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E.R. Vrscay, “Iterated function systems: theory, applications and inverse problem”, in: Fractal Geometry and Analysis, edited by: Belair, J. and Dubuc, S., Kluwer, Dordrecht, pp. 405-468, 1991.

has been cited by the following article:

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

  AUTHORS: Zu-Guo Yu, Long Shi, Qian-Jun Xiao, Vo Anh

  KEYWORDS: Genomes; chaos game representation; recurrent iterated function systems.

  JOURNAL NAME: Journal of Biomedical Science and Engineering, Vol.1 No.1, June 6, 2008

  ABSTRACT: Chaos game representation (CGR) of DNA sequences and linked protein sequences from genomes was proposed by Jeffrey (1990) and Yu et al. (2004), 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.