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Fractals from genomes – exact solutions of a biology-inspired problem

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  • Hao, Bai-Lin

Abstract

This is a review of a few recent papers with some new results added. After a brief biological introduction a visualization scheme of the string composition of long DNA sequences, in particular, of bacterial complete genomes, will be described. This scheme leads to a class of self-similar and self-overlapping fractals in the limit of infinitely long constituent strings. The calculation of their exact dimensions and the counting of true and redundant avoided strings at different string lengths turn out to be one and the same problem. We give exact solution of the problem using two independent methods: the Goulden–Jackson cluster method in combinatorics and the method of formal language theory.

Suggested Citation

  • Hao, Bai-Lin, 2000. "Fractals from genomes – exact solutions of a biology-inspired problem," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 282(1), pages 225-246.
    • Handle: RePEc:eee:phsmap:v:282:y:2000:i:1:p:225-246
    DOI: 10.1016/S0378-4371(00)00102-3
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    Cited by:

    1. Zhang, Yagang & Wang, Changjiang, 2007. "Multiformity of inherent randomicity and visitation density in n symbolic dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 33(2), pages 685-694.
    2. Zhang, Yagang & Wang, Changjiang & Zhou, Zhong, 2006. "Inherent randomicity in 4-symbolic dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 28(1), pages 236-243.
    3. Wu, Zuo-Bing, 2010. "Global transposable characteristics in the complete DNA sequence of the yeast," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(24), pages 5698-5705.
    4. Katsaloulis, P. & Theoharis, T. & Zheng, W.M. & Hao, B.L. & Bountis, A. & Almirantis, Y. & Provata, A., 2006. "Long-range correlations of RNA polymerase II promoter sequences across organisms," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 366(C), pages 308-322.

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