Dimensions of fractals related to languages defined by tagged strings in complete genomes

A representation of frequency of strings of length K in complete genomes of many organisms in a square has led to seemingly self-similar patterns when K increases. These patterns are caused by under-represented strings with a certain “tag”-string and they define some fractals in the K→∞ limit. The B...

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Bibliographic Details
Published in:Chaos, solitons and fractals solitons and fractals, 2000-11, Vol.11 (14), p.2215-2222
Main Authors: Yu, Zu-Guo, Hao, Bai-lin, Xie, Hui-min, Chen, Guo-Yi
Format: Article
Language:English
Subjects:
Computational linguistics
DNA sequences
Integer programming
Linear equations
Matrix algebra
Theorem proving
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Summary:A representation of frequency of strings of length K in complete genomes of many organisms in a square has led to seemingly self-similar patterns when K increases. These patterns are caused by under-represented strings with a certain “tag”-string and they define some fractals in the K→∞ limit. The Box and Hausdorff dimensions of the limit set are discussed. Although the method proposed by Mauldin and Williams to calculate Box and Hausdorff dimension is valid in our case, a different and sampler method is proposed in this paper.
ISSN:0960-0779
1873-2887
DOI:10.1016/S0960-0779(99)00141-1