRs of these sequences from genomes and erence to the CGR. their induced measures. Numerical results Deschavanne et al. (1999) used CGR of genomes on 50 genomes show that the RIFS model can to discuss the classification of species. Almeida et al. s i m u l a t e v e r y w e l l t h e C G R s a n d t h e i r (2001) showed the distribution of positions in the induced measures. The parameters est iCGR plane is a generalization of Markov Chain probmated in the RIFS model reflect information ability tables that accommodates non-integer orders. on species classification. Joseph and Sasikumar (2006) proposed a fast algo-